/usr/lib/python2.7/dist-packages/getfem/getfem.py is in python-getfem++ 4.2.1~beta1~svn4635~dfsg-3+b1.
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# -*- coding: iso-8859-1 -*-
#
# Python GetFEM++ interface
#
# Copyright (C) 2004-2013 Yves Renard, Julien Pommier.
#
# This file is a part of GetFEM++
#
# GetFEM++ is free software; you can redistribute it and/or modify it
# under the terms of the GNU Lesser General Public License as published
# by the Free Software Foundation; either version 3 of the License, or
# (at your option) any later version along with the GCC Runtime Library
# Exception either version 3.1 or (at your option) any later version.
# This program is distributed in the hope that it will be useful, but
# WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY
# or FITNESS FOR A PARTICULAR PURPOSE. See the GNU Lesser General Public
# License and GCC Runtime Library Exception for more details.
# You should have received a copy of the GNU Lesser General Public License
# along with this program; if not, write to the Free Software Foundation,
# Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301, USA.
#
# File autogenerated by bin/extract_doc. Do not edit it.
"""GetFEM-interface classes.
Provides access to the pseudo-objects exported by the python-getfem
interface.
"""
import sys
import numpy
getfem_python_par=False
try:
import numbers
except ImportError:
numbers = numpy
numbers.Number = (int,float,complex)
from numpy import *
from _getfem import *
obj_count = {}
getfem('workspace', 'clear all')
def generic_constructor(self, clname, *args):
"""Internal function -- acts as a constructor for all getfem objects."""
#print 'generic_constructor.'+clname+'('+str(args)+')'
if (len(args)==1 and type(args[0]) is GetfemObject):
if hasattr(self,'id'):
print "warning: hasattr(self,'id')!"
print "self.id: ",self.id
print "args[0]: ",args[0]
else:
self.id = args[0]
if obj_count.get(self.id,0)==0:
#print "Reviviendo objeto..."
#print "self: ",self
#print "self.id: ",self.id
#if hasattr(self.id,'classid'):
# print "self.id.classid: ",self.id.classid
#else:
# print "self.id.classid not found!"
getfem("undelete",self.id)
#print "self.id: ",self.id
#pass
else:
self.id = getfem_from_constructor(clname,*args)
obj_count[self.id] = obj_count.get(self.id,0)+1
def generic_destructor(self, destructible=True):
"""Internal function -- acts as a destructor for all getfem objects."""
if (not hasattr(self,'id')):
return
#print "Mesh.__del__ ",self.id,'count=',obj_count[self.id]
if (obj_count.has_key(self.id)):
obj_count[self.id] = obj_count[self.id]-1
if (destructible and obj_count[self.id] == 0):
getfem('delete',self.id)
#print "effective deletion"
#
# GetFEM class ContStruct definition.
#
class ContStruct:
"""GetFEM ContStruct object
This object serves for storing parameters and data used in numerical
continuation of solution branches of models (for more details about
continuation see the Getfem++ user documentation).
"""
def __init__(self, *args):
"""General constructor for ContStruct objects
* ``S = ContStruct(Model md, string dataname_parameter[,string dataname_init, string dataname_final, string dataname_current], scalar sc_fac[, ...])``
The variable `dataname_parameter` should parametrise the model given by
`md`. If the parametrisation is done via a vector datum, `dataname_init`
and `dataname_final` should store two given values of this datum
determining the parametrisation, and `dataname_current` serves for actual
values of this datum. `sc_fac` is a scale factor involved in the weighted
norm used in the continuation.
Additional options:
- 'lsolver', string SOLVER_NAME
name of the solver to be used for the incorporated linear systems
(the default value is 'auto', which lets getfem choose itself);
possible values are 'superlu', 'mumps' (if supported), 'cg/ildlt',
'gmres/ilu' and 'gmres/ilut';
- 'h_init', scalar HIN
initial step size (the default value is 1e-2);
- 'h_max', scalar HMAX
maximum step size (the default value is 1e-1);
- 'h_min', scalar HMIN
minimum step size (the default value is 1e-5);
- 'h_inc', scalar HINC
factor for enlarging the step size (the default value is 1.3);
- 'h_dec', scalar HDEC
factor for diminishing the step size (the default value is 0.5);
- 'max_iter', int MIT
maximum number of iterations allowed in the correction (the default
value is 10);
- 'thr_iter', int TIT
threshold number of iterations of the correction for enlarging the
step size (the default value is 4);
- 'max_res', scalar RES
target residual value of a new point on the solution curve (the
default value is 1e-6);
- 'max_diff', scalar DIFF
determines a convergence criterion for two consecutive points (the
default value is 1e-6);
- 'min_cos', scalar MCOS
minimal value of the cosine of the angle between tangents to the
solution curve at an old point and a new one (the default value is
0.9);
- 'max_res_solve', scalar RES_SOLVE
target residual value for the linear systems to be solved (the
default value is 1e-8);
- 'bifurcations'
activates tools for detection and treatment of bifurcation points;
- 'non-smooth'
determines that some special methods for non-smooth problems can be
used;
- 'delta_max', scalar DMAX
maximum size of division for evaluating the test function on the
convex combination of two augmented Jacobians that belong to different
smooth pieces (the default value is 0.005);
- 'delta_min', scalar DMIN
minimum size of division for evaluating the test function on the
convex combination (the default value is 0.00012);
- 'thr_var', scalar TVAR
threshold variation for refining the division (the default value is
0.02);
- 'nb_dir', int NDIR
number of linear combinations of vectors in one subspace when
searching for new tangent predictions during location of new one-sided
branches (the default value is 40);
- 'nb_comb', int NCOMB
maximum number of couples of reference vectors forming the linear
combinations (the default value is 1);
- 'noisy' or 'very_noisy'
determines how detailed information has to be displayed during the
continuation process (residual values etc.).
"""
generic_constructor(self,'cont_struct',*args)
def __del__(self):
generic_destructor(self, destructible=True)
def get(self, *args):
return getfem('cont_struct_get',self.id, *args)
def __repr__(self):
getfem('cont_struct_get',self.id, 'display')
return ''
def __str__(self):
return self.char()
def init_step_size(self):
"""Return an initial step size for continuation."""
return self.get("init_step_size")
def init_test_function(self, solution, parameter, tangent_sol, tangent_par):
"""Save the value of a test function for the point given by `solution` and
`parameter` and the tangent given by `tangent_sol` and `tangent_par`
into the ContStruct object and return it."""
return self.get("init_test_function", solution, parameter, tangent_sol, tangent_par)
def init_Moore_Penrose_continuation(self, solution, parameter, init_dir):
"""Initialise the Moore-Penrose continuation: Return a unit tangent to
the solution curve at the point given by `solution` and `parameter`,
and an initial step size for the continuation. Orientation of the
computed tangent with respect to the parameter is determined by the
sign of `init_dir`."""
return self.get("init_Moore_Penrose_continuation", solution, parameter, init_dir)
def Moore_Penrose_continuation(self, solution, parameter, tangent_sol, tangent_par, h):
"""Compute one step of the Moore-Penrose continuation: Take the point
given by `solution` and `parameter`, the tangent given by `tangent_sol`
and `tangent_par`, and the step size `h`. Return a new point on the
solution curve, the corresponding tangent and a step size for the next
step. If the returned step size equals zero, the continuation has
failed. Optionally, return the type of any detected bifurcation point.
NOTE: The new point need not to be saved in the model in the end!"""
return self.get("Moore_Penrose_continuation", solution, parameter, tangent_sol, tangent_par, h)
def test_function(self):
"""Return the last value of the test function and eventaully the whole
calculated graph when passing between subdomains of different smooth
pieces."""
return self.get("test_function")
def sing_data(self):
"""Return a singular point (`X`, `gamma`) encountered in the last
continuation step (if any) and a couple of arrays (`T_X`, `T_gamma`) of
tangents to all located solution branches, which emanate from there."""
return self.get("sing_data")
def char(self):
"""Output a (unique) string representation of the ContStruct.
This can be used for performing comparisons between two
different ContStruct objects.
This function is to be completed.
"""
return self.get("char")
def display(self):
"""Display a short summary for a ContStruct object."""
return self.get("display")
#
# GetFEM class CvStruct definition.
#
class CvStruct:
"""GetFEM CvStruct object
"""
def __init__(self, *args):
"""General constructor for CvStruct objects
"""
generic_constructor(self,'cvstruct',*args)
def __del__(self):
generic_destructor(self, destructible=False)
def get(self, *args):
return getfem('cvstruct_get',self.id, *args)
def __repr__(self):
getfem('cvstruct_get',self.id, 'display')
return ''
def __str__(self):
return self.char()
def nbpts(self):
"""Get the number of points of the convex structure."""
return self.get("nbpts")
def dim(self):
"""Get the dimension of the convex structure."""
return self.get("dim")
def basic_structure(self):
"""Get the simplest convex structure.
For example, the 'basic structure' of the 6-node triangle, is the
canonical 3-noded triangle."""
return self.get("basic_structure")
def face(self, F):
"""Return the convex structure of the face `F`."""
return self.get("face", F)
def facepts(self, F):
"""Return the list of point indices for the face `F`."""
return self.get("facepts", F)
def char(self):
"""Output a string description of the CvStruct."""
return self.get("char")
def display(self):
"""displays a short summary for a CvStruct object."""
return self.get("display")
#
# GetFEM class Eltm definition.
#
class Eltm:
"""GetFEM Eltm object
This object represents a type of elementary matrix. In order to obtain a
numerical value of these matrices, see MeshIm.eltm().
If you have very particular assembling needs, or if you just want to check
the content of an elementary matrix, this function might be useful. But
the generic assembly abilities of gf_asm(...) should suit most needs.
"""
def __init__(self, *args):
"""General constructor for Eltm objects
* ``E = Eltm('base', Fem FEM)``
return a descriptor for the integration of shape functions on
elements, using the Fem `FEM`.
* ``E = Eltm('grad', Fem FEM)``
return a descriptor for the integration of the gradient of shape
functions on elements, using the Fem `FEM`.
* ``E = Eltm('hessian', Fem FEM)``
return a descriptor for the integration of the hessian of shape
functions on elements, using the Fem `FEM`.
* ``E = Eltm('normal')``
return a descriptor for the unit normal of convex faces.
* ``E = Eltm('grad_geotrans')``
return a descriptor to the gradient matrix of the geometric
transformation.
* ``E = Eltm('grad_geotrans_inv')``
return a descriptor to the inverse of the gradient matrix of the
geometric transformation (this is rarely used).
* ``E = Eltm('product', Eltm A, Eltm B)``
return a descriptor for the integration of the tensorial product of
elementary matrices `A` and `B`.
"""
generic_constructor(self,'eltm',*args)
def __del__(self):
generic_destructor(self, destructible=False)
def __str__(self):
return self.char()
#
# GetFEM class Fem definition.
#
class Fem:
"""GetFEM Fem object
This object represents a finite element method on a reference element.
"""
def __init__(self, *args):
"""General constructor for Fem objects
* ``F = Fem('interpolated_fem', MeshFem mf, MeshIm mim, [ivec blocked_dof])``
Build a special Fem which is interpolated from another MeshFem.
Using this special finite element, it is possible to interpolate a given
MeshFem `mf` on another mesh, given the integration method `mim` that will
be used on this mesh.
Note that this finite element may be quite slow, and eats much
memory.
* ``F = Fem(string fem_name)``
The `fem_name` should contain a description of the finite element
method. Please refer to the getfem++ manual (especially the
description of finite element and integration methods) for a complete
reference. Here is a list of some of them:
- FEM_PK(n,k) :
classical Lagrange element Pk on a simplex of dimension `n`.
- FEM_PK_DISCONTINUOUS(n,k[,alpha]) :
discontinuous Lagrange element Pk on a simplex of dimension `n`.
- FEM_QK(n,k) :
classical Lagrange element Qk on quadrangles, hexahedrons etc.
- FEM_QK_DISCONTINUOUS(n,k[,alpha]) :
discontinuous Lagrange element Qk on quadrangles, hexahedrons etc.
- FEM_Q2_INCOMPLETE(n) :
incomplete Q2 elements with 8 and 20 dof (serendipity Quad 8 and
Hexa 20 elements).
- FEM_PK_PRISM(n,k) :
classical Lagrange element Pk on a prism of dimension `n`.
- FEM_PK_PRISM_DISCONTINUOUS(n,k[,alpha]) :
classical discontinuous Lagrange element Pk on a prism.
- FEM_PK_WITH_CUBIC_BUBBLE(n,k) :
classical Lagrange element Pk on a simplex with an additional
volumic bubble function.
- FEM_P1_NONCONFORMING :
non-conforming P1 method on a triangle.
- FEM_P1_BUBBLE_FACE(n) :
P1 method on a simplex with an additional bubble function on face 0.
- FEM_P1_BUBBLE_FACE_LAG :
P1 method on a simplex with an additional lagrange dof on face 0.
- FEM_PK_HIERARCHICAL(n,k) :
PK element with a hierarchical basis.
- FEM_QK_HIERARCHICAL(n,k) :
QK element with a hierarchical basis
- FEM_PK_PRISM_HIERARCHICAL(n,k) :
PK element on a prism with a hierarchical basis.
- FEM_STRUCTURED_COMPOSITE(Fem f,k) :
Composite Fem `f` on a grid with `k` divisions.
- FEM_PK_HIERARCHICAL_COMPOSITE(n,k,s) :
Pk composite element on a grid with `s` subdivisions and with a
hierarchical basis.
- FEM_PK_FULL_HIERARCHICAL_COMPOSITE(n,k,s) :
Pk composite element with `s` subdivisions and a hierarchical basis
on both degree and subdivision.
- FEM_PRODUCT(A,B) :
tensorial product of two polynomial elements.
- FEM_HERMITE(n) :
Hermite element P3 on a simplex of dimension `n = 1, 2, 3`.
- FEM_ARGYRIS :
Argyris element P5 on the triangle.
- FEM_HCT_TRIANGLE :
Hsieh-Clough-Tocher element on the triangle (composite P3 element
which is C1), should be used with IM_HCT_COMPOSITE() integration
method.
- FEM_QUADC1_COMPOSITE :
Quadrilateral element, composite P3 element and C1 (16 dof).
- FEM_REDUCED_QUADC1_COMPOSITE :
Quadrilateral element, composite P3 element and C1 (12 dof).
- FEM_RT0(n) :
Raviart-Thomas element of order 0 on a simplex of dimension `n`.
- FEM_NEDELEC(n) :
Nedelec edge element of order 0 on a simplex of dimension `n`.
Of course, you have to ensure that the selected fem is compatible with
the geometric transformation: a Pk fem has no meaning on a quadrangle.
"""
generic_constructor(self,'fem',*args)
def __del__(self):
generic_destructor(self, destructible=False)
def get(self, *args):
return getfem('fem_get',self.id, *args)
def __repr__(self):
getfem('fem_get',self.id, 'display')
return ''
def __str__(self):
return self.char()
def nbdof(self, cv=None):
"""Return the number of dof for the Fem.
Some specific Fem (for example 'interpolated_fem') may require a
convex number `cv` to give their result. In most of the case, you
can omit this convex number."""
return self.get("nbdof", cv)
def index_of_global_dof(self, cv):
"""Return the index of global dof for special fems such as interpolated fem.
"""
return self.get("index_of_global_dof", cv)
def dim(self):
"""Return the dimension (dimension of the reference convex) of the Fem."""
return self.get("dim")
def target_dim(self):
"""Return the dimension of the target space.
The target space dimension is usually 1, except for vector Fem. """
return self.get("target_dim")
def pts(self, cv=None):
"""Get the location of the dof on the reference element.
Some specific Fem may require a convex number `cv` to give their
result (for example 'interpolated_fem'). In most of the case, you
can omit this convex number. """
return self.get("pts", cv)
def is_equivalent(self):
"""Return 0 if the Fem is not equivalent.
Equivalent Fem are evaluated on the reference convex. This is
the case of most classical Fem's."""
return self.get("is_equivalent")
def is_lagrange(self):
"""Return 0 if the Fem is not of Lagrange type."""
return self.get("is_lagrange")
def is_polynomial(self):
"""Return 0 if the basis functions are not polynomials."""
return self.get("is_polynomial")
def estimated_degree(self):
"""Return an estimation of the polynomial degree of the Fem.
This is an estimation for fem which are not polynomials."""
return self.get("estimated_degree")
def base_value(self, p):
"""Evaluate all basis functions of the FEM at point `p`.
`p` is supposed to be in the reference convex!"""
return self.get("base_value", p)
def grad_base_value(self, p):
"""Evaluate the gradient of all base functions of the Fem at point `p`.
`p` is supposed to be in the reference convex!"""
return self.get("grad_base_value", p)
def hess_base_value(self, p):
"""Evaluate the Hessian of all base functions of the Fem at point `p`.
`p` is supposed to be in the reference convex!."""
return self.get("hess_base_value", p)
def poly_str(self):
"""Return the polynomial expressions of its basis functions in
the reference convex.
The result is expressed as a tuple of
strings. Of course this will fail on non-polynomial Fem's. """
return self.get("poly_str")
def char(self):
"""Ouput a (unique) string representation of the Fem.
This can be used to perform comparisons between two different Fem
objects."""
return self.get("char")
def display(self):
"""displays a short summary for a Fem object."""
return self.get("display")
#
# GetFEM class GeoTrans definition.
#
class GeoTrans:
"""GetFEM GeoTrans object
The geometric transformation must be used when you are building a custom
mesh convex by convex (see the add_convex() function of Mesh): it also
defines the kind of convex (triangle, hexahedron, prism, etc..)
"""
def __init__(self, *args):
"""General constructor for GeoTrans objects
* ``GT = GeoTrans(string name)``
The name argument contains the specification of the geometric transformation
as a string, which may be:
- GT_PK(n,k) :
Transformation on simplexes, dim `n`, degree `k`.
- GT_QK(n,k) :
Transformation on parallelepipeds, dim `n`, degree `k`.
- GT_PRISM(n,k) :
Transformation on prisms, dim `n`, degree `k`.
- GT_PRODUCT(A,B) :
Tensorial product of two transformations.
- GT_LINEAR_PRODUCT(GeoTrans gt1,GeoTrans gt2) :
Linear tensorial product of two transformations
"""
generic_constructor(self,'geotrans',*args)
def __del__(self):
generic_destructor(self, destructible=False)
def get(self, *args):
return getfem('geotrans_get',self.id, *args)
def __repr__(self):
getfem('geotrans_get',self.id, 'display')
return ''
def __str__(self):
return self.char()
def dim(self):
"""Get the dimension of the GeoTrans.
This is the dimension of the source space, i.e. the dimension of
the reference convex."""
return self.get("dim")
def is_linear(self):
"""Return 0 if the GeoTrans is not linear."""
return self.get("is_linear")
def nbpts(self):
"""Return the number of points of the GeoTrans."""
return self.get("nbpts")
def pts(self):
"""Return the reference convex points of the GeoTrans.
The points are stored in the columns of the output matrix."""
return self.get("pts")
def normals(self):
"""Get the normals for each face of the reference convex of the GeoTrans.
The normals are stored in the columns of the output matrix."""
return self.get("normals")
def transform(self, G, Pr):
"""Apply the GeoTrans to a set of points.
`G` is the set of vertices of the real convex, `Pr` is the set
of points (in the reference convex) that are to be transformed.
The corresponding set of points in the real convex is returned."""
return self.get("transform", G, Pr)
def char(self):
"""Output a (unique) string representation of the GeoTrans.
This can be used to perform comparisons between two
different GeoTrans objects. """
return self.get("char")
def display(self):
"""displays a short summary for a GeoTrans object."""
return self.get("display")
#
# GetFEM class GlobalFunction definition.
#
class GlobalFunction:
"""GetFEM GlobalFunction object
Global function object is represented by three functions:
* The function `val`.
* The function gradient `grad`.
* The function Hessian `hess`.
this type of function is used as local and global enrichment function. The
global function Hessian is an optional parameter (only for fourth order
derivative problems).
"""
def __init__(self, *args):
"""General constructor for GlobalFunction objects
* ``GF = GlobalFunction('cutoff', int fn, scalar r, scalar r1, scalar r0)``
Create a cutoff global function.
* ``GF = GlobalFunction('crack', int fn)``
Create a near-tip asymptotic global function for modelling cracks.
* ``GF = GlobalFunction('parser', string val[, string grad[, string hess]])``
Create a global function from strings `val`, `grad` and `hess`.
* ``GF = GlobalFunction('product', GlobalFunction F, GlobalFunction G)``
Create a product of two global functions.
* ``GF = GlobalFunction('add', GlobalFunction gf1, GlobalFunction gf2)``
Create a add of two global functions.
"""
generic_constructor(self,'global_function',*args)
def __del__(self):
generic_destructor(self, destructible=False)
def get(self, *args):
return getfem('global_function_get',self.id, *args)
def __repr__(self):
getfem('global_function_get',self.id, 'display')
return ''
def __str__(self):
return self.char()
def __mul__(self,other):
if isinstance(other,numbers.Number):
return GlobalFunction('product',self,GlobalFunction('parser',"%e"%(other)))
return GlobalFunction('product',self,other)
def __add__(self,other):
if isinstance(other,numbers.Number):
return GlobalFunction('add',self,GlobalFunction('parser',"%e"%(other)))
return GlobalFunction('add',self,other)
def __call__(self,Pts):
return getfem('global_function_get',self.id, 'val', Pts)
def val(self, PTs):
"""Return `val` function evaluation in `PTs` (column points)."""
return self.get("val", PTs)
def grad(self, PTs):
"""Return `grad` function evaluation in `PTs` (column points).
On return, each column of `GRADs` is of the
form [Gx,Gy]."""
return self.get("grad", PTs)
def hess(self, PTs):
"""Return `hess` function evaluation in `PTs` (column points).
On return, each column of `HESSs` is of the
form [Hxx,Hxy,Hyx,Hyy]."""
return self.get("hess", PTs)
def char(self):
"""Output a (unique) string representation of the GlobalFunction.
This can be used to perform comparisons between two
different GlobalFunction objects.
This function is to be completed.
"""
return self.get("char")
def display(self):
"""displays a short summary for a GlobalFunction object."""
return self.get("display")
#
# GetFEM class Integ definition.
#
class Integ:
"""GetFEM Integ object
General object for obtaining handles to various integrations methods on
convexes (used when the elementary matrices are built).
"""
def __init__(self, *args):
"""General constructor for Integ objects
* ``I = Integ(string method)``
Here is a list of some integration methods defined in getfem++ (see the
description of finite element and integration methods for a complete
reference):
- IM_EXACT_SIMPLEX(n) :
Exact integration on simplices (works only with linear geometric
transformations and PK Fem's).
- IM_PRODUCT(A,B) :
Product of two integration methods.
- IM_EXACT_PARALLELEPIPED(n) :
Exact integration on parallelepipeds.
- IM_EXACT_PRISM(n) :
Exact integration on prisms.
- IM_GAUSS1D(k) :
Gauss method on the segment, order `k=1,3,...,99`.
- IM_NC(n,k) :
Newton-Cotes approximative integration on simplexes, order `k`.
- IM_NC_PARALLELEPIPED(n,k) :
Product of Newton-Cotes integration on parallelepipeds.
- IM_NC_PRISM(n,k) :
Product of Newton-Cotes integration on prisms.
- IM_GAUSS_PARALLELEPIPED(n,k) :
Product of Gauss1D integration on parallelepipeds.
- IM_TRIANGLE(k) :
Gauss methods on triangles `k=1,3,5,6,7,8,9,10,13,17,19`.
- IM_QUAD(k) :
Gauss methods on quadrilaterons `k=2,3,5, ...,17`. Note that
IM_GAUSS_PARALLELEPIPED should be prefered for QK Fem's.
- IM_TETRAHEDRON(k) :
Gauss methods on tetrahedrons `k=1,2,3,5,6 or 8`.
- IM_SIMPLEX4D(3) :
Gauss method on a 4-dimensional simplex.
- IM_STRUCTURED_COMPOSITE(im,k) :
Composite method on a grid with `k` divisions.
- IM_HCT_COMPOSITE(im) :
Composite integration suited to the HCT composite finite element.
Example:
- I = Integ('IM_PRODUCT(IM_GAUSS1D(5),IM_GAUSS1D(5))')
is the same as:
- I = Integ('IM_GAUSS_PARALLELEPIPED(2,5)')
Note that 'exact integration' should be avoided in general, since they
only apply to linear geometric transformations, are quite slow, and
subject to numerical stability problems for high degree Fem's.
"""
generic_constructor(self,'integ',*args)
def __del__(self):
generic_destructor(self, destructible=False)
def get(self, *args):
return getfem('integ_get',self.id, *args)
def __repr__(self):
getfem('integ_get',self.id, 'display')
return ''
def __str__(self):
return self.char()
def is_exact(self):
"""Return 0 if the integration is an approximate one."""
return self.get("is_exact")
def dim(self):
"""Return the dimension of the reference convex of
the method."""
return self.get("dim")
def nbpts(self):
"""Return the total number of integration points.
Count the points for the volume integration, and points for
surface integration on each face of the reference convex.
Only for approximate methods, this has no meaning for exact
integration methods!"""
return self.get("nbpts")
def pts(self):
"""Return the list of integration points
Only for approximate methods, this has no meaning for exact
integration methods!"""
return self.get("pts")
def face_pts(self, F):
"""Return the list of integration points for a face.
Only for approximate methods, this has no meaning for exact
integration methods!"""
return self.get("face_pts", F)
def coeffs(self):
"""Returns the coefficients associated to each integration point.
Only for approximate methods, this has no meaning for exact
integration methods!"""
return self.get("coeffs")
def face_coeffs(self, F):
"""Returns the coefficients associated to each integration of a face.
Only for approximate methods, this has no meaning for exact
integration methods!"""
return self.get("face_coeffs", F)
def char(self):
"""Ouput a (unique) string representation of the integration method.
This can be used to comparisons between two different Integ
objects."""
return self.get("char")
def display(self):
"""displays a short summary for a Integ object."""
return self.get("display")
#
# GetFEM class LevelSet definition.
#
class LevelSet:
"""GetFEM LevelSet object
The level-set object is represented by a primary level-set and optionally
a secondary level-set used to represent fractures (if p(x) is the primary
level-set function and s(x) is the secondary level-set, the crack is
defined by :math:`p(x)=0` and :math:`s(x)\\leq0` : the role of the secondary is to determine
the crack front/tip).
note:
All tools listed below need the package qhull installed on your
system. This package is widely available. It computes convex hull and
delaunay triangulations in arbitrary dimension.
"""
def __init__(self, *args):
"""General constructor for LevelSet objects
* ``LS = LevelSet(Mesh m, int d[, string 'ws'| string f1[, string f2 | string 'ws']])``
Create a LevelSet object on a Mesh represented by a primary function
(and optional secondary function, both) defined on a lagrange MeshFem of
degree `d`.
If `ws` (with secondary) is set; this levelset is represented by a
primary function and a secondary function. If `f1` is set; the primary
function is defined by that expression. If `f2` is set; this levelset
is represented by a primary function and a secondary function defined
by these expressions.
"""
generic_constructor(self,'levelset',*args)
def __del__(self):
generic_destructor(self, destructible=True)
def get(self, *args):
return getfem('levelset_get',self.id, *args)
def __repr__(self):
getfem('levelset_get',self.id, 'display')
return ''
def set(self, *args):
return getfem('levelset_set',self.id, *args)
def __str__(self):
return self.char()
def values(self, nls):
"""Return the vector of dof for `nls` funtion.
If `nls` is 0, the method return the vector of dof for the primary
level-set funtion. If `nls` is 1, the method return the vector of
dof for the secondary level-set function (if any)."""
return self.get("values", nls)
def degree(self):
"""Return the degree of lagrange representation."""
return self.get("degree")
def mf(self):
"""Return a reference on the MeshFem object."""
return self.get("mf")
def memsize(self):
"""Return the amount of memory (in bytes) used by the level-set."""
return self.get("memsize")
def char(self):
"""Output a (unique) string representation of the LevelSet.
This can be used to perform comparisons between two
different LevelSet objects.
This function is to be completed.
"""
return self.get("char")
def display(self):
"""displays a short summary for a LevelSet."""
return self.get("display")
def set_values(self, *args):
"""Synopsis: LevelSet.set_values(self, {mat v1|string func_1}[, mat v2|string func_2])
Set values of the vector of dof for the level-set functions.
Set the primary function with the vector of dof `v1` (or the expression
`func_1`) and the secondary function (if any) with the vector of dof
`v2` (or the expression `func_2`)"""
return self.set("values", *args)
def simplify(self, eps=0.01):
"""Simplify dof of level-set optionally with the parameter `eps`."""
return self.set("simplify", eps)
#
# GetFEM class MdBrick definition.
#
class MdBrick:
"""GetFEM MdBrick object
"""
def __init__(self, *args):
"""General constructor for MdBrick objects
* ``B = MdBrick('constraint', MdBrick pb, string CTYPE[, int nfem])``
Build a generic constraint brick.
It may be useful in some situations, such as the Stokes problem
where the pressure is defined modulo a constant. In such a
situation, this brick can be used to add an additional constraint
on the pressure value.
`CTYPE` has to be chosen among 'augmented', 'penalized', and
'eliminated'. The constraint can be specified with
MdBrick.constraints(). Note that Dirichlet bricks (except
the 'generalized Dirichlet' one) are also specializations of
the 'constraint' brick.
* ``B = MdBrick('dirichlet', MdBrick pb, int bnum, MeshFem mf_m, string CTYPE[, int nfem])``
Build a Dirichlet condition brick which impose the value of a field along a mesh boundary.
The `bnum` parameter selects on which mesh region the Dirichlet
condition is imposed. `CTYPE` has to be chosen among 'augmented',
'penalized', and 'eliminated'. The `mf_m` may generally be taken
as the MeshFem of the unknown, but for 'augmented' Dirichlet
conditions, you may have to respect the Inf-Sup condition and
choose an adequate MeshFem.
* ``B = MdBrick('dirichlet on normal component', MdBrick pb, int bnum, MeshFem mf_m, string CTYPE[, int nfem])``
Build a Dirichlet condition brick which imposes the value of the normal component of a vector field.
* ``B = MdBrick('dirichlet on normal derivative', MdBrick pb, int bnum, MeshFem mf_m, string CTYPE[, int nfem])``
Build a Dirichlet condition brick which imposes the value of the normal derivative of the unknown.
* ``B = MdBrick('generalized dirichlet', MdBrick pb, int bnum[, int nfem])``
This is the "old" Dirichlet brick of getfem.
This brick can be used to impose general Dirichlet conditions
`h(x)u(x) = r(x)`, however it may have some issues with elaborated
Fem's (such as Argyris, etc). It should be avoided when possible.
* ``B = MdBrick('source term', MdBrick pb[, int bnum=-1[, int nfem]])``
Add a boundary or volumic source term ( \\int B.v ).
If `bnum` is omitted (or set to -1) , the brick adds a volumic
source term on the whole mesh. For `bnum` >= 0, the source term is
imposed on the mesh region `bnum`. Use MdBrick.set_param('source
term',mf,B) to set the source term field. The source term is
expected as a vector field of size Q (with Q = qdim).
* ``B = MdBrick('normal source term', MdBrick pb, int bnum[, int nfem])``
Add a boundary source term ( \\int (Bn).v ).
The source term is imposed on the mesh region `bnum` (which of course
is not allowed to be a volumic region, only boundary regions are
allowed). Use MdBrick.set_param('source term',mf,B) to set the
source term field. The source term B is expected as tensor field
of size QxN (with Q = qdim, N = mesh dim). For example, if you
consider an elasticity problem, this brick may be used to impose
a force on the boundary with B as the stress tensor.
* ``B = MdBrick('normal derivative source term', MdBrick parent, int bnum[, int nfem])``
Add a boundary source term ( \\int (\\partial_n B).v ).
The source term is imposed on the mesh region `bnum`. Use
MdBrick.set_param('source term',mf,B) to set the source term
field, which is expected as a vector field of size Q (with Q =
qdim).
* ``B = MdBrick('neumann KirchhoffLove source term', MdBrick pb, int bnum[, int nfem])``
Add a boundary source term for neumann Kirchhoff-Love plate problems.
Should be used with the Kirchhoff-Love flavour of the bilaplacian
brick.
* ``B = MdBrick('qu term', MdBrick pb[, int bnum[, int nfem]])``
Update the tangent matrix with a \\int (Qu).v term.
The Q(x) parameter is a matrix field of size qdim x qdim. An example
of use is for the "iku" part of Robin boundary conditions
\\partial_n u + iku = ...
* ``B = MdBrick('mass matrix', MeshIm mim, MeshFem mf_u[, 'real'|'complex'])``
Build a mass-matrix brick.
* ``B = MdBrick('generic elliptic', MeshIm mim, MeshFem mfu[, 'scalar'|'matrix'|'tensor'][, 'real'|'complex'])``
Setup a generic elliptic problem.
a(x)*grad(U).grad(V)
The brick parameter `a` may be a scalar field, a matrix field, or
a tensor field (default is scalar).
* ``B = MdBrick('helmholtz', MeshIm mim, MeshFem mfu[, 'real'|'complex'])``
Setup a Helmholtz problem.
The brick has one parameter, 'wave_number'.
* ``B = MdBrick('isotropic linearized elasticity', MeshIm mim, MeshFem mfu)``
Setup a linear elasticity problem.
The brick has two scalar parameter, 'lambda' and 'mu' (the Lame
coefficients).
* ``B = MdBrick('linear incompressibility term', MdBrick pb, MeshFem mfp[, int nfem])``
Add an incompressibily constraint (div u = 0).
* ``B = MdBrick('nonlinear elasticity', MeshIm mim, MeshFem mfu, string law)``
Setup a nonlinear elasticity (large deformations) problem.
The material `law` can be chosen among:
- 'SaintVenant Kirchhoff' :
Linearized material law.
- 'Mooney Rivlin' :
Can be preceded with the words 'compressible' or 'incompressible' to force
a specific version. By default, the incompressible version is considered,
which has to be used with the nonlinear incompressibily term.
The compressible version requires one additional material coefficient.
- 'neo Hookean' :
A special case of the 'Mooney Rivlin' law that requires one material
coefficient less. By default, its compressible version is used.
- 'Ciarlet Geymonat'
* ``B = MdBrick('nonlinear elasticity incompressibility term', MdBrick pb, MeshFem mfp[, int nfem])``
Add an incompressibily constraint to a large strain elasticity problem.
* ``B = MdBrick('small deformations plasticity', MeshIm mim, MeshFem mfu, scalar THRESHOLD)``
Setup a plasticity problem (with small deformations).
The `THRESHOLD` parameter is the maximum value of the Von Mises
stress before 'plastification' of the material.
* ``B = MdBrick('dynamic', MdBrick pb, scalar rho[, int numfem])``
Dynamic brick. This brick is not fully working.
* ``B = MdBrick('bilaplacian', MeshIm mim, MeshFem mfu[, 'Kirchhoff-Love'])``
Setup a bilaplacian problem.
If the 'Kirchhoff-Love' option is specified, the Kirchhoff-Love
plate model is used.
* ``B = MdBrick('navier stokes', MeshIm mim, MeshFem mfu, MeshFem mfp)``
Setup a Navier-Stokes problem (this brick is not ready, do not use it).
* ``B = MdBrick('isotropic_linearized_plate', MeshIm mim, MeshIm mims, MeshFem mfut, MeshFem mfu3, MeshFem mftheta, scalar eps)``
Setup a linear plate model brick.
For moderately thick plates, using the Reissner-Mindlin model.
`eps` is the plate thinkness, the MeshFem `mfut` and `mfu3` are used
respectively for the membrane displacement and the transverse
displacement of the plate. The MeshFem `mftheta` is the rotation of
the normal ("section rotations").
The second integration method `mims` can be chosen equal to
`mim`, or different if you want to perform sub-integration on
the transverse shear term (mitc4 projection).
This brick has two parameters "lambda" and "mu" (the Lame
coefficients)
* ``B = MdBrick('mixed_isotropic_linearized_plate', MeshIm mim, MeshFem mfut, MeshFem mfu3, MeshFem mftheta, scalar eps)``
Setup a mixed linear plate model brick.
For thin plates, using Kirchhoff-Love model. For a non-mixed version,
use the bilaplacian brick.
* ``B = MdBrick('plate_source_term', MdBrick pb[, int bnum=-1[, int nfem]])``
Add a boundary or a volumic source term to a plate problem.
This brick has two parameters: "B" is the displacement (ut and u3)
source term, "M" is the moment source term (i.e. the source term
on the rotation of the normal).
* ``B = MdBrick('plate_simple_support', MdBrick pb, int bnum, string CTYPE[, int nfem])``
Add a "simple support" boundary condition to a plate problem.
Homogeneous Dirichlet condition on the displacement, free rotation.
`CTYPE` specifies how the constraint is enforced ('penalized',
'augmented' or 'eliminated').
* ``B = MdBrick('plate_clamped_support', MdBrick pb, int bnum, string CTYPE[, int nfem])``
Add a "clamped support" boundary condition to a plate problem.
Homogeneous Dirichlet condition on the displacement and on the
rotation. `CTYPE` specifies how the constraint is enforced
('penalized', 'augmented' or 'eliminated').
* ``B = MdBrick('plate_closing', MdBrick pb[, int nfem])``
Add a free edges condition for the mixed plate model brick.
This brick is required when the mixed linearized plate brick is
used. It must be inserted after all other boundary conditions
(the reason is that the brick has to inspect all other boundary
conditions to determine the number of disconnected boundary parts
which are free edges).
"""
generic_constructor(self,'mdbrick',*args)
def __del__(self):
generic_destructor(self, destructible=True)
def get(self, *args):
return getfem('mdbrick_get',self.id, *args)
def __repr__(self):
getfem('mdbrick_get',self.id, 'display')
return ''
def set(self, *args):
return getfem('mdbrick_set',self.id, *args)
def __str__(self):
return self.char()
def nbdof(self):
"""Get the total number of dof of the current problem.
This is the sum of the brick specific dof plus the dof of the
parent bricks."""
return self.get("nbdof")
def dim(self):
"""Get the dimension of the main mesh (2 for a 2D mesh, etc)."""
return self.get("dim")
def nb_constraints(self):
"""Get the total number of dof constraints of the current problem.
This is the sum of the brick specific dof constraints plus the
dof constraints of the parent bricks."""
return self.get("nb_constraints")
def is_linear(self):
"""Return true if the problem is linear."""
return self.get("is_linear")
def is_symmetric(self):
"""Return true if the problem is symmetric."""
return self.get("is_symmetric")
def is_coercive(self):
"""Return true if the problem is coercive."""
return self.get("is_coercive")
def is_complex(self):
"""Return true if the problem uses complex numbers."""
return self.get("is_complex")
def mixed_variables(self):
"""Identify the indices of mixed variables (typically the pressure,
etc.) in the tangent matrix."""
return self.get("mixed_variables")
def subclass(self):
"""Get the typename of the brick."""
return self.get("subclass")
def param_list(self):
"""Get the list of parameters names.
Each brick embeds a number of parameters (the Lame coefficients
for the linearized elasticity brick, the wave number for the
Helmholtz brick,...), described as a (scalar, or vector, tensor
etc) field on a mesh_fem. You can read/change the parameter values
with MdBrick.param() and MdBrick.param()."""
return self.get("param_list")
def param(self, parameter_name):
"""Get the parameter value.
When the parameter has been assigned a specific MeshFem, it is returned
as a large array (the last dimension being the MeshFem dof). When no
MeshFem has been assigned, the parameter is considered to be constant
over the mesh."""
return self.get("param", parameter_name)
def solve(self, mds, *args):
"""Synopsis: MdBrick.solve(self,MdState mds[,...])
Run the standard getfem solver.
Note that you should be able to use your own solver if you want
(it is possible to obtain the tangent matrix and its right hand
side with the MdState.tangent_matrix() etc.).
Various options can be specified:
- 'noisy' or 'very noisy'
the solver will display some information showing the progress
(residual values etc.).
- 'max_iter', NIT
set the maximum iterations numbers.
- 'max_res', RES
set the target residual value.
- 'lsolver', SOLVERNAME
select explicitely the solver used for the linear systems (the
default value is 'auto', which lets getfem choose itself).
Possible values are 'superlu', 'mumps' (if supported),
'cg/ildlt', 'gmres/ilu' and 'gmres/ilut'."""
return self.get("solve", mds, *args)
def von_mises(self, mds, mfvm):
"""Compute the Von Mises stress on the MeshFem `mfvm`.
Only available on bricks where it has a meaning: linearized
elasticity, plasticity, nonlinear elasticity. Note that in 2D
it is not the "real" Von Mises (which should take into account
the 'plane stress' or 'plane strain' aspect), but a pure 2D Von
Mises."""
return self.get("von_mises", mds, mfvm)
def tresca(self, mds, mft):
"""Compute the Tresca stress criterion on the MeshFem `mft`.
Only available on bricks where it has a meaning: linearized
elasticity, plasticity, nonlinear elasticity."""
return self.get("tresca", mds, mft)
def memsize(self):
"""Return the amount of memory (in bytes) used by the model brick."""
return self.get("memsize")
def char(self):
"""Output a (unique) string representation of the MdBrick.
This can be used to perform comparisons between two
different MdBrick objects.
This function is to be completed.
"""
return self.get("char")
def display(self):
"""displays a short summary for a MdBrick."""
return self.get("display")
def set_param(self, name, *args):
"""Synopsis: MdBrick.set_param(self, string name, {MeshFem mf,V | V})
Change the value of a brick parameter.
`name` is the name of the parameter. `V` should contain the
new parameter value (vector or float). If a MeshFem is given,
`V` should hold the field values over that MeshFem (i.e. its
last dimension should be MeshFem.nbdof() or 1 for
constant field)."""
return self.set("param", name, *args)
def penalization_epsilon(self, eps):
"""Change the penalization coefficient of a constraint brick.
This is only applicable to the bricks which inherit from the
constraint brick, such as the Dirichlet ones. And of course it
is not effective when the constraint is enforced via direct
elimination or via Lagrange multipliers. The default value of
`eps` is 1e-9."""
return self.set("penalization_epsilon", eps)
def constraints(self, H, R):
"""Set the constraints imposed by a constraint brick.
This is only applicable to the bricks which inherit from the
constraint brick, such as the Dirichlet ones. Imposes `H.U=R`."""
return self.set("constraints", H, R)
def constraints_rhs(self, H, R):
"""Set the right hand side of the constraints imposed by a constraint brick.
This is only applicable to the bricks which inherit from the
constraint brick, such as the Dirichlet ones."""
return self.set("constraints_rhs", H, R)
#
# GetFEM class MdState definition.
#
class MdState:
"""GetFEM MdState object
A model state is an object which store the state data for a chain of model
bricks. This includes the global tangent matrix, the right hand side and
the constraints.
This object is now deprecated and replaced by the Model object.
There are two sorts of model states, the `real` and the `complex` models
states.
"""
def __init__(self, *args):
"""General constructor for MdState objects
* ``MDS = MdState('real')``
Build a model state for real unknowns.
* ``MDS = MdState('complex')``
Build a model state for complex unknowns.
* ``MDS = MdState(MdBrick B)``
Build a modelstate for the brick `B`.
Selects the real or complex state from the complexity of `B`.
"""
generic_constructor(self,'mdstate',*args)
def __del__(self):
generic_destructor(self, destructible=True)
def get(self, *args):
return getfem('mdstate_get',self.id, *args)
def __repr__(self):
getfem('mdstate_get',self.id, 'display')
return ''
def set(self, *args):
return getfem('mdstate_set',self.id, *args)
def __str__(self):
return self.char()
def is_complex(self):
"""Return 0 is the model state is real, 1 if it is complex."""
return self.get("is_complex")
def tangent_matrix(self):
"""Return the tangent matrix stored in the model state."""
return self.get("tangent_matrix")
def constraints_matrix(self):
"""Return the constraints matrix stored in the model state."""
return self.get("constraints_matrix")
def reduced_tangent_matrix(self):
"""Return the reduced tangent matrix (i.e. the tangent matrix after
elimination of the constraints)."""
return self.get("reduced_tangent_matrix")
def constraints_nullspace(self):
"""Return the nullspace of the constraints matrix."""
return self.get("constraints_nullspace")
def state(self):
"""Return the vector of unknowns, which contains the solution after MdBrick.solve()."""
return self.get("state")
def residual(self):
"""Return the residual."""
return self.get("residual")
def reduced_residual(self):
"""Return the residual on the reduced system."""
return self.get("reduced_residual")
def unreduce(self, U):
"""Reinsert the constraint eliminated from the system."""
return self.get("unreduce", U)
def memsize(self):
"""Return the amount of memory (in bytes) used by the model state."""
return self.get("memsize")
def char(self):
"""Output a (unique) string representation of the MdState.
This can be used to perform comparisons between two
different MdState objects.
This function is to be completed.
"""
return self.get("char")
def display(self):
"""displays a short summary for a MdState."""
return self.get("display")
def compute_reduced_system(self):
"""Compute the reduced system from the tangent matrix and constraints."""
return self.set("compute_reduced_system")
def compute_reduced_residual(self):
"""Compute the reduced residual from the residual and constraints."""
return self.set("compute_reduced_residual")
def compute_residual(self, B):
"""Compute the residual for the brick `B`."""
return self.set("compute_residual", B)
def compute_tangent_matrix(self, B):
"""Update the tangent matrix from the brick `B`."""
return self.set("compute_tangent_matrix", B)
def set_state(self, U):
"""Update the internal state with the vector `U`."""
return self.set("state", U)
def clear(self):
"""Clear the model state."""
return self.set("clear")
#
# GetFEM class Mesh definition.
#
class Mesh:
"""GetFEM Mesh object
This object is able to store any element in any dimension even if you mix
elements with different dimensions.
"""
def __init__(self, *args):
"""General constructor for Mesh objects
* ``M = Mesh('empty', int dim)``
Create a new empty mesh.
* ``M = Mesh('cartesian', vec X[, vec Y[, vec Z,..]])``
Build quickly a regular mesh of quadrangles, cubes, etc.
* ``M = Mesh('cartesian Q1', vec X, vec Y[, vec Z,..])``
Build quickly a regular mesh of quadrangles, cubes, etc. with
Q1 elements.
* ``M = Mesh('triangles grid', vec X, vec Y)``
Build quickly a regular mesh of triangles.
This is a very limited and somehow deprecated function (See also
``Mesh('ptND')``, ``Mesh('regular simplices')`` and
``Mesh('cartesian')``).
* ``M = Mesh('regular simplices', vec X[, vec Y[, vec Z,...]]['degree', int k]['noised'])``
Mesh a n-dimensionnal parallelepipeded with simplices (triangles,
tetrahedrons etc) .
The optional degree may be used to build meshes with non linear
geometric transformations.
* ``M = Mesh('curved', Mesh m, vec F)``
Build a curved (n+1)-dimensions mesh from a n-dimensions mesh `m`.
The points of the new mesh have one additional coordinate, given by
the vector `F`. This can be used to obtain meshes for shells. `m` may
be a MeshFem object, in that case its linked mesh will be used.
* ``M = Mesh('prismatic', Mesh m, int nl)``
Extrude a prismatic Mesh `M` from a Mesh `m`.
In the additional dimension there are `nl` layers of elements built
from ``0`` to ``1``.
* ``M = Mesh('pt2D', mat P, imat T[, int n])``
Build a mesh from a 2D triangulation.
Each column of `P` contains a point coordinate, and each column of `T`
contains the point indices of a triangle. `n` is optional and is a
zone number. If `n` is specified then only the zone number `n` is
converted (in that case, `T` is expected to have 4 rows, the fourth
containing these zone numbers).
* ``M = Mesh('ptND', mat P, imat T)``
Build a mesh from a n-dimensional "triangulation".
Similar function to 'pt2D', for building simplexes meshes from a
triangulation given in `T`, and a list of points given in `P`. The
dimension of the mesh will be the number of rows of `P`, and the
dimension of the simplexes will be the number of rows of `T`.
* ``M = Mesh('load', string filename)``
Load a mesh from a getfem++ ascii mesh file.
See also ``Mesh.save(string filename)``.
* ``M = Mesh('from string', string s)``
Load a mesh from a string description.
For example, a string returned by ``Mesh.char()``.
* ``M = Mesh('import', string format, string filename)``
Import a mesh.
`format` may be:
- 'gmsh' for a mesh created with `Gmsh`
- 'gid' for a mesh created with `GiD`
- 'am_fmt' for a mesh created with `EMC2`
* ``M = Mesh('clone', Mesh m2)``
Create a copy of a mesh.
* ``M = Mesh('generate', MesherObject mo, scalar h[, int K = 1[, mat vertices]])``
Call the (very) experimental mesher of Getfem on the geometry
represented by `mo`. please control the conformity of the produced mesh.
You can add the mesher by adding a priori vertices in the array
`vertices` which should be of size ``n x m`` where ``n`` n is the
dimension of the mesh and ``m`` the number of points. `h` is
approximate diameter of the elements. `K` is the degree of the
mesh ( > 1 for curved boundaries). The mesher try to optimize the
quality of the elements. This operation may be time consuming.
Note that if the mesh generation fails, because of some random
procedure used, it will not give necessarily the same result due
to random procedures used.
The messages send to the console by the mesh generation can be
desactivated using `gf_util('trace level', 2)`. More information
can be obtained by `gf_util('trace level', 4)`.
"""
generic_constructor(self,'mesh',*args)
def __del__(self):
generic_destructor(self, destructible=True)
def get(self, *args):
return getfem('mesh_get',self.id, *args)
def __repr__(self):
getfem('mesh_get',self.id, 'display')
return ''
def set(self, *args):
return getfem('mesh_set',self.id, *args)
def __str__(self):
return self.char()
def dim(self):
"""Get the dimension of the mesh (2 for a 2D mesh, etc)."""
return self.get("dim")
def nbpts(self):
"""Get the number of points of the mesh."""
return self.get("nbpts")
def nbcvs(self):
"""Get the number of convexes of the mesh."""
return self.get("nbcvs")
def pts(self, PIDs=None):
"""Return the list of point coordinates of the mesh.
Each column of the returned matrix contains the coordinates of one
point. If the optional argument `PIDs` was given, only the points
whose #id is listed in this vector are returned. Otherwise, the
returned matrix will have Mesh.max_pid() columns, which might
be greater than Mesh.nbpts() (if some points of the mesh have
been destroyed and no call to Mesh.optimize_structure() have
been issued). The columns corresponding to deleted points will be
filled with NaN. You can use Mesh.pid() to filter such invalid
points."""
return self.get("pts", PIDs)
def pid(self):
"""Return the list of points #id of the mesh.
Note that their numbering is not supposed to be contiguous from
0 to Mesh.nbpts()-1,
especially if some points have been removed from the mesh. You
can use Mesh.optimize_structure() to enforce a contiguous
numbering."""
return self.get("pid")
def pid_in_faces(self, CVFIDs):
"""Search point #id listed in `CVFIDs`.
`CVFIDs` is a two-rows matrix, the first row lists convex #ids,
and the second lists face numbers. On return, `PIDs` is a
vector containing points #id."""
return self.get("pid_in_faces", CVFIDs)
def pid_in_cvids(self, CVIDs):
"""Search point #id listed in `CVIDs`.
`PIDs` is a vector containing points #id."""
return self.get("pid_in_cvids", CVIDs)
def pid_in_regions(self, RIDs):
"""Search point #id listed in `RIDs`.
`PIDs` is a vector containing points #id."""
return self.get("pid_in_regions", RIDs)
def pid_from_coords(self, PTS, radius=0):
"""Search point #id whose coordinates are listed in `PTS`.
`PTS` is an array containing a list of point coordinates. On
return, `PIDs` is a vector containing points
#id for each point found in `eps` range, and -1 for those
which where not found in the mesh."""
return self.get("pid_from_coords", PTS, radius)
def pid_from_cvid(self, CVIDs=None):
"""Return the points attached to each convex of the mesh.
If `CVIDs` is omitted, all the convexes will be considered
(equivalent to `CVIDs = Mesh.max_cvid()`). `IDx` is a
vector, length(IDx) = length(CVIDs)+1. `Pid` is a
vector containing the concatenated list of #id of
points of each convex in `CVIDs`. Each entry of `IDx` is the
position of the corresponding convex point list in `Pid`. Hence,
for example, the list of #id of points of the second convex is
Pid[IDx(2):IDx(3)].
If `CVIDs` contains convex #id which do not exist in the mesh,
their point list will be empty."""
return self.get("pid_from_cvid", CVIDs)
def pts_from_cvid(self, CVIDs=None):
"""Search point listed in `CVID`.
If `CVIDs` is omitted, all the convexes will be considered
(equivalent to `CVIDs = Mesh.max_cvid()`). `IDx` is a
vector, length(IDx) = length(CVIDs)+1. `Pts` is a
vector containing the concatenated list of points
of each convex in `CVIDs`. Each entry of `IDx` is the position
of the corresponding convex point list in `Pts`. Hence, for
example, the list of points of the second convex is
Pts[:,IDx[2]:IDx[3]].
If `CVIDs` contains convex #id which do not exist in the mesh,
their point list will be empty."""
return self.get("pts_from_cvid", CVIDs)
def cvid(self):
"""Return the list of all convex #id.
Note that their numbering is not supposed to be contiguous from
0 to Mesh.nbcvs()-1,
especially if some points have been removed from the mesh. You
can use Mesh.optimize_structure() to enforce a contiguous
numbering."""
return self.get("cvid")
def max_pid(self):
"""Return the maximum #id of all points in the mesh (see 'max cvid')."""
return self.get("max_pid")
def max_cvid(self):
"""Return the maximum #id of all convexes in the mesh (see 'max pid')."""
return self.get("max_cvid")
def edges(self, CVLST=None, *args):
"""Synopsis: [E,C] = Mesh.edges(self [, CVLST][, 'merge'])
[OBSOLETE FUNCTION! will be removed in a future release]
Return the list of edges of mesh M for the convexes listed in the
row vector CVLST. E is a 2 x nb_edges matrix containing point
indices. If CVLST is omitted, then the edges of all convexes are
returned. If CVLST has two rows then the first row is supposed to
contain convex numbers, and the second face numbers, of which the
edges will be returned. If 'merge' is indicated, all common
edges of convexes are merged in a single edge. If the optional
output argument C is specified, it will contain the convex number
associated with each edge."""
return self.get("edges", CVLST, *args)
def curved_edges(self, N, CVLST=None):
"""[OBSOLETE FUNCTION! will be removed in a future release]
More sophisticated version of Mesh.edges() designed for
curved elements. This one will return N (N>=2) points of the
(curved) edges. With N==2, this is equivalent to
Mesh.edges(). Since the points are no more always part of
the mesh, their coordinates are returned instead of points
number, in the array E which is a [ mesh_dim x 2 x nb_edges ]
array. If the optional output argument C is specified, it will
contain the convex number associated with each edge."""
return self.get("curved_edges", N, CVLST)
def orphaned_pid(self):
"""Search point #id which are not linked to a convex."""
return self.get("orphaned_pid")
def cvid_from_pid(self, PIDs, share=False):
"""Search convex #ids related with the point #ids given in `PIDs`.
If `share=False`, search convex whose vertex #ids are in `PIDs`.
If `share=True`, search convex #ids that share the point #ids
given in `PIDs`. `CVIDs` is a vector (possibly
empty)."""
return self.get("cvid_from_pid", PIDs, share)
def faces_from_pid(self, PIDs):
"""Return the convex faces whose vertex #ids are in `PIDs`.
`CVFIDs` is a two-rows matrix, the first row lists convex #ids,
and the second lists face numbers (local number in the convex).
For a convex face to be returned, EACH of its points have to be
listed in `PIDs`."""
return self.get("faces_from_pid", PIDs)
def outer_faces(self, CVIDs=None):
"""Return the faces which are not shared by two convexes.
`CVFIDs` is a two-rows matrix, the first row lists convex #ids,
and the second lists face numbers (local number in the convex).
If `CVIDs` is not given, all convexes are considered, and it
basically returns the mesh boundary. If `CVIDs` is given, it
returns the boundary of the convex set whose #ids are listed
in `CVIDs`."""
return self.get("outer_faces", CVIDs)
def faces_from_cvid(self, CVIDs=None, *args):
"""Synopsis: CVFIDs = Mesh.faces_from_cvid(self[, ivec CVIDs][, 'merge'])
Return a list of convexes faces from a list of convex #id.
`CVFIDs` is a two-rows matrix, the first row lists convex #ids,
and the second lists face numbers (local number in the convex).
If `CVIDs` is not given, all convexes are considered. The optional
argument 'merge' merges faces shared by the convex of `CVIDs`."""
return self.get("faces_from_cvid", CVIDs, *args)
def triangulated_surface(self, Nrefine, CVLIST=None):
"""[DEPRECATED FUNCTION! will be removed in a future release]
Similar function to Mesh.curved_edges() : split (if
necessary, i.e. if the geometric transformation if non-linear)
each face into sub-triangles and return their coordinates in T
(see also gf_compute('eval on P1 tri mesh'))"""
return self.get("triangulated_surface", Nrefine, CVLIST)
def normal_of_face(self, cv, f, nfpt=None):
"""Evaluates the normal of convex `cv`, face `f` at the `nfpt` point of the face.
If `nfpt` is not specified, then the normal is evaluated at each
geometrical node of the face."""
return self.get("normal_of_face", cv, f, nfpt)
def normal_of_faces(self, CVFIDs):
"""Evaluates (at face centers) the normals of convexes.
`CVFIDs` is supposed a two-rows matrix, the first row lists convex
#ids, and the second lists face numbers (local number in the convex)."""
return self.get("normal_of_faces", CVFIDs)
def quality(self, CVIDs=None):
"""Return an estimation of the quality of each convex (:math:`0 \\leq Q \\leq 1`)."""
return self.get("quality", CVIDs)
def convex_area(self, CVIDs=None):
"""Return an estimate of the area of each convex."""
return self.get("convex_area", CVIDs)
def convex_radius(self, CVIDs=None):
"""Return an estimate of the radius of each convex."""
return self.get("convex_radius", CVIDs)
def cvstruct(self, CVIDs=None):
"""Return an array of the convex structures.
If `CVIDs` is not given, all convexes are considered. Each convex
structure is listed once in `S`, and `CV2S` maps the convexes
indice in `CVIDs` to the indice of its structure in `S`."""
return self.get("cvstruct", CVIDs)
def geotrans(self, CVIDs=None):
"""Returns an array of the geometric transformations.
See also Mesh.cvstruct()."""
return self.get("geotrans", CVIDs)
def boundaries(self):
"""DEPRECATED FUNCTION. Use 'regions' instead."""
return self.get("boundaries")
def regions(self):
"""Return the list of valid regions stored in the mesh."""
return self.get("regions")
def boundary(self):
"""DEPRECATED FUNCTION. Use 'region' instead."""
return self.get("boundary")
def region(self, RIDs):
"""Return the list of convexes/faces on the regions `RIDs`.
`CVFIDs` is a two-rows matrix, the first row lists convex #ids,
and the second lists face numbers (local number in the convex).
(and -1 when the whole convex is in the
regions)."""
return self.get("region", RIDs)
def save(self, filename):
"""Save the mesh object to an ascii file.
This mesh can be restored with Mesh('load', filename)."""
return self.get("save", filename)
def char(self):
"""Output a string description of the mesh."""
return self.get("char")
def export_to_vtk(self, filename, *args):
"""Synopsis: Mesh.export_to_vtk(self, string filename, ... [,'ascii'][,'quality'])
Exports a mesh to a VTK file .
If 'quality' is specified, an estimation of the quality of each
convex will be written to the file.
See also MeshFem.export_to_vtk(), Slice.export_to_vtk()."""
return self.get("export_to_vtk", filename, *args)
def export_to_dx(self, filename, *args):
"""Synopsis: Mesh.export_to_dx(self, string filename, ... [,'ascii'][,'append'][,'as',string name,[,'serie',string serie_name]][,'edges'])
Exports a mesh to an OpenDX file.
See also MeshFem.export_to_dx(), Slice.export_to_dx()."""
return self.get("export_to_dx", filename, *args)
def export_to_pos(self, filename, name=None):
"""Exports a mesh to a POS file .
See also MeshFem.export_to_pos(), Slice.export_to_pos()."""
return self.get("export_to_pos", filename, name)
def memsize(self):
"""Return the amount of memory (in bytes) used by the mesh."""
return self.get("memsize")
def display(self):
"""displays a short summary for a Mesh object."""
return self.get("display")
def set_pts(self, PTS):
"""Replace the coordinates of the mesh points with those given in `PTS`."""
return self.set("pts", PTS)
def add_point(self, PTS):
"""Insert new points in the mesh and return their #ids.
`PTS` should be an ``nxm`` matrix , where ``n`` is the mesh
dimension, and ``m`` is the number of points that will be
added to the mesh. On output, `PIDs` contains the point #ids
of these new points.
Remark: if some points are already part of the mesh (with a small
tolerance of approximately ``1e-8``), they won't be inserted again,
and `PIDs` will contain the previously assigned #ids of these
points."""
return self.set("add_point", PTS)
def del_point(self, PIDs):
"""Removes one or more points from the mesh.
`PIDs` should contain the point #ids, such as the one returned by
the 'add point' command."""
return self.set("del_point", PIDs)
def add_convex(self, GT, PTS):
"""Add a new convex into the mesh.
The convex structure (triangle, prism,...) is given by `GT`
(obtained with GeoTrans('...')), and its points are given by
the columns of `PTS`. On return, `CVIDs` contains the convex #ids.
`PTS` might be a 3-dimensional array in order to insert more than
one convex (or a two dimensional array correctly shaped according
to Fortran ordering)."""
return self.set("add_convex", GT, PTS)
def del_convex(self, CVIDs):
"""Remove one or more convexes from the mesh.
`CVIDs` should contain the convexes #ids, such as the ones
returned by the 'add convex' command."""
return self.set("del_convex", CVIDs)
def del_convex_of_dim(self, DIMs):
"""Remove all convexes of dimension listed in `DIMs`.
For example; ``Mesh.del_convex_of_dim([1,2])`` remove
all line segments, triangles and quadrangles."""
return self.set("del_convex_of_dim", DIMs)
def translate(self, V):
"""Translates each point of the mesh from `V`."""
return self.set("translate", V)
def transform(self, T):
"""Applies the matrix `T` to each point of the mesh.
Note that `T` is not required to be a ``NxN`` matrix (with
``N = Mesh.dim()``). Hence it is possible to transform
a 2D mesh into a 3D one (and reciprocally)."""
return self.set("transform", T)
def set_boundary(self, rnum, CVFIDs):
"""DEPRECATED FUNCTION. Use 'region' instead."""
return self.set("boundary", rnum, CVFIDs)
def set_region(self, rnum, CVFIDs):
"""Assigns the region number `rnum` to the convex faces (or convexes)
stored in each column of the matrix `CVFIDs`.
The first row of `CVFIDs` contains a convex #ids, and the second row
contains a face number in the convex (or ``-1``
for the whole convex (regions are usually used to store a list of
convex faces, but you may also use them to store a list of convexes).
If a vector is provided (or a one row matrix) the region will represent
the corresponding set of convex."""
return self.set("region", rnum, CVFIDs)
def region_intersect(self, r1, r2):
"""Replace the region number `r1` with its intersection with region number `r2`."""
return self.set("region_intersect", r1, r2)
def region_merge(self, r1, r2):
"""Merge region number `r2` into region number `r1`."""
return self.set("region_merge", r1, r2)
def region_substract(self, r1, r2):
"""Replace the region number `r1` with its difference with region
number `r2`."""
return self.set("region_substract", r1, r2)
def delete_boundary(self, rnum, CVFIDs):
"""DEPRECATED FUNCTION. Use 'delete region' instead."""
return self.set("delete_boundary", rnum, CVFIDs)
def delete_region(self, RIDs):
"""Remove the regions whose #ids are listed in `RIDs`"""
return self.set("delete_region", RIDs)
def merge(self, m2):
"""Merge with the Mesh `m2`.
Overlapping points won't be duplicated. If `m2` is a MeshFem object,
its linked mesh will be used."""
return self.set("merge", m2)
def optimize_structure(self):
"""Reset point and convex numbering.
After optimisation, the points (resp. convexes) will
be consecutively numbered from ``0`` to
``Mesh.max_pid()-1`` (resp. ``Mesh.max_cvid()-1``)."""
return self.set("optimize_structure")
def refine(self, CVIDs=None):
"""Use a Bank strategy for mesh refinement.
If `CVIDs` is not given, the whole mesh is refined. Note
that the regions, and the finite element methods and
integration methods of the MeshFem and MeshIm objects linked
to this mesh will be automagically refined."""
return self.set("refine", CVIDs)
#
# GetFEM class MeshFem definition.
#
class MeshFem:
"""GetFEM MeshFem object
This object represents a finite element method defined on a whole mesh.
"""
def __init__(self, *args):
"""General constructor for MeshFem objects
* ``MF = MeshFem('load', string fname[, Mesh m])``
Load a MeshFem from a file.
If the mesh `m` is not supplied (this kind of file does not store the
mesh), then it is read from the file `fname` and its descriptor is
returned as the second output argument.
* ``MF = MeshFem('from string', string s[, Mesh m])``
Create a MeshFem object from its string description.
See also ``MeshFem.char()``
* ``MF = MeshFem('clone', MeshFem mf)``
Create a copy of a MeshFem.
* ``MF = MeshFem('sum', MeshFem mf1, MeshFem mf2[, MeshFem mf3[, ...]])``
Create a MeshFem that combines two (or more) MeshFem's.
All MeshFem must share the same mesh (see
``Fem('interpolated_fem')`` to map a MeshFem onto another).
After that, you should not modify the FEM of `mf1`, `mf2` etc.
* ``MF = MeshFem('levelset', MeshLevelSet mls, MeshFem mf)``
Create a MeshFem that is conformal to implicit surfaces defined in
MeshLevelSet.
* ``MF = MeshFem('global function', Mesh m, LevelSet ls, (GlobalFunction GF1,...)[, int Qdim_m])``
Create a MeshFem whose base functions are global function given by the
user in the system of coordinate defined by the iso-values of the two
level-set function of `ls`.
* ``MF = MeshFem('partial', MeshFem mf, ivec DOFs[, ivec RCVs])``
Build a restricted MeshFem by keeping only a subset of the degrees of
freedom of `mf`.
If `RCVs` is given, no FEM will be put on the convexes listed in
`RCVs`.
* ``MF = MeshFem(Mesh m[, int Qdim1=1[, int Qdim2=1, ...]])``
Build a new MeshFem object.
The `Qdim` parameters specifies the dimension of the field represented
by the finite element method. Qdim1 = 1 for a scalar field,
Qdim1 = n for a vector field off size n, Qdim1=m, Qdim2=n for
a matrix field of size mxn ...
Returns the handle of the created object.
"""
generic_constructor(self,'mesh_fem',*args)
def __del__(self):
generic_destructor(self, destructible=True)
def get(self, *args):
return getfem('mesh_fem_get',self.id, *args)
def __repr__(self):
getfem('mesh_fem_get',self.id, 'display')
return ''
def set(self, *args):
return getfem('mesh_fem_set',self.id, *args)
def __str__(self):
return self.char()
def nbdof(self):
"""Return the number of degrees of freedom (dof) of the MeshFem."""
return self.get("nbdof")
def nb_basic_dof(self):
"""Return the number of basic degrees of freedom (dof) of the MeshFem."""
return self.get("nb_basic_dof")
def dof_from_cv(self, CVids):
"""Deprecated function. Use MeshFem.basic_dof_from_cv() instead."""
return self.get("dof_from_cv", CVids)
def basic_dof_from_cv(self, CVids):
"""Return the dof of the convexes listed in `CVids`.
WARNING: the Degree of Freedom might be returned in ANY order, do
not use this function in your assembly routines. Use 'basic dof from cvid'
instead, if you want to be able to map a convex number with its
associated degrees of freedom.
One can also get the list of basic dof on a set on convex faces, by
indicating on the second row of `CVids` the faces numbers (with
respect to the convex number on the first row)."""
return self.get("basic_dof_from_cv", CVids)
def dof_from_cvid(self, CVids=None):
"""Deprecated function. Use MeshFem.basic_dof_from_cvid() instead."""
return self.get("dof_from_cvid", CVids)
def basic_dof_from_cvid(self, CVids=None):
"""Return the degrees of freedom attached to each convex of the mesh.
If `CVids` is omitted, all the convexes will be considered (equivalent
to `CVids = 1 ... Mesh.max_cvid()`).
`IDx` is a vector, `length(IDx) = length(CVids)+1`.
`DOFs` is a vector containing the concatenated list
of dof of each convex in `CVids`. Each entry of `IDx` is the position
of the corresponding convex point list in `DOFs`. Hence, for example,
the list of points of the second convex is DOFs[IDx(2):IDx(3)].
If `CVids` contains convex #id which do not exist in the mesh, their
point list will be empty."""
return self.get("basic_dof_from_cvid", CVids)
def non_conformal_dof(self, CVids=None):
"""Deprecated function. Use MeshFem.non_conformal_basic_dof() instead."""
return self.get("non_conformal_dof", CVids)
def non_conformal_basic_dof(self, CVids=None):
"""Return partially linked degrees of freedom.
Return the basic dof located on the border of a convex and which belong
to only one convex, except the ones which are located on the border
of the mesh. For example, if the convex 'a' and 'b' share a common
face, 'a' has a P1 FEM, and 'b' has a P2 FEM, then the basic dof on the
middle of the face will be returned by this function (this can be
useful when searching the interfaces between classical FEM and
hierarchical FEM)."""
return self.get("non_conformal_basic_dof", CVids)
def qdim(self):
"""Return the dimension Q of the field interpolated by the MeshFem.
By default, Q=1 (scalar field). This has an impact on the dof numbering."""
return self.get("qdim")
def fem(self, CVids=None):
"""Return a list of FEM used by the MeshFem.
`FEMs` is an array of all Fem objects found in the convexes
given in `CVids`. If `CV2F` was supplied as an output argument,
it contains, for each convex listed in `CVids`, the index of its
correspounding FEM in `FEMs`.
Convexes which are not part of the mesh, or convexes which do not
have any FEM have their correspounding entry in `CV2F` set to -1.
"""
return self.get("fem", CVids)
def convex_index(self):
"""Return the list of convexes who have a FEM."""
return self.get("convex_index")
def is_lagrangian(self, CVids=None):
"""Test if the MeshFem is Lagrangian.
Lagrangian means that each base function Phi[i] is such that
Phi[i](P[j]) = delta(i,j), where P[j] is the dof location of
the jth base function, and delta(i,j) = 1 if i==j, else 0.
If `CVids` is omitted, it returns 1 if all convexes in the mesh
are Lagrangian. If `CVids` is used, it returns the convex indices
(with respect to `CVids`) which are Lagrangian."""
return self.get("is_lagrangian", CVids)
def is_equivalent(self, CVids=None):
"""Test if the MeshFem is equivalent.
See MeshFem.is_lagrangian()"""
return self.get("is_equivalent", CVids)
def is_polynomial(self, CVids=None):
"""Test if all base functions are polynomials.
See MeshFem.is_lagrangian()"""
return self.get("is_polynomial", CVids)
def is_reduced(self):
"""Return 1 if the optional reduction matrix is applied to the dofs."""
return self.get("is_reduced")
def reduction_matrix(self):
"""Return the optional reduction matrix."""
return self.get("reduction_matrix")
def extension_matrix(self):
"""Return the optional extension matrix."""
return self.get("extension_matrix")
def basic_dof_on_region(self, Rs):
"""Return the list of basic dof (before the optional reduction) lying on one
of the mesh regions listed in `Rs`.
More precisely, this function returns the basic dof whose support is
non-null on one of regions whose #ids are listed in `Rs` (note
that for boundary regions, some dof nodes may not lie exactly
on the boundary, for example the dof of Pk(n,0) lies on the center
of the convex, but the base function in not null on the convex
border)."""
return self.get("basic_dof_on_region", Rs)
def dof_on_region(self, Rs):
"""Return the list of dof (after the optional reduction) lying on one
of the mesh regions listed in `Rs`.
More precisely, this function returns the basic dof whose support is
non-null on one of regions whose #ids are listed in `Rs` (note
that for boundary regions, some dof nodes may not lie exactly
on the boundary, for example the dof of Pk(n,0) lies on the center
of the convex, but the base function in not null on the convex
border).
For a reduced mesh_fem
a dof is lying on a region if its potential corresponding shape
function is nonzero on this region. The extension matrix is used
to make the correspondance between basic and reduced dofs."""
return self.get("dof_on_region", Rs)
def dof_nodes(self, DOFids=None):
"""Deprecated function. Use MeshFem.basic_dof_nodes() instead."""
return self.get("dof_nodes", DOFids)
def basic_dof_nodes(self, DOFids=None):
"""Get location of basic degrees of freedom.
Return the list of interpolation points for the specified
dof #IDs in `DOFids` (if `DOFids` is omitted, all basic dof are
considered)."""
return self.get("basic_dof_nodes", DOFids)
def dof_partition(self):
"""Get the 'dof_partition' array.
Return the array which associates an integer (the partition number)
to each convex of the MeshFem. By default, it is an all-zero array.
The degrees of freedom of each convex of the MeshFem are connected
only to the dof of neighbouring convexes which have the same
partition number, hence it is possible to create partially
discontinuous MeshFem very easily."""
return self.get("dof_partition")
def save(self, filename, opt=None):
"""Save a MeshFem in a text file (and optionaly its linked mesh object
if `opt` is the string 'with_mesh')."""
return self.get("save", filename, opt)
def char(self, opt=None):
"""Output a string description of the MeshFem.
By default, it does not include the description of the linked mesh
object, except if `opt` is 'with_mesh'."""
return self.get("char", opt)
def display(self):
"""displays a short summary for a MeshFem object."""
return self.get("display")
def linked_mesh(self):
"""Return a reference to the Mesh object linked to `mf`."""
return self.get("linked_mesh")
def mesh(self):
"""Return a reference to the Mesh object linked to `mf`.
(identical to Mesh.linked_mesh())"""
return self.get("mesh")
def export_to_vtk(self, filename, *args):
"""Synopsis: MeshFem.export_to_vtk(self,string filename, ... ['ascii'], U, 'name'...)
Export a MeshFem and some fields to a vtk file.
The FEM and geometric transformations will be mapped to order 1
or 2 isoparametric Pk (or Qk) FEMs (as VTK does not handle higher
order elements). If you need to represent high-order FEMs or
high-order geometric transformations, you should consider
Slice.export_to_vtk()."""
return self.get("export_to_vtk", filename, *args)
def export_to_dx(self, filename, *args):
"""Synopsis: MeshFem.export_to_dx(self,string filename, ...['as', string mesh_name][,'edges']['serie',string serie_name][,'ascii'][,'append'], U, 'name'...)
Export a MeshFem and some fields to an OpenDX file.
This function will fail if the MeshFem mixes different convex types
(i.e. quads and triangles), or if OpenDX does not handle a specific
element type (i.e. prism connections are not known by OpenDX).
The FEM will be mapped to order 1 Pk (or Qk) FEMs. If you need to
represent high-order FEMs or high-order geometric transformations,
you should consider Slice.export_to_dx()."""
return self.get("export_to_dx", filename, *args)
def export_to_pos(self, filename, name=None, *args):
"""Synopsis: MeshFem.export_to_pos(self,string filename[, string name][[,MeshFem mf1], mat U1, string nameU1[[,MeshFem mf2], mat U2, string nameU2,...]])
Export a MeshFem and some fields to a pos file.
The FEM and geometric transformations will be mapped to order 1
isoparametric Pk (or Qk) FEMs (as GMSH does not handle higher
order elements)."""
return self.get("export_to_pos", filename, name, *args)
def dof_from_im(self, mim, p=None):
"""Return a selection of dof who contribute significantly to the
mass-matrix that would be computed with `mf` and the integration
method `mim`.
`p` represents the dimension on what the integration method
operates (default `p = mesh dimension`).
IMPORTANT: you still have to set a valid integration method on
the convexes which are not crosses by the levelset!"""
return self.get("dof_from_im", mim, p)
def interpolate_convex_data(self, Ucv):
"""Interpolate data given on each convex of the mesh to the MeshFem dof.
The MeshFem has to be lagrangian, and should be discontinuous (typically
a FEM_PK(N,0) or FEM_QK(N,0) should be used).
The last dimension of the input vector Ucv should have
Mesh.max_cvid() elements.
Example of use: MeshFem.interpolate_convex_data(Mesh.quality())"""
return self.get("interpolate_convex_data", Ucv)
def memsize(self):
"""Return the amount of memory (in bytes) used by the mesh_fem object.
The result does not take into account the linked mesh object."""
return self.get("memsize")
def has_linked_mesh_levelset(self):
"""Is a mesh_fem_level_set or not."""
return self.get("has_linked_mesh_levelset")
def linked_mesh_levelset(self):
"""if it is a mesh_fem_level_set gives the linked mesh_level_set."""
return self.get("linked_mesh_levelset")
def eval(self, expression, gl={}, lo={}):
"""interpolate an expression on the (lagrangian) MeshFem.
Examples::
mf.eval('x*y') # interpolates the function 'x*y'
mf.eval('[x,y]') # interpolates the vector field '[x,y]'
import numpy as np
mf.eval('np.sin(x)',globals(),locals()) # interpolates the function sin(x)
"""
P = self.basic_dof_nodes()
nbd = P.shape[1]
if (getfem_python_par):
rk = mpi.COMM_WORLD.rank
nbp = mpi.COMM_WORLD.size
else:
rk = 0
nbp = 1
if not self.is_lagrangian:
raise RuntimeError('cannot eval on a non-Lagragian MeshFem')
if self.qdim() != 1:
Ind = numpy.arange(0,nbd,self.qdim())
P = P[:,Ind]
nbd = P.shape[1]
vars = ('x','y','z','u','v','w')
nbvars = min(P.shape[0],len(vars))
for i in xrange(0,nbvars):
gl[vars[i]] = P[i,0]
lo[vars[i]] = P[i,0]
ccode = compile(expression, '<string>', 'eval');
r = numpy.array(eval(ccode,gl,lo))
Z = numpy.zeros(r.shape + (nbd,), r.dtype)
nbd_p = nbd/nbp
nbd_end = nbd_p*(rk+1)
if (rk == nbp-1):
nbd_end = nbd
for j in xrange(nbd_p*rk,nbd_end):
for i in xrange(0,nbvars):
gl[vars[i]] = P[i,j]
lo[vars[i]] = P[i,j]
Z[...,j] = eval(ccode,gl,lo)
if (nbp > 1):
W = numpy.zeros(r.shape + (nbd,), r.dtype)
mpi.COMM_WORLD.Allreduce(Z, W, op=mpi.SUM)
Z = W
return Z
def set_fem(self, f, CVids=None):
"""Set the Finite Element Method.
Assign a FEM `f` to all convexes whose #ids are listed in `CVids`.
If `CVids` is not given, the integration is assigned to all convexes.
See the help of Fem to obtain a list of available FEM methods."""
return self.set("fem", f, CVids)
def set_classical_fem(self, k, CVids=None):
"""Assign a classical (Lagrange polynomial) fem of order `k` to the MeshFem.
Uses FEM_PK for simplexes, FEM_QK for parallelepipeds etc."""
return self.set("classical_fem", k, CVids)
def set_classical_discontinuous_fem(self, K, alpha=None, *args):
"""Synopsis: MeshFem.set_classical_discontinuous_fem(self, int K[, @tscalar alpha[, ivec CVIDX]])
Assigns a classical (Lagrange polynomial) discontinuous fem or order K.
Similar to MeshFem.classical_fem() except that
FEM_PK_DISCONTINUOUS is used. Param `alpha` the node inset,
:math:`0 \\leq alpha < 1`, where 0 implies usual dof nodes, greater values
move the nodes toward the center of gravity, and 1 means that all
degrees of freedom collapse on the center of gravity."""
return self.set("classical_discontinuous_fem", K, alpha, *args)
def set_qdim(self, Q):
"""Change the `Q` dimension of the field that is interpolated by the MeshFem.
`Q = 1` means that the MeshFem describes a scalar field, `Q = N` means
that the MeshFem describes a vector field of dimension N."""
return self.set("qdim", Q)
def reduction_matrices(self, R, E):
"""Set the reduction and extension matrices and valid their use."""
return self.set("reduction_matrices", R, E)
def reduction(self, s):
"""Set or unset the use of the reduction/extension matrices."""
return self.set("reduction", s)
def reduce_meshfem(self, RM):
"""Set reduction mesh fem
This function selects the degrees of freedom of the finite element
method by selecting a set of independent vectors of the matrix RM.
The numer of columns of RM should corresponds to the number of degrees
of fredoom of the finite element method. """
return self.set("reduce_meshfem", RM)
def set_dof_partition(self, DOFP):
"""Change the 'dof_partition' array.
`DOFP` is a vector holding a integer value for each convex of the MeshFem.
See MeshFem.dof_partition() for a description of "dof partition"."""
return self.set("dof_partition", DOFP)
def set_partial(self, DOFs, RCVs=None):
"""Can only be applied to a partial MeshFem. Change the subset of the
degrees of freedom of `mf`.
If `RCVs` is given, no FEM will be put on the convexes listed
in `RCVs`."""
return self.set("set_partial", DOFs, RCVs)
#
# GetFEM class MeshIm definition.
#
class MeshIm:
"""GetFEM MeshIm object
This object represents an integration method defined on a whole mesh (an
potentialy on its boundaries).
"""
def __init__(self, *args):
"""General constructor for MeshIm objects
* ``MIM = MeshIm('load', string fname[, Mesh m])``
Load a MeshIm from a file.
If the mesh `m` is not supplied (this kind of file does not store the
mesh), then it is read from the file and its descriptor is returned as
the second output argument.
* ``MIM = MeshIm('from string', string s[, Mesh m])``
Create a MeshIm object from its string description.
See also ``MeshIm.char()``
* ``MIM = MeshIm('clone', MeshIm mim)``
Create a copy of a MeshIm.
* ``MIM = MeshIm('levelset', MeshLevelSet mls, string where, Integ im[, Integ im_tip[, Integ im_set]])``
Build an integration method conformal to a partition defined
implicitely by a levelset.
The `where` argument define the domain of integration with respect to
the levelset, it has to be chosen among 'ALL', 'INSIDE', 'OUTSIDE' and
'BOUNDARY'.
it can be completed by a string defining the boolean operation
to define the integration domain when there is more than one levelset.
the syntax is very simple, for example if there are 3 different
levelset,
"a*b*c" is the intersection of the domains defined by each
levelset (this is the default behaviour if this function is not
called).
"a+b+c" is the union of their domains.
"c-(a+b)" is the domain of the third levelset minus the union of
the domains of the two others.
"!a" is the complementary of the domain of a (i.e. it is the
domain where a(x)>0)
The first levelset is always referred to with "a", the second
with "b", and so on.
for intance INSIDE(a*b*c)
CAUTION: this integration method will be defined only on the element
cut by the level-set. For the 'ALL', 'INSIDE' and 'OUTSIDE' options
it is mandatory to use the method ``MeshIm.set_integ()`` to define
the integration method on the remaining elements.
* ``MIM = MeshIm(Mesh m, [{Integ im|int im_degree}])``
Build a new MeshIm object.
For convenience, optional arguments (`im` or `im_degree`) can be
provided, in that case a call to ``MeshIm.integ()`` is issued
with these arguments.
"""
generic_constructor(self,'mesh_im',*args)
def __del__(self):
generic_destructor(self, destructible=True)
def get(self, *args):
return getfem('mesh_im_get',self.id, *args)
def __repr__(self):
getfem('mesh_im_get',self.id, 'display')
return ''
def set(self, *args):
return getfem('mesh_im_set',self.id, *args)
def __str__(self):
return self.char()
def integ(self, CVids=None):
"""Return a list of integration methods used by the MeshIm.
`I` is an array of all Integ objects found in the convexes
given in `CVids`. If `CV2I` was supplied as an output argument, it
contains, for each convex listed in `CVids`, the index of its
correspounding integration method in `I`.
Convexes which are not part of the mesh, or convexes which do
not have any integration method have their correspounding entry
in `CV2I` set to -1.
"""
return self.get("integ", CVids)
def convex_index(self):
"""Return the list of convexes who have a integration method.
Convexes who have the dummy IM_NONE method are not listed."""
return self.get("convex_index")
def eltm(self, em, cv, f=None):
"""Return the elementary matrix (or tensor) integrated on the convex `cv`.
**WARNING**
Be sure that the fem used for the construction of `em` is compatible
with the fem assigned to element `cv` ! This is not checked by the
function ! If the argument `f` is given, then the elementary tensor
is integrated on the face `f` of `cv` instead of the whole convex."""
return self.get("eltm", em, cv, f)
def im_nodes(self, CVids=None):
"""Return the coordinates of the integration points, with their weights.
`CVids` may be a list of convexes, or a list of convex faces, such
as returned by Mesh.region()
**WARNING**
Convexes which are not part of the mesh, or convexes which
do not have an approximate integration method don't have
their correspounding entry (this has no meaning for exact
integration methods!)."""
return self.get("im_nodes", CVids)
def save(self, filename):
"""Saves a MeshIm in a text file (and optionaly its linked mesh object)."""
return self.get("save", filename)
def char(self):
"""Output a string description of the MeshIm.
By default, it does not include the description of the linked
Mesh object."""
return self.get("char")
def display(self):
"""displays a short summary for a MeshIm object."""
return self.get("display")
def linked_mesh(self):
"""Returns a reference to the Mesh object linked to `mim`."""
return self.get("linked_mesh")
def memsize(self):
"""Return the amount of memory (in bytes) used by the MeshIm object.
The result does not take into account the linked Mesh object."""
return self.get("memsize")
def set_integ(self, *args):
"""Synopsis: MeshIm.set_integ(self,{Integ im|int im_degree}[, ivec CVids])
Set the integration method.
Assign an integration method to all convexes whose #ids are
listed in `CVids`. If `CVids` is not given, the integration is
assigned to all convexes. It is possible to assign a specific
integration method with an integration method handle `im` obtained
via Integ('IM_SOMETHING'), or to let getfem choose a suitable
integration method with `im_degree` (choosen such that polynomials
of :math:`\\text{degree} \\leq \\text{im\\_degree}` are exactly integrated.
If `im_degree=-1`, then the dummy integration method IM_NONE will
be used.)"""
return self.set("integ", *args)
def adapt(self):
"""For a MeshIm levelset object only. Adapt the integration methods to a
change of the levelset function."""
return self.set("adapt")
#
# GetFEM class MeshLevelSet definition.
#
class MeshLevelSet:
"""GetFEM MeshLevelSet object
General constructor for mesh_levelset objects. The role of this object is
to provide a mesh cut by a certain number of level_set. This object is
used to build conformal integration method (object mim and enriched finite
element methods (Xfem)).
"""
def __init__(self, *args):
"""General constructor for MeshLevelSet objects
* ``MLS = MeshLevelSet(Mesh m)``
Build a new MeshLevelSet object from a Mesh and returns its handle.
"""
generic_constructor(self,'mesh_levelset',*args)
def __del__(self):
generic_destructor(self, destructible=True)
def get(self, *args):
return getfem('mesh_levelset_get',self.id, *args)
def __repr__(self):
getfem('mesh_levelset_get',self.id, 'display')
return ''
def set(self, *args):
return getfem('mesh_levelset_set',self.id, *args)
def __str__(self):
return self.char()
def cut_mesh(self):
"""Return a Mesh cut by the linked LevelSet's."""
return self.get("cut_mesh")
def linked_mesh(self):
"""Return a reference to the linked Mesh."""
return self.get("linked_mesh")
def nb_ls(self):
"""Return the number of linked LevelSet's."""
return self.get("nb_ls")
def levelsets(self):
"""Return a list of references to the linked LevelSet's."""
return self.get("levelsets")
def crack_tip_convexes(self):
"""Return the list of convex #id's of the linked Mesh on
which have a tip of any linked LevelSet's."""
return self.get("crack_tip_convexes")
def memsize(self):
"""Return the amount of memory (in bytes) used by the MeshLevelSet."""
return self.get("memsize")
def char(self):
"""Output a (unique) string representation of the MeshLevelSetn.
This can be used to perform comparisons between two
different MeshLevelSet objects.
This function is to be completed.
"""
return self.get("char")
def display(self):
"""displays a short summary for a MeshLevelSet object."""
return self.get("display")
def add(self, ls):
"""Add a link to the LevelSet `ls`.
Only a reference is kept, no copy is done. In order to indicate
that the linked Mesh is cut by a LevelSet one has to call this
method, where `ls` is an LevelSet object. An arbitrary number of
LevelSet can be added.
**WARNING**
The Mesh of `ls` and the linked Mesh must be the same."""
return self.set("add", ls)
def sup(self, ls):
"""Remove a link to the LevelSet `ls`."""
return self.set("sup", ls)
def adapt(self):
"""Do all the work (cut the convexes with the levelsets).
To initialice the MeshLevelSet object or to actualize it when the
value of any levelset function is modified, one has to call
this method."""
return self.set("adapt")
#
# GetFEM class MesherObject definition.
#
class MesherObject:
"""GetFEM MesherObject object
This object represents a geometric object to be meshed by the (very)
experimental meshing procedure of Getfem.
"""
def __init__(self, *args):
"""General constructor for MesherObject objects
* ``MF = MesherObject('ball', vec center, scalar radius)``
Represents a ball of corresponding center and radius.
* ``MF = MesherObject('half space', vec origin, vec normal_vector)``
Represents an half space delimited by the plane which contains the
origin and normal to `normal_vector`. The selected part is the part
in the direction of the normal vector. This allows to cut a geometry
with a plane for instance to build a polygon or a polyhedron.
* ``MF = MesherObject('cylinder', vec origin, vec n, scalar length, scalar radius)``
Represents a cylinder (in any dimension) of a certain radius whose axis is determined by the origin, a vector `n` and a certain length.
* ``MF = MesherObject('cone', vec origin, vec n, scalar length, scalar half_angle)``
Represents a cone (in any dimension) of a certain half-angle (in radians) whose axis is determined by the origin, a vector `n` and a certain length.
* ``MF = MesherObject('torus', scalar R, scalar r)``
Represents a torus in 3d of axis along the z axis with a great radius
equal to `R` and small radius equal to `r`. For the moment, the
possibility to change the axis is not given.
* ``MF = MesherObject('rectangle', vec rmin, vec rmax)``
Represents a rectangle (or parallelepiped in 3D) parallel to the axes.
* ``MF = MesherObject('intersect', MesherObject object1 , MesherObject object2, ...)``
Intersection of several objects.
* ``MF = MesherObject('union', MesherObject object1 , MesherObject object2, ...)``
Union of several objects.
* ``MF = MesherObject('set minus', MesherObject object1 , MesherObject object2)``
Geometric object being object1 minus object2.
"""
generic_constructor(self,'mesher_object',*args)
def __del__(self):
generic_destructor(self, destructible=False)
def get(self, *args):
return getfem('mesher_object_get',self.id, *args)
def __repr__(self):
getfem('mesher_object_get',self.id, 'display')
return ''
def __str__(self):
return self.char()
def char(self):
"""Output a (unique) string representation of the MesherObject.
This can be used to perform comparisons between two
different MesherObject objects.
This function is to be completed.
"""
return self.get("char")
def display(self):
"""displays a short summary for a MesherObject object."""
return self.get("display")
#
# GetFEM class Model definition.
#
class Model:
"""GetFEM Model object
Model variables store the variables and the state data and the
description of a model. This includes the global tangent matrix, the right
hand side and the constraints. There are two kinds of models, the `real`
and the `complex` models.
Model object is the evolution for getfem++ 4.0 of the MdState object.
"""
def __init__(self, *args):
"""General constructor for Model objects
* ``MD = Model('real')``
Build a model for real unknowns.
* ``MD = Model('complex')``
Build a model for complex unknowns.
"""
generic_constructor(self,'model',*args)
def __del__(self):
generic_destructor(self, destructible=True)
def get(self, *args):
return getfem('model_get',self.id, *args)
def __repr__(self):
getfem('model_get',self.id, 'display')
return ''
def set(self, *args):
return getfem('model_set',self.id, *args)
def __str__(self):
return self.char()
def is_complex(self):
"""Return 0 is the model is real, 1 if it is complex."""
return self.get("is_complex")
def nbdof(self):
"""Return the total number of degrees of freedom of the model."""
return self.get("nbdof")
def tangent_matrix(self):
"""Return the tangent matrix stored in the model ."""
return self.get("tangent_matrix")
def rhs(self):
"""Return the right hand side of the tangent problem."""
return self.get("rhs")
def brick_term_rhs(self, ind_brick, ind_term=None, sym=None, ind_iter=None):
"""Gives the access to the part of the right hand side of a term
of a particular nonlinear brick. Does not account of the eventual
time dispatcher. An assembly of the rhs has to be done first.
`ind_brick` is the brick index. `ind_term` is the index of the
term inside the brick (default value : 0).
`sym` is to access to the second right hand side of for symmetric
terms acting on two different variables (default is 0).
`ind_iter` is the iteration number when time dispatchers are
used (default is 0).
"""
return self.get("brick_term_rhs", ind_brick, ind_term, sym, ind_iter)
def memsize(self):
"""Return a rough approximation of the amount of memory (in bytes) used by
the model."""
return self.get("memsize")
def variable_list(self):
"""print to the output the list of variables and constants of the model."""
return self.get("variable_list")
def brick_list(self):
"""print to the output the list of bricks of the model."""
return self.get("brick_list")
def variable(self, name, niter=None):
"""Gives the value of a variable or data."""
return self.get("variable", name, niter)
def interpolation(self, expr, mf, region=None):
"""Interpolate a certain expression relatively to the mesh_fem `mf`.
The expression have to be a valid expression in the sense of the
high-level generic assembly with authorised references to the variables
and data of the model. """
return self.get("interpolation", expr, mf, region)
def mesh_fem_of_variable(self, name):
"""Gives access to the `mesh_fem` of a variable or data."""
return self.get("mesh_fem_of_variable", name)
def mult_varname_Dirichlet(self, ind_brick):
"""Gives the name of the multiplier variable for a Dirichlet brick.
If the brick is not a Dirichlet condition with multiplier brick,
this function has an undefined behavior"""
return self.get("mult_varname_Dirichlet", ind_brick)
def interval_of_variable(self, varname):
"""Gives the interval of the variable `varname` in the linear system of
the model."""
return self.get("interval_of_variable", varname)
def from_variables(self):
"""Return the vector of all the degrees of freedom of the model consisting
of the concatenation of the variables of the model (useful
to solve your problem with you own solver). """
return self.get("from_variables")
def assembly(self, option=None):
"""Assembly of the tangent system taking into account the terms
from all bricks. `option`, if specified, should be 'build_all',
'build_rhs', 'build_matrix' or 'pseudo_potential' (in that case,
the pseudo_potential is returned).
The default is to build the whole
tangent linear system (matrix and rhs). This function is useful
to solve your problem with you own solver. """
return self.get("assembly", option)
def solve(self, *args):
"""Synopsis: (nbit, converged) = Model.solve(self[, ...])
Run the standard getfem solver.
Note that you should be able to use your own solver if you want
(it is possible to obtain the tangent matrix and its right hand
side with the Model.tangent_matrix() etc.).
Various options can be specified:
- 'noisy' or 'very_noisy'
the solver will display some information showing the progress
(residual values etc.).
- 'max_iter', int NIT
set the maximum iterations numbers.
- 'max_res', @float RES
set the target residual value.
- 'diverged_res', @float RES
set the threshold value of the residual beyond which the iterative
method is considered to diverge (default is 1e200).
- 'lsolver', string SOLVER_NAME
select explicitely the solver used for the linear systems (the
default value is 'auto', which lets getfem choose itself).
Possible values are 'superlu', 'mumps' (if supported),
'cg/ildlt', 'gmres/ilu' and 'gmres/ilut'.
- 'lsearch', string LINE_SEARCH_NAME
select explicitely the line search method used for the linear systems (the
default value is 'default').
Possible values are 'simplest', 'systematic', 'quadratic' or 'basic'.
- 'with pseudo potential'
for nonlinear problems, the criterion of the line search will
be a pseudo potential instead of the residual. Still experimental since
not all bricks define a pseudo potential.
Return the number of iterations, if an iterative method is used.
Note that it is possible to disable some variables
(see Model.disable_variable() ) in order to
solve the problem only with respect to a subset of variables (the
disabled variables are the considered as data) for instance to
replace the global Newton strategy with a fixed point one."""
return self.get("solve", *args)
def test_tangent_matrix(self, EPS=None, *args):
"""Synopsis: Model.test_tangent_matrix(self[, scalar EPS[, int NB[, scalar scale]]])
Test the consistency of the tangent matrix in some random positions
and random directions (useful to test newly created bricks).
`EPS` is the value of the small parameter for the finite difference
computation of the derivative is the random direction (default is 1E-6).
`NN` is the number of tests (default is 100). `scale` is a parameter
for the random position (default is 1, 0 is an acceptable value) around
the current position.
Each dof of the random position is chosen in the range
[current-scale, current+scale].
"""
return self.get("test_tangent_matrix", EPS, *args)
def test_tangent_matrix_term(self, varname1, varname2, EPS=None, *args):
"""Synopsis: Model.test_tangent_matrix_term(self, string varname1, string varname2[, scalar EPS[, int NB[, scalar scale]]])
Test the consistency of a part of the tangent matrix in some
random positions and random directions
(useful to test newly created bricks).
The increment is only made on variable `varname2` and tested on the
part of the residual corresponding to `varname1`. This means that
only the term (`varname1`, `varname2`) of the tangent matrix is tested.
`EPS` is the value of the small parameter for the finite difference
computation of the derivative is the random direction (default is 1E-6).
`NN` is the number of tests (default is 100). `scale` is a parameter
for the random position (default is 1, 0 is an acceptable value)
around the current position.
Each dof of the random position is chosen in the range
[current-scale, current+scale].
"""
return self.get("test_tangent_matrix_term", varname1, varname2, EPS, *args)
def compute_isotropic_linearized_Von_Mises_or_Tresca(self, varname, dataname_lambda, dataname_mu, mf_vm, version=None):
"""Compute the Von-Mises stress or the Tresca stress of a field (only
valid for isotropic linearized elasticity in 3D). `version` should
be 'Von_Mises' or 'Tresca' ('Von_Mises' is the default). """
return self.get("compute_isotropic_linearized_Von_Mises_or_Tresca", varname, dataname_lambda, dataname_mu, mf_vm, version)
def compute_Von_Mises_or_Tresca(self, varname, lawname, dataname, mf_vm, version=None):
"""Compute on `mf_vm` the Von-Mises stress or the Tresca stress of a field
for nonlinear elasticity in 3D. `lawname` is the constitutive law which
could be 'SaintVenant Kirchhoff', 'Mooney Rivlin', 'neo Hookean' or
'Ciarlet Geymonat'.
`dataname` is a vector of parameters for the constitutive law. Its length
depends on the law. It could be a short vector of constant values or a
vector field described on a finite element method for variable coefficients.
`version` should be 'Von_Mises' or 'Tresca' ('Von_Mises' is the default). """
return self.get("compute_Von_Mises_or_Tresca", varname, lawname, dataname, mf_vm, version)
def finite_strain_elasticity_Von_Mises(self, varname, lawname, params, mf_vm, region=None):
"""Compute on `mf_vm` the Von-Mises stress of a field `varname`
for nonlinear elasticity in 3D. `lawname` is the constitutive law which
should be a valid name. `params` are the parameters law. It could be
a short vector of constant values or may depend on data or variables
of the model.
Uses the high-level generic assembly.
"""
return self.get("finite_strain_elasticity_Von_Mises", varname, lawname, params, mf_vm, region)
def compute_second_Piola_Kirchhoff_tensor(self, varname, lawname, dataname, mf_sigma):
"""Compute on `mf_sigma` the second Piola Kirchhoff stress tensor of a field
for nonlinear elasticity in 3D. `lawname` is the constitutive law which
could be 'SaintVenant Kirchhoff', 'Mooney Rivlin', 'neo Hookean' or
'Ciarlet Geymonat'.
`dataname` is a vector of parameters for the constitutive law. Its length
depends on the law. It could be a short vector of constant values or a
vector field described on a finite element method for variable
coefficients.
"""
return self.get("compute_second_Piola_Kirchhoff_tensor", varname, lawname, dataname, mf_sigma)
def compute_elastoplasticity_Von_Mises_or_Tresca(self, datasigma, mf_vm, version=None):
"""Compute on `mf_vm` the Von-Mises or the Tresca stress of a field for plasticity and return it into the vector V.
`datasigma` is a vector which contains the stress constraints values supported by the mesh.
`version` should be 'Von_Mises' or 'Tresca' ('Von_Mises' is the default)."""
return self.get("compute_elastoplasticity_Von_Mises_or_Tresca", datasigma, mf_vm, version)
def elastoplasticity_next_iter(self, mim, varname, projname, datalambda, datamu, datathreshold, datasigma):
"""Compute and save the stress constraints sigma for other hypothetical iterations.
'mim' is the integration method to use for the computation.
'varname' is the main variable of the problem.
'projname' is the type of projection to use. For the moment it could only be 'Von Mises' or 'VM'.
'datalambda' and 'datamu' are the Lame coefficients of the material.
'datasigma' is a vector which will contains the new stress constraints values."""
return self.get("elastoplasticity_next_iter", mim, varname, projname, datalambda, datamu, datathreshold, datasigma)
def compute_plastic_part(self, mim, mf_pl, varname, projname, datalambda, datamu, datathreshold, datasigma):
"""Compute on `mf_pl` the plastic part and return it into the vector V.
`datasigma` is a vector which contains the stress constraints values supported by the mesh."""
return self.get("compute_plastic_part", mim, mf_pl, varname, projname, datalambda, datamu, datathreshold, datasigma)
def matrix_term(self, ind_brick, ind_term):
"""Gives the matrix term ind_term of the brick ind_brick if it exists
"""
return self.get("matrix_term", ind_brick, ind_term)
def char(self):
"""Output a (unique) string representation of the Model.
This can be used to perform comparisons between two
different Model objects.
This function is to be completed.
"""
return self.get("char")
def display(self):
"""displays a short summary for a Model object."""
return self.get("display")
def clear(self):
"""Clear the model."""
return self.set("clear")
def add_fem_variable(self, name, mf, niter=None):
"""Add a variable to the model linked to a MeshFem. `name` is the variable
name and `niter` is the optional number of version of the data stored,
for time integration schemes."""
return self.set("add_fem_variable", name, mf, niter)
def add_filtered_fem_variable(self, name, mf, region, niter=None):
"""Add a variable to the model linked to a MeshFem. The variable is filtered
in the sense that only the dof on the region are considered.
`name` is the variable name and `niter` is the optional number of
version of the data stored, for time integration schemes."""
return self.set("add_filtered_fem_variable", name, mf, region, niter)
def add_variable(self, name, size, niter=None):
"""Add a variable to the model of constant size. `name` is the variable
name and `niter` is the optional number of version of the data stored,
for time integration schemes. """
return self.set("add_variable", name, size, niter)
def delete_variable(self, name):
"""Delete a variable or a data from the model."""
return self.set("delete_variable", name)
def resize_variable(self, name, size):
"""Resize a constant size variable of the model. `name` is the variable
name. """
return self.set("resize_variable", name, size)
def add_multiplier(self, name, mf, primalname, mim=None, region=None, *args):
"""Synopsis: Model.add_multiplier(self, string name, MeshFem mf, string primalname[, MeshIm mim, int region][, int niter])
Add a particular variable linked to a fem being a multiplier with
respect to a primal variable. The dof will be filtered with the
``gmm::range_basis`` function applied on the terms of the model
which link the multiplier and the primal variable. This in order to
retain only linearly independant constraints on the primal variable.
Optimized for boundary multipliers. `niter` is the optional number
of version of the data stored, for time integration schemes. """
return self.set("add_multiplier", name, mf, primalname, mim, region, *args)
def add_fem_data(self, name, mf, qdim=None, *args):
"""Synopsis: Model.add_fem_data(self, string name, MeshFem mf[, int qdim[, int niter]])
Add a data to the model linked to a MeshFem. `name` is the data name,
`qdim` is the optional dimension of the data over the MeshFem and
`niter` is the optional number of version of the data stored,
for time integration schemes. """
return self.set("add_fem_data", name, mf, qdim, *args)
def add_initialized_fem_data(self, name, mf, V):
"""Add a data to the model linked to a MeshFem. `name` is the data name.
The data is initiakized with `V`. The data can be a scalar or vector
field."""
return self.set("add_initialized_fem_data", name, mf, V)
def add_data(self, name, size, niter=None):
"""Add a data to the model of constant size. `name` is the data name
and `niter` is the optional number of version of the data stored,
for time integration schemes. """
return self.set("add_data", name, size, niter)
def add_initialized_data(self, name, V):
"""Add a fixed size data to the model linked to a MeshFem.
`name` is the data name and `V` is the value of the data."""
return self.set("add_initialized_data", name, V)
def set_variable(self, name, V, niter=None):
"""Set the value of a variable or data. `name` is the data name
and `niter` is the optional number of version of the data stored,
for time integration schemes."""
return self.set("variable", name, V, niter)
def to_variables(self, V):
"""Set the value of the variables of the model with the vector `V`.
Typically, the vector `V` results of the solve of the tangent
linear system (useful to solve your problem with you own solver)."""
return self.set("to_variables", V)
def delete_brick(self, ind_brick):
"""Delete a variable or a data from the model."""
return self.set("delete_brick", ind_brick)
def add_linear_generic_assembly_brick(self, mim, expression, region=None, *args):
"""Synopsis: ind = Model.add_linear_generic_assembly_brick(self, MeshIm mim, string expression[, int region[, int is_symmetric[, int is_coercive]]])
Adds a matrix term given by the assembly string `expr` which will
be assembled in region `region` and with the integration method `mim`.
Only the matrix term will be taken into account, assuming that it is
linear.
The advantage of declaring a term linear instead of nonlinear is that
it will be assembled only once and no assembly is necessary for the
residual.
Take care that if the expression contains some variables and if the
expression is a potential or of first order (i.e. describe the weak
form, not the derivative of the weak form), the expression will be
derivated with respect to all variables.
You can specify if the term is symmetric, coercive or not.
If you are not sure, the better is to declare the term not symmetric
and not coercive. But some solvers (conjugate gradient for instance)
are not allowed for non-coercive problems.
`brickname` is an otpional name for the brick."""
return self.set("add_linear_generic_assembly_brick", mim, expression, region, *args)
def add_nonlinear_generic_assembly_brick(self, mim, expression, region=None, *args):
"""Synopsis: ind = Model.add_nonlinear_generic_assembly_brick(self, MeshIm mim, string expression[, int region[, int is_symmetric[, int is_coercive]]])
Adds a nonlinear term given by the assembly string `expr` which will
be assembled in region `region` and with the integration method `mim`.
The expression can describe a potential or a weak form. Second order
terms (i.e. containing second order test functions, Test2) are not
allowed.
You can specify if the term is symmetric, coercive or not.
If you are not sure, the better is to declare the term not symmetric
and not coercive. But some solvers (conjugate gradient for instance)
are not allowed for non-coercive problems.
`brickname` is an otpional name for the brick."""
return self.set("add_nonlinear_generic_assembly_brick", mim, expression, region, *args)
def add_source_term_generic_assembly_brick(self, mim, expression, region=None):
"""Adds a source term given by the assembly string `expr` which will
be assembled in region `region` and with the integration method `mim`.
Only the residual term will be taken into account.
Take care that if the expression contains some variables and if the
expression is a potential, the expression will be
derivated with respect to all variables.
`brickname` is an otpional name for the brick."""
return self.set("add_source_term_generic_assembly_brick", mim, expression, region)
def add_Laplacian_brick(self, mim, varname, region=None):
"""Add a Laplacian term to the model relatively to the variable `varname`
(in fact with a minus : :math:`-\\text{div}(\\nabla u)`).
If this is a vector valued variable, the Laplacian term is added
componentwise. `region` is an optional mesh region on which the term
is added. If it is not specified, it is added on the whole mesh. Return
the brick index in the model."""
return self.set("add_Laplacian_brick", mim, varname, region)
def add_generic_elliptic_brick(self, mim, varname, dataname, region=None):
"""Add a generic elliptic term to the model relatively to the variable `varname`.
The shape of the elliptic term depends both on the variable and the data.
This corresponds to a term
:math:`-\\text{div}(a\\nabla u)`
where :math:`a` is the data and :math:`u` the variable. The data can be a scalar,
a matrix or an order four tensor. The variable can be vector valued or
not. If the data is a scalar or a matrix and the variable is vector
valued then the term is added componentwise. An order four tensor data
is allowed for vector valued variable only. The data can be constant or
describbed on a fem. Of course, when the data is a tensor describe on a
finite element method (a tensor field) the data can be a huge vector.
The components of the matrix/tensor have to be stored with the fortran
order (columnwise) in the data vector (compatibility with blas). The
symmetry of the given matrix/tensor is not verified (but assumed). If
this is a vector valued variable, the elliptic term is added
componentwise. `region` is an optional mesh region on which the term is
added. If it is not specified, it is added on the whole mesh. Return the
brick index in the model."""
return self.set("add_generic_elliptic_brick", mim, varname, dataname, region)
def add_source_term_brick(self, mim, varname, dataname, region=None, *args):
"""Synopsis: ind = Model.add_source_term_brick(self, MeshIm mim, string varname, string dataname[, int region[, string directdataname]])
Add a source term to the model relatively to the variable `varname`.
The source term is represented by the data `dataname` which could be
constant or described on a fem. `region` is an optional mesh region
on which the term is added. An additional optional data `directdataname`
can be provided. The corresponding data vector will be directly added
to the right hand side without assembly. Note that when region is a
boundary, this brick allows to prescribe a nonzero Neumann boundary
condition. Return the brick index in the model."""
return self.set("add_source_term_brick", mim, varname, dataname, region, *args)
def add_normal_source_term_brick(self, mim, varname, dataname, region):
"""Add a source term on the variable `varname` on a boundary `region`.
This region should be a boundary. The source term is represented by the
data `dataname` which could be constant or described on a fem. A scalar
product with the outward normal unit vector to the boundary is performed.
The main aim of this brick is to represent a Neumann condition with a
vector data without performing the scalar product with the normal as a
pre-processing. Return the brick index in the model."""
return self.set("add_normal_source_term_brick", mim, varname, dataname, region)
def add_Dirichlet_condition_with_simplification(self, varname, region, dataname=None):
"""Adds a (simple) Dirichlet condition on the variable `varname` and
the mesh region `region`. The Dirichlet condition is prescribed by
a simple post-treatment of the final linear system (tangent system
for nonlinear problems) consisting of modifying the lines corresponding
to the degree of freedom of the variable on `region` (0 outside the
diagonal, 1 on the diagonal of the matrix and the expected value on
the right hand side).
The symmetry of the linear system is kept if all other bricks are
symmetric.
This brick is to be reserved for simple Dirichlet conditions (only dof
declared on the correspodning boundary are prescribed). The application
of this brick on reduced dof may be problematic. Intrinsic vectorial
finite element method are not supported.
`dataname` is the optional right hand side of the Dirichlet condition.
It could be constant (but in that case, it can only be applied to
Lagrange f.e.m.) or (important) described on the same finite
element method as `varname`.
Returns the brick index in the model. """
return self.set("add_Dirichlet_condition_with_simplification", varname, region, dataname)
def add_Dirichlet_condition_with_multipliers(self, mim, varname, mult_description, region, dataname=None):
"""Add a Dirichlet condition on the variable `varname` and the mesh
region `region`. This region should be a boundary. The Dirichlet
condition is prescribed with a multiplier variable described by
`mult_description`. If `mult_description` is a string this is assumed
to be the variable name corresponding to the multiplier (which should be
first declared as a multiplier variable on the mesh region in the model).
If it is a finite element method (mesh_fem object) then a multiplier
variable will be added to the model and build on this finite element
method (it will be restricted to the mesh region `region` and eventually
some conflicting dofs with some other multiplier variables will be
suppressed). If it is an integer, then a multiplier variable will be
added to the model and build on a classical finite element of degree
that integer. `dataname` is the optional right hand side of the
Dirichlet condition. It could be constant or described on a fem; scalar
or vector valued, depending on the variable on which the Dirichlet
condition is prescribed. Return the brick index in the model."""
return self.set("add_Dirichlet_condition_with_multipliers", mim, varname, mult_description, region, dataname)
def add_Dirichlet_condition_with_Nitsche_method(self, mim, varname, gamma0name, region, theta=None, *args):
"""Synopsis: ind = Model.add_Dirichlet_condition_with_Nitsche_method(self, MeshIm mim, string varname, string gamma0name, int region[, scalar theta][, string dataname])
Add a Dirichlet condition on the variable `varname` and the mesh
region `region`. This region should be a boundary. The Dirichlet
condition is prescribed with Nitsche's method. `dataname` is the optional
right hand side of the Dirichlet condition. It could be constant or
described on a fem; scalar or vector valued, depending on the variable
on which the Dirichlet condition is prescribed. `gamma0name` is the
Nitsche's method parameter. `theta` is a scalar value which can be
positive or negative. `theta = 1` corresponds to the standard symmetric
method which is conditionnaly coercive for `gamma0` small.
`theta = -1` corresponds to the skew-symmetric method which is
inconditionnaly coercive. `theta = 0` is the simplest method
for which the second derivative of the Neumann term is not necessary.
CAUTION: This brick has to be added in the model after all the bricks
corresponding to partial differential terms having a Neumann term.
Moreover, This brick can only be applied to bricks declaring their
Neumann terms. Returns the brick index in the model.
"""
return self.set("add_Dirichlet_condition_with_Nitsche_method", mim, varname, gamma0name, region, theta, *args)
def add_Dirichlet_condition_with_penalization(self, mim, varname, coeff, region, dataname=None, mf_mult=None):
"""Add a Dirichlet condition on the variable `varname` and the mesh
region `region`. This region should be a boundary. The Dirichlet
condition is prescribed with penalization. The penalization coefficient
is initially `coeff` and will be added to the data of the model.
`dataname` is the optional right hand side of the Dirichlet condition.
It could be constant or described on a fem; scalar or vector valued,
depending on the variable on which the Dirichlet condition is prescribed.
`mf_mult` is an optional parameter which allows to weaken the
Dirichlet condition specifying a multiplier space.
Return the brick index in the model."""
return self.set("add_Dirichlet_condition_with_penalization", mim, varname, coeff, region, dataname, mf_mult)
def add_normal_Dirichlet_condition_with_multipliers(self, mim, varname, mult_description, region, dataname=None):
"""Add a Dirichlet condition to the normal component of the vector
or tensor) valued variable `varname` and the mesh
region `region`. This region should be a boundary. The Dirichlet
condition is prescribed with a multiplier variable described by
`mult_description`. If `mult_description` is a string this is assumed
to be the variable name corresponding to the multiplier (which should be
first declared as a multiplier variable on the mesh region in the model).
If it is a finite element method (mesh_fem object) then a multiplier
variable will be added to the model and build on this finite element
method (it will be restricted to the mesh region `region` and eventually
some conflicting dofs with some other multiplier variables will be
suppressed). If it is an integer, then a multiplier variable will be
added to the model and build on a classical finite element of degree
that integer. `dataname` is the optional right hand side of the
Dirichlet condition. It could be constant or described on a fem; scalar
or vector valued, depending on the variable on which the Dirichlet
condition is prescribed (scalar if the variable
is vector valued, vector if the variable is tensor valued).
Returns the brick index in the model."""
return self.set("add_normal_Dirichlet_condition_with_multipliers", mim, varname, mult_description, region, dataname)
def add_normal_Dirichlet_condition_with_penalization(self, mim, varname, coeff, region, dataname=None, mf_mult=None):
"""Add a Dirichlet condition to the normal component of the vector
(or tensor) valued variable `varname` and the mesh
region `region`. This region should be a boundary. The Dirichlet
condition is prescribed with penalization. The penalization coefficient
is initially `coeff` and will be added to the data of the model.
`dataname` is the optional right hand side of the Dirichlet condition.
It could be constant or described on a fem; scalar or vector valued,
depending on the variable on which the Dirichlet condition is prescribed
(scalar if the variable
is vector valued, vector if the variable is tensor valued).
`mf_mult` is an optional parameter which allows to weaken the
Dirichlet condition specifying a multiplier space.
Returns the brick index in the model."""
return self.set("add_normal_Dirichlet_condition_with_penalization", mim, varname, coeff, region, dataname, mf_mult)
def add_normal_Dirichlet_condition_with_Nitsche_method(self, mim, varname, gamma0name, region, theta=None, *args):
"""Synopsis: ind = Model.add_normal_Dirichlet_condition_with_Nitsche_method(self, MeshIm mim, string varname, string gamma0name, int region[, scalar theta][, string dataname])
Add a Dirichlet condition to the normal component of the vector
(or tensor) valued variable `varname` and the mesh region `region`.
This region should be a boundary. The Dirichlet
condition is prescribed with Nitsche's method. `dataname` is the optional
right hand side of the Dirichlet condition. It could be constant or
described on a fem. `gamma0name` is the
Nitsche's method parameter. `theta` is a scalar value which can be
positive or negative. `theta = 1` corresponds to the standard symmetric
method which is conditionnaly coercive for `gamma0` small.
`theta = -1` corresponds to the skew-symmetric method which is
inconditionnaly coercive. `theta = 0` is the simplest method
for which the second derivative of the Neumann term is not necessary
even for nonlinear problems.
CAUTION: This brick has to be added in the model after all the bricks
corresponding to partial differential terms having a Neumann term.
Moreover, This brick can only be applied to bricks declaring their
Neumann terms. Returns the brick index in the model.
(This brick is not fully tested)
"""
return self.set("add_normal_Dirichlet_condition_with_Nitsche_method", mim, varname, gamma0name, region, theta, *args)
def add_generalized_Dirichlet_condition_with_multipliers(self, mim, varname, mult_description, region, dataname, Hname):
"""Add a Dirichlet condition on the variable `varname` and the mesh
region `region`. This version is for vector field.
It prescribes a condition :math:`Hu = r`
where `H` is a matrix field. The region should be a boundary. The Dirichlet
condition is prescribed with a multiplier variable described by
`mult_description`. If `mult_description` is a string this is assumed
to be the variable name corresponding to the multiplier (which should be
first declared as a multiplier variable on the mesh region in the model).
If it is a finite element method (mesh_fem object) then a multiplier
variable will be added to the model and build on this finite element
method (it will be restricted to the mesh region `region` and eventually
some conflicting dofs with some other multiplier variables will be
suppressed). If it is an integer, then a multiplier variable will be
added to the model and build on a classical finite element of degree
that integer. `dataname` is the right hand side of the
Dirichlet condition. It could be constant or described on a fem; scalar
or vector valued, depending on the variable on which the Dirichlet
condition is prescribed. `Hname` is the data
corresponding to the matrix field `H`.
Returns the brick index in the model."""
return self.set("add_generalized_Dirichlet_condition_with_multipliers", mim, varname, mult_description, region, dataname, Hname)
def add_generalized_Dirichlet_condition_with_penalization(self, mim, varname, coeff, region, dataname, Hname, mf_mult=None):
"""Add a Dirichlet condition on the variable `varname` and the mesh
region `region`. This version is for vector field.
It prescribes a condition :math:`Hu = r`
where `H` is a matrix field.
The region should be a boundary. The Dirichlet
condition is prescribed with penalization. The penalization coefficient
is intially `coeff` and will be added to the data of the model.
`dataname` is the right hand side of the Dirichlet condition.
It could be constant or described on a fem; scalar or vector valued,
depending on the variable on which the Dirichlet condition is prescribed.
`Hname` is the data
corresponding to the matrix field `H`. It has to be a constant matrix
or described on a scalar fem.
`mf_mult` is an optional parameter which allows to weaken the
Dirichlet condition specifying a multiplier space.
Return the brick index in the model."""
return self.set("add_generalized_Dirichlet_condition_with_penalization", mim, varname, coeff, region, dataname, Hname, mf_mult)
def add_generalized_Dirichlet_condition_with_Nitsche_method(self, mim, varname, gamma0name, region, theta=None):
"""Add a Dirichlet condition on the variable `varname` and the mesh
region `region`.
This version is for vector field. It prescribes a condition
@f$ Hu = r @f$ where `H` is a matrix field.
CAUTION : the matrix H should have all eigenvalues equal to 1 or 0.
The region should be a
boundary. This region should be a boundary. The Dirichlet
condition is prescribed with Nitsche's method. `dataname` is the optional
right hand side of the Dirichlet condition. It could be constant or
described on a fem. `gamma0name` is the
Nitsche's method parameter. `theta` is a scalar value which can be
positive or negative. `theta = 1` corresponds to the standard symmetric
method which is conditionnaly coercive for `gamma0` small.
`theta = -1` corresponds to the skew-symmetric method which is
inconditionnaly coercive. `theta = 0` is the simplest method
for which the second derivative of the Neumann term is not necessary
even for nonlinear problems. `Hname' is the data
corresponding to the matrix field `H`. It has to be a constant matrix
or described on a scalar fem.
CAUTION: This brick has to be added in the model after all the bricks
corresponding to partial differential terms having a Neumann term.
Moreover, This brick can only be applied to bricks declaring their
Neumann terms. Returns the brick index in the model.
(This brick is not fully tested)
"""
return self.set("add_generalized_Dirichlet_condition_with_Nitsche_method", mim, varname, gamma0name, region, theta)
def add_pointwise_constraints_with_multipliers(self, varname, dataname_pt, dataname_unitv=None, *args):
"""Synopsis: ind = Model.add_pointwise_constraints_with_multipliers(self, string varname, string dataname_pt[, string dataname_unitv] [, string dataname_val])
Add some pointwise constraints on the variable `varname` using
multiplier. The multiplier variable is automatically added to the model.
The conditions are prescribed on a set of points given in the data
`dataname_pt` whose dimension is the number of points times the dimension
of the mesh.
If the variable represents a vector field, one has to give the data
`dataname_unitv` which represents a vector of dimension the number of
points times the dimension of the vector field which should store some
unit vectors. In that case the prescribed constraint is the scalar
product of the variable at the corresponding point with the corresponding
unit vector.
The optional data `dataname_val` is the vector of values to be prescribed
at the different points.
This brick is specifically designed to kill rigid displacement
in a Neumann problem.
Returns the brick index in the model."""
return self.set("add_pointwise_constraints_with_multipliers", varname, dataname_pt, dataname_unitv, *args)
def add_pointwise_constraints_with_given_multipliers(self, varname, multname, dataname_pt, dataname_unitv=None, *args):
"""Synopsis: ind = Model.add_pointwise_constraints_with_given_multipliers(self, string varname, string multname, string dataname_pt[, string dataname_unitv] [, string dataname_val])
Add some pointwise constraints on the variable `varname` using a given
multiplier `multname`.
The conditions are prescribed on a set of points given in the data
`dataname_pt` whose dimension is the number of points times the dimension
of the mesh.
The multiplier variable should be a fixed size variable of size the
number of points.
If the variable represents a vector field, one has to give the data
`dataname_unitv` which represents a vector of dimension the number of
points times the dimension of the vector field which should store some
unit vectors. In that case the prescribed constraint is the scalar
product of the variable at the corresponding point with the corresponding
unit vector.
The optional data `dataname_val` is the vector of values to be prescribed
at the different points.
This brick is specifically designed to kill rigid displacement
in a Neumann problem.
Returns the brick index in the model."""
return self.set("add_pointwise_constraints_with_given_multipliers", varname, multname, dataname_pt, dataname_unitv, *args)
def add_pointwise_constraints_with_penalization(self, varname, coeff, dataname_pt, dataname_unitv=None, *args):
"""Synopsis: ind = Model.add_pointwise_constraints_with_penalization(self, string varname, scalar coeff, string dataname_pt[, string dataname_unitv] [, string dataname_val])
Add some pointwise constraints on the variable `varname` thanks to
a penalization. The penalization coefficient is initially
`penalization_coeff` and will be added to the data of the model.
The conditions are prescribed on a set of points given in the data
`dataname_pt` whose dimension is the number of points times the dimension
of the mesh.
If the variable represents a vector field, one has to give the data
`dataname_unitv` which represents a vector of dimension the number of
points times the dimension of the vector field which should store some
unit vectors. In that case the prescribed constraint is the scalar
product of the variable at the corresponding point with the corresponding
unit vector.
The optional data `dataname_val` is the vector of values to be prescribed
at the different points.
This brick is specifically designed to kill rigid displacement
in a Neumann problem.
Returns the brick index in the model."""
return self.set("add_pointwise_constraints_with_penalization", varname, coeff, dataname_pt, dataname_unitv, *args)
def change_penalization_coeff(self, ind_brick, coeff):
"""Change the penalization coefficient of a Dirichlet condition with
penalization brick. If the brick is not of this kind, this
function has an undefined behavior."""
return self.set("change_penalization_coeff", ind_brick, coeff)
def add_Helmholtz_brick(self, mim, varname, dataname, region=None):
"""Add a Helmholtz term to the model relatively to the variable `varname`.
`dataname` should contain the wave number. `region` is an optional mesh
region on which the term is added. If it is not specified, it is added
on the whole mesh. Return the brick index in the model."""
return self.set("add_Helmholtz_brick", mim, varname, dataname, region)
def add_Fourier_Robin_brick(self, mim, varname, dataname, region):
"""Add a Fourier-Robin term to the model relatively to the variable
`varname`. This corresponds to a weak term of the form
:math:`\\int (qu).v`. `dataname`
should contain the parameter :math:`q` of
the Fourier-Robin condition. `region` is the mesh region on which
the term is added. Return the brick index in the model."""
return self.set("add_Fourier_Robin_brick", mim, varname, dataname, region)
def add_basic_nonlinear_brick(self, mim, varname, f, dfdu, dataname=None, region=None):
"""Add a brick representing a scalar term :math:`f(u)` to the left-hand
side of the model. In the weak form, one adds :math:`+\\int f(u)v`.
The function :math:`f` may optionally depend on :math:`\\lambda`, i.e.,
:math:`f(u)=f(u,\\lambda)`.
`f` and `dfdu` should contain the expressions for
:math:`f(u)` and :math:`\\frac{df}{du}(u)`, respectively.
`dataname` represents the optional real scalar parameter :math:`\\lambda`
in the model. `region` is an optional mesh region on which the term is
added. If it is not specified, the term is added on the whole mesh.
Return the brick index in the model."""
return self.set("add_basic_nonlinear_brick", mim, varname, f, dfdu, dataname, region)
def add_constraint_with_multipliers(self, varname, multname, B, L):
"""Add an additional explicit constraint on the variable `varname` thank to
a multiplier `multname` peviously added to the model (should be a fixed
size variable). The constraint is :math:`BU=L`
with `B` being a rectangular sparse matrix. It is possible to change
the constraint at any time whith the methods Model.set_private_matrix()
and Model.set_private_rhs(). Return the brick index in the model."""
return self.set("add_constraint_with_multipliers", varname, multname, B, L)
def add_constraint_with_penalization(self, varname, coeff, B, L):
"""Add an additional explicit penalized constraint on the variable `varname`.
The constraint is :math`BU=L` with `B` being a rectangular sparse matrix.
Be aware that `B` should not contain a palin row, otherwise the whole
tangent matrix will be plain. It is possible to change the constraint
at any time whith the methods Model.set_private_matrix()
and Model.set_private_rhs(). The method
Model.change_penalization_coeff() can be used. Return the brick
index in the model."""
return self.set("add_constraint_with_penalization", varname, coeff, B, L)
def add_explicit_matrix(self, varname1, varname2, B, issymmetric=None, *args):
"""Synopsis: ind = Model.add_explicit_matrix(self, string varname1, string varname2, Spmat B[, int issymmetric[, int iscoercive]])
Add a brick representing an explicit matrix to be added to the tangent
linear system relatively to the variables `varname1` and `varname2`.
The given matrix should have has many rows as the dimension of
`varname1` and as many columns as the dimension of `varname2`.
If the two variables are different and if `issymmetric` is set to 1
then the transpose of the matrix is also added to the tangent system
(default is 0). Set `iscoercive` to 1 if the term does not affect the
coercivity of the tangent system (default is 0). The matrix can be
changed by the command Model.set_private_matrix(). Return the
brick index in the model."""
return self.set("add_explicit_matrix", varname1, varname2, B, issymmetric, *args)
def add_explicit_rhs(self, varname, L):
"""Add a brick representing an explicit right hand side to be added to
the right hand side of the tangent linear system relatively to the
variable `varname`. The given rhs should have the same size than the
dimension of `varname`. The rhs can be changed by the command
Model.set_private_rhs(). Return the brick index in the model."""
return self.set("add_explicit_rhs", varname, L)
def set_private_matrix(self, indbrick, B):
"""For some specific bricks having an internal sparse matrix
(explicit bricks: 'constraint brick' and 'explicit matrix brick'),
set this matrix. """
return self.set("set_private_matrix", indbrick, B)
def set_private_rhs(self, indbrick, B):
"""For some specific bricks having an internal right hand side vector
(explicit bricks: 'constraint brick' and 'explicit rhs brick'),
set this rhs. """
return self.set("set_private_rhs", indbrick, B)
def add_isotropic_linearized_elasticity_brick(self, mim, varname, dataname_lambda, dataname_mu, region=None):
"""Add an isotropic linearized elasticity term to the model relatively to
the variable `varname`. `dataname_lambda` and `dataname_mu` should
contain the Lame coefficients. `region` is an optional mesh region
on which the term is added. If it is not specified, it is added
on the whole mesh. Return the brick index in the model."""
return self.set("add_isotropic_linearized_elasticity_brick", mim, varname, dataname_lambda, dataname_mu, region)
def add_linear_incompressibility_brick(self, mim, varname, multname_pressure, region=None, *args):
"""Synopsis: ind = Model.add_linear_incompressibility_brick(self, MeshIm mim, string varname, string multname_pressure[, int region[, string dataname_coeff]])
Add an linear incompressibility condition on `variable`. `multname_pressure`
is a variable which represent the pressure. Be aware that an inf-sup
condition between the finite element method describing the pressure and the
primal variable has to be satisfied. `region` is an optional mesh region on
which the term is added. If it is not specified, it is added on the whole mesh.
`dataname_coeff` is an optional penalization coefficient for nearly
incompressible elasticity for instance. In this case, it is the inverse
of the Lame coefficient :math:`\\lambda`. Return the brick index in the model."""
return self.set("add_linear_incompressibility_brick", mim, varname, multname_pressure, region, *args)
def add_nonlinear_elasticity_brick(self, mim, varname, constitutive_law, dataname, region=None):
"""Add a nonlinear elasticity term to the model relatively to the
variable `varname`. `lawname` is the constitutive law which
could be 'SaintVenant Kirchhoff', 'Mooney Rivlin', 'neo Hookean',
'Ciarlet Geymonat' or 'generalized Blatz Ko'.
'Mooney Rivlin' and 'neo Hookean' law names can be preceded with the word
'compressible' or 'incompressible' to force using the corresponding version.
The compressible version of these laws requires one additional material
coefficient. By default, the incompressible version of 'Mooney Rivlin' law
and the compressible one of the 'neo Hookean' law are considered. In general,
'neo Hookean' is a special case of the 'Mooney Rivlin' law that requires one
coefficient less.
IMPORTANT : if the variable is defined on a 2D mesh, the plane strain
approximation is automatically used.
`dataname` is a vector of parameters for the constitutive law. Its length
depends on the law. It could be a short vector of constant values or a
vector field described on a finite element method for variable
coefficients. `region` is an optional mesh region on which the term
is added. If it is not specified, it is added on the whole mesh.
This brick use the low-level generic assembly.
Returns the brick index in the model."""
return self.set("add_nonlinear_elasticity_brick", mim, varname, constitutive_law, dataname, region)
def add_finite_strain_elasticity_brick(self, mim, varname, constitutive_law, params, region=None):
"""Add a nonlinear elasticity term to the model relatively to the
variable `varname`. `lawname` is the constitutive law which
could be 'SaintVenant Kirchhoff', 'Mooney Rivlin', 'Neo Hookean',
'Ciarlet Geymonat' or 'Generalized Blatz Ko'.
'Mooney Rivlin' and 'Neo Hookean' law names have to be preceeded with
the word 'Compressible' or 'Incompressible' to force using the
corresponding version.
The compressible version of these laws requires one additional material
coefficient.
IMPORTANT : if the variable is defined on a 2D mesh, the plane strain
approximation is automatically used.
`params` is a vector of parameters for the constitutive law. Its length
depends on the law. It could be a short vector of constant values or a
vector field described on a finite element method for variable
coefficients. `region` is an optional mesh region on which the term
is added. If it is not specified, it is added on the whole mesh.
This brick use the high-level generic assembly.
Returns the brick index in the model."""
return self.set("add_finite_strain_elasticity_brick", mim, varname, constitutive_law, params, region)
def add_elastoplasticity_brick(self, mim, projname, varname, datalambda, datamu, datathreshold, datasigma, region=None):
"""Add a nonlinear elastoplastic term to the model relatively to the
variable `varname`, in small deformations, for an isotropic material
and for a quasistatic model. `projname` is the type of projection that
we want to use. For the moment, only the Von Mises projection is
computing that we could entering 'VM' or 'Von Mises'.
`datasigma` is the variable representing the constraints on the material.
Be careful that `varname` and `datasigma` are composed of two iterates
for the time scheme needed for the Newton algorithm used.
Moreover, the finite element method on which `varname` is described
is an K ordered mesh_fem, the `datasigma` one have to be at least
an K-1 ordered mesh_fem.
`datalambda` and `datamu` are the Lame coefficients of the studied
material.
`datathreshold` is the plasticity threshold of the material.
The three last variable could be constants or described on the
same finite element method.
`region` is an optional mesh region on which the term is added.
If it is not specified, it is added on the whole mesh.
Return the brick index in the model."""
return self.set("add_elastoplasticity_brick", mim, projname, varname, datalambda, datamu, datathreshold, datasigma, region)
def add_nonlinear_incompressibility_brick(self, mim, varname, multname_pressure, region=None):
"""Add an nonlinear incompressibility condition on `variable` (for large
strain elasticity). `multname_pressure`
is a variable which represent the pressure. Be aware that an inf-sup
condition between the finite element method describing the pressure and the
primal variable has to be satisfied. `region` is an optional mesh region on
which the term is added. If it is not specified, it is added on the
whole mesh. Return the brick index in the model."""
return self.set("add_nonlinear_incompressibility_brick", mim, varname, multname_pressure, region)
def add_finite_strain_incompressibility_brick(self, mim, varname, multname_pressure, region=None):
"""Add an finite strain incompressibility condition on `variable` (for large
strain elasticity). `multname_pressure`
is a variable which represent the pressure. Be aware that an inf-sup
condition between the finite element method describing the pressure and the
primal variable has to be satisfied. `region` is an optional mesh region on
which the term is added. If it is not specified, it is added on the
whole mesh. Return the brick index in the model.
This brick is equivalent to the ``nonlinear incompressibility brick`` but
uses the high-level generic assembly adding the term
``p*(1-Det(Id(meshdim)+Grad_u))`` if ``p`` is the multiplier and
``u`` the variable which represent the displacement."""
return self.set("add_finite_strain_incompressibility_brick", mim, varname, multname_pressure, region)
def add_bilaplacian_brick(self, mim, varname, dataname, region=None):
"""Add a bilaplacian brick on the variable
`varname` and on the mesh region `region`.
This represent a term :math:`\\Delta(D \\Delta u)`.
where :math:`D(x)` is a coefficient determined by `dataname` which
could be constant or described on a f.e.m. The corresponding weak form
is :math:`\\int D(x)\\Delta u(x) \\Delta v(x) dx`.
Return the brick index in the model."""
return self.set("add_bilaplacian_brick", mim, varname, dataname, region)
def add_Kirchhoff_Love_plate_brick(self, mim, varname, dataname_D, dataname_nu, region=None):
"""Add a bilaplacian brick on the variable
`varname` and on the mesh region `region`.
This represent a term :math:`\\Delta(D \\Delta u)` where :math:`D(x)`
is a the flexion modulus determined by `dataname_D`. The term is
integrated by part following a Kirchhoff-Love plate model
with `dataname_nu` the poisson ratio.
Return the brick index in the model."""
return self.set("add_Kirchhoff_Love_plate_brick", mim, varname, dataname_D, dataname_nu, region)
def add_normal_derivative_source_term_brick(self, mim, varname, dataname, region):
"""Add a normal derivative source term brick
:math:`F = \\int b.\\partial_n v` on the variable `varname` and the
mesh region `region`.
Update the right hand side of the linear system.
`dataname` represents `b` and `varname` represents `v`.
Return the brick index in the model."""
return self.set("add_normal_derivative_source_term_brick", mim, varname, dataname, region)
def add_Kirchhoff_Love_Neumann_term_brick(self, mim, varname, dataname_M, dataname_divM, region):
"""Add a Neumann term brick for Kirchhoff-Love model
n the variable `varname` and the mesh region `region`.
dataname_M` represents the bending moment tensor and `dataname_divM`
ts divergence.
eturn the brick index in the model."""
return self.set("add_Kirchhoff_Love_Neumann_term_brick", mim, varname, dataname_M, dataname_divM, region)
def add_normal_derivative_Dirichlet_condition_with_multipliers(self, mim, varname, mult_description, region, dataname=None, R_must_be_derivated=None):
"""Add a Dirichlet condition on the normal derivative of the variable
varname` and on the mesh region `region` (which should be a boundary.
he general form is
math:`\\int \\partial_n u(x)v(x) = \\int r(x)v(x) \\forall v`
here :math:`r(x)` is
he right hand side for the Dirichlet condition (0 for
omogeneous conditions) and :math:`v` is in a space of multipliers
efined by `mult_description`.
f `mult_description` is a string this is assumed
o be the variable name corresponding to the multiplier (which should be
irst declared as a multiplier variable on the mesh region in the model).
f it is a finite element method (mesh_fem object) then a multiplier
ariable will be added to the model and build on this finite element
ethod (it will be restricted to the mesh region `region` and eventually
ome conflicting dofs with some other multiplier variables will be
uppressed). If it is an integer, then a multiplier variable will be
dded to the model and build on a classical finite element of degree
hat integer. `dataname` is an optional parameter which represents
he right hand side of the Dirichlet condition.
f `R_must_be_derivated` is set to `true` then the normal
erivative of `dataname` is considered.
eturn the brick index in the model."""
return self.set("add_normal_derivative_Dirichlet_condition_with_multipliers", mim, varname, mult_description, region, dataname, R_must_be_derivated)
def add_normal_derivative_Dirichlet_condition_with_penalization(self, mim, varname, coeff, region, dataname=None, R_must_be_derivated=None):
"""Add a Dirichlet condition on the normal derivative of the variable
varname` and on the mesh region `region` (which should be a boundary.
he general form is
math:`\\int \\partial_n u(x)v(x) = \\int r(x)v(x) \\forall v`
here :math:`r(x)` is
he right hand side for the Dirichlet condition (0 for
omogeneous conditions).
he penalization coefficient
s initially `coeff` and will be added to the data of the model.
t can be changed with the command Model.change_penalization_coeff().
dataname` is an optional parameter which represents
he right hand side of the Dirichlet condition.
f `R_must_be_derivated` is set to `true` then the normal
erivative of `dataname` is considered.
eturn the brick index in the model."""
return self.set("add_normal_derivative_Dirichlet_condition_with_penalization", mim, varname, coeff, region, dataname, R_must_be_derivated)
def add_mass_brick(self, mim, varname, dataname_rho=None, *args):
"""Synopsis: ind = Model.add_mass_brick(self, MeshIm mim, string varname[, string dataname_rho[, int region]])
Add mass term to the model relatively to the variable `varname`.
If specified, the data `dataname_rho` should contain the
density (1 if omitted). `region` is an optional mesh region on
which the term is added. If it is not specified, it
is added on the whole mesh. Return the brick index in the model."""
return self.set("add_mass_brick", mim, varname, dataname_rho, *args)
def add_basic_d_on_dt_brick(self, mim, varnameU, dataname_dt, dataname_rho=None, *args):
"""Synopsis: ind = Model.add_basic_d_on_dt_brick(self, MeshIm mim, string varnameU, string dataname_dt[, string dataname_rho[, int region]])
Add the standard discretization of a first order time derivative on
`varnameU`. The parameter `dataname_rho` is the density which could
be omitted (the defaul value is 1). This brick should be used in
addition to a time dispatcher for the other terms. Return the brick
index in the model."""
return self.set("add_basic_d_on_dt_brick", mim, varnameU, dataname_dt, dataname_rho, *args)
def add_basic_d2_on_dt2_brick(self, mim, varnameU, datanameV, dataname_dt, dataname_alpha, dataname_rho=None, *args):
"""Synopsis: ind = Model.add_basic_d2_on_dt2_brick(self, MeshIm mim, string varnameU, string datanameV, string dataname_dt, string dataname_alpha,[, string dataname_rho[, int region]])
Add the standard discretization of a second order time derivative
on `varnameU`. `datanameV` is a data represented on the same finite
element method as U which represents the time derivative of U. The
parameter `dataname_rho` is the density which could be omitted (the defaul
value is 1). This brick should be used in addition to a time dispatcher for
the other terms. The time derivative :math:`v` of the
variable :math:`u` is preferably computed as a
post-traitement which depends on each scheme. The parameter `dataname_alpha`
depends on the time integration scheme. Return the brick index in the model."""
return self.set("add_basic_d2_on_dt2_brick", mim, varnameU, datanameV, dataname_dt, dataname_alpha, dataname_rho, *args)
def add_theta_method_dispatcher(self, bricks_indices, theta):
"""Add a theta-method time dispatcher to a list of bricks. For instance,
a matrix term :math:`K` will be replaced by
:math:`\\theta K U^{n+1} + (1-\\theta) K U^{n}`.
"""
return self.set("add_theta_method_dispatcher", bricks_indices, theta)
def add_midpoint_dispatcher(self, bricks_indices):
"""Add a midpoint time dispatcher to a list of bricks. For instance, a
nonlinear term :math:`K(U)` will be replaced by
:math:`K((U^{n+1} + U^{n})/2)`."""
return self.set("add_midpoint_dispatcher", bricks_indices)
def velocity_update_for_order_two_theta_method(self, varnameU, datanameV, dataname_dt, dataname_theta):
"""Function which udpate the velocity :math:`v^{n+1}` after
the computation of the displacement :math:`u^{n+1}` and
before the next iteration. Specific for theta-method and when the velocity is
included in the data of the model. """
return self.set("velocity_update_for_order_two_theta_method", varnameU, datanameV, dataname_dt, dataname_theta)
def velocity_update_for_Newmark_scheme(self, id2dt2_brick, varnameU, datanameV, dataname_dt, dataname_twobeta, dataname_alpha):
"""Function which udpate the velocity
:math:`v^{n+1}` after
the computation of the displacement
:math:`u^{n+1}` and
before the next iteration. Specific for Newmark scheme
and when the velocity is
included in the data of the model.*
This version inverts the mass matrix by a
conjugate gradient."""
return self.set("velocity_update_for_Newmark_scheme", id2dt2_brick, varnameU, datanameV, dataname_dt, dataname_twobeta, dataname_alpha)
def disable_bricks(self, bricks_indices):
"""Disable a brick (the brick will no longer participate to the
building of the tangent linear system)."""
return self.set("disable_bricks", bricks_indices)
def enable_bricks(self, bricks_indices):
"""Enable a disabled brick."""
return self.set("enable_bricks", bricks_indices)
def disable_variable(self, varname):
"""Disable a variable for a solve. The next solve will operate only on
the remaining variables. This allows to solve separately different
parts of a model. If there is a strong coupling of the variables,
a fixed point strategy can the be used. """
return self.set("disable_variable", varname)
def enable_variable(self, varname):
"""Enable a disabled variable."""
return self.set("enable_variable", varname)
def first_iter(self):
"""To be executed before the first iteration of a time integration
scheme. """
return self.set("first_iter")
def next_iter(self):
"""To be executed at the end of each iteration of a time
integration scheme. """
return self.set("next_iter")
def add_basic_contact_brick(self, varname_u, multname_n, multname_t=None, *args):
"""Synopsis: ind = Model.add_basic_contact_brick(self, string varname_u, string multname_n[, string multname_t], string dataname_r, Spmat BN[, Spmat BT, string dataname_friction_coeff][, string dataname_gap[, string dataname_alpha[, int augmented_version[, string dataname_gamma, string dataname_wt]]])
Add a contact with or without friction brick to the model.
If U is the vector
of degrees of freedom on which the unilateral constraint is applied,
the matrix `BN` have to be such that this constraint is defined by
:math:`B_N U \\le 0`. A friction condition can be considered by adding
the three parameters `multname_t`, `BT` and `dataname_friction_coeff`.
In this case, the tangential displacement is :math:`B_T U` and
the matrix `BT` should have as many rows as `BN` multiplied by
:math:`d-1` where :math:`d` is the domain dimension.
In this case also, `dataname_friction_coeff` is a data which represents
the coefficient of friction. It can be a scalar or a vector representing a
value on each contact condition. The unilateral constraint is prescribed
thank to a multiplier
`multname_n` whose dimension should be equal to the number of rows of
`BN`. If a friction condition is added, it is prescribed with a
multiplier `multname_t` whose dimension should be equal to the number
of rows of `BT`. The augmentation parameter `r` should be chosen in
a range of
acceptabe values (see Getfem user documentation). `dataname_gap` is an
optional parameter representing the initial gap. It can be a single value
or a vector of value. `dataname_alpha` is an optional homogenization
parameter for the augmentation parameter
(see Getfem user documentation). The parameter `augmented_version`
indicates the augmentation strategy : 1 for the non-symmetric
Alart-Curnier augmented Lagrangian, 2 for the symmetric one (except for
the coupling between contact and Coulomb friction), 3 for the
unsymmetric method with augmented multipliers, 4 for the unsymmetric
method with augmented multipliers and De Saxce projection. """
return self.set("add_basic_contact_brick", varname_u, multname_n, multname_t, *args)
def contact_brick_set_BN(self, indbrick, BN):
"""Can be used to set the BN matrix of a basic contact/friction brick."""
return self.set("contact_brick_set_BN", indbrick, BN)
def contact_brick_set_BT(self, indbrick, BT):
"""Can be used to set the BT matrix of a basic contact with
friction brick. """
return self.set("contact_brick_set_BT", indbrick, BT)
def add_nodal_contact_with_rigid_obstacle_brick(self, mim, varname_u, multname_n, multname_t=None, *args):
"""Synopsis: ind = Model.add_nodal_contact_with_rigid_obstacle_brick(self, MeshIm mim, string varname_u, string multname_n[, string multname_t], string dataname_r[, string dataname_friction_coeff], int region, string obstacle[, int augmented_version])
Add a contact with or without friction condition with a rigid obstacle
to the model. The condition is applied on the variable `varname_u`
on the boundary corresponding to `region`. The rigid obstacle should
be described with the string `obstacle` being a signed distance to
the obstacle. This string should be an expression where the coordinates
are 'x', 'y' in 2D and 'x', 'y', 'z' in 3D. For instance, if the rigid
obstacle correspond to :math:`z \\le 0`, the corresponding signed distance
will be simply "z". `multname_n` should be a fixed size variable whose size
is the number of degrees of freedom on boundary `region`. It represents the
contact equivalent nodal forces. In order to add a friction condition
one has to add the `multname_t` and `dataname_friction_coeff` parameters.
`multname_t` should be a fixed size variable whose size is
the number of degrees of freedom on boundary `region` multiplied by
:math:`d-1` where :math:`d` is the domain dimension. It represents
the friction equivalent nodal forces.
The augmentation parameter `r` should be chosen in a
range of acceptabe values (close to the Young modulus of the elastic
body, see Getfem user documentation). `dataname_friction_coeff` is
the friction coefficient. It could be a scalar or a vector of values
representing the friction coefficient on each contact node.
The parameter `augmented_version`
indicates the augmentation strategy : 1 for the non-symmetric
Alart-Curnier augmented Lagrangian, 2 for the symmetric one (except for
the coupling between contact and Coulomb friction),
3 for the new unsymmetric method.
Basically, this brick compute the matrix BN
and the vectors gap and alpha and calls the basic contact brick. """
return self.set("add_nodal_contact_with_rigid_obstacle_brick", mim, varname_u, multname_n, multname_t, *args)
def add_contact_with_rigid_obstacle_brick(self, mim, varname_u, multname_n, multname_t=None, *args):
"""Synopsis: ind = Model.add_contact_with_rigid_obstacle_brick(self, MeshIm mim, string varname_u, string multname_n[, string multname_t], string dataname_r[, string dataname_friction_coeff], int region, string obstacle[, int augmented_version])
DEPRECATED FUNCTION. Use 'add nodal contact with rigid obstacle brick' instead."""
return self.set("add_contact_with_rigid_obstacle_brick", mim, varname_u, multname_n, multname_t, *args)
def add_integral_contact_with_rigid_obstacle_brick(self, mim, varname_u, multname, dataname_obstacle, dataname_r, dataname_friction_coeff=None, *args):
"""Synopsis: ind = Model.add_integral_contact_with_rigid_obstacle_brick(self, MeshIm mim, string varname_u, string multname, string dataname_obstacle, string dataname_r [, string dataname_friction_coeff], int region [, int option [, string dataname_alpha [, string dataname_wt [, string dataname_gamma [, string dataname_vt]]]]])
Add a contact with or without friction condition with a rigid obstacle
to the model. This brick adds a contact which is defined
in an integral way. It is the direct approximation of an augmented
Lagrangian formulation (see Getfem user documentation) defined at the
continuous level. The advantage is a better scalability: the number of
Newton iterations should be more or less independent of the mesh size.
The contact condition is applied on the variable `varname_u`
on the boundary corresponding to `region`. The rigid obstacle should
be described with the data `dataname_obstacle` being a signed distance to
the obstacle (interpolated on a finite element method).
`multname` should be a fem variable representing the contact stress.
An inf-sup condition beetween `multname` and `varname_u` is required.
The augmentation parameter `dataname_r` should be chosen in a
range of acceptabe values.
The optional parameter `dataname_friction_coeff` is the friction
coefficient which could be constant or defined on a finite element method.
Possible values for `option` is 1 for the non-symmetric Alart-Curnier
augmented Lagrangian method, 2 for the symmetric one, 3 for the
non-symmetric Alart-Curnier method with an additional augmentation
and 4 for a new unsymmetric method. The default value is 1.
In case of contact with friction, `dataname_alpha` and `dataname_wt`
are optional parameters to solve evolutionary friction problems.
`dataname_gamma` and `dataname_vt` represent optional data for adding
a parameter-dependent sliding velocity to the friction condition.
"""
return self.set("add_integral_contact_with_rigid_obstacle_brick", mim, varname_u, multname, dataname_obstacle, dataname_r, dataname_friction_coeff, *args)
def add_penalized_contact_with_rigid_obstacle_brick(self, mim, varname_u, dataname_obstacle, dataname_r, dataname_coeff=None, *args):
"""Synopsis: ind = Model.add_penalized_contact_with_rigid_obstacle_brick(self, MeshIm mim, string varname_u, string dataname_obstacle, string dataname_r [, string dataname_coeff], int region [, int option, string dataname_lambda, [, string dataname_alpha [, string dataname_wt]]])
Add a penalized contact with or without friction condition with a
rigid obstacle to the model.
The condition is applied on the variable `varname_u`
on the boundary corresponding to `region`. The rigid obstacle should
be described with the data `dataname_obstacle` being a signed distance to
the obstacle (interpolated on a finite element method).
The penalization parameter `dataname_r` should be chosen
large enough to prescribe approximate non-penetration and friction
conditions but not too large not to deteriorate too much the
conditionning of the tangent system.
`dataname_lambda` is an optional parameter used if option
is 2. In that case, the penalization term is shifted by lambda (this
allows the use of an Uzawa algorithm on the corresponding augmented
Lagrangian formulation)
"""
return self.set("add_penalized_contact_with_rigid_obstacle_brick", mim, varname_u, dataname_obstacle, dataname_r, dataname_coeff, *args)
def add_Nitsche_contact_with_rigid_obstacle_brick(self, mim, varname, dataname_obstacle, gamma0name, region, theta=None, *args):
"""Synopsis: ind = Model.add_Nitsche_contact_with_rigid_obstacle_brick(self, MeshIm mim, string varname, string dataname_obstacle, string gamma0name, int region[, scalar theta[, string dataname_friction_coeff[, string dataname_alpha, string dataname_wt]]])
Adds a contact condition with or without Coulomb friction on the variable
`varname` and the mesh boundary `region`. The contact condition
is prescribed with Nitsche's method. The rigid obstacle should
be described with the data `dataname_obstacle` being a signed distance to
the obstacle (interpolated on a finite element method).
`gamma0name` is the Nitsche's method parameter.
`theta` is a scalar value which can be
positive or negative. `theta = 1` corresponds to the standard symmetric
method which is conditionnaly coercive for `gamma0` small.
`theta = -1` corresponds to the skew-symmetric method which is
inconditionnaly coercive. `theta = 0` is the simplest method
for which the second derivative of the Neumann term is not necessary.
The optional parameter `dataname_friction_coeff` is the friction
coefficient which could be constant or defined on a finite element
method.
CAUTION: This brick has to be added in the model after all the bricks
corresponding to partial differential terms having a Neumann term.
Moreover, This brick can only be applied to bricks declaring their
Neumann terms. Returns the brick index in the model.
"""
return self.set("add_Nitsche_contact_with_rigid_obstacle_brick", mim, varname, dataname_obstacle, gamma0name, region, theta, *args)
def add_Nitsche_midpoint_contact_with_rigid_obstacle_brick(self, mim, varname, dataname_obstacle, gamma0name, region, theta, dataname_friction_coeff, dataname_alpha, dataname_wt, option):
"""EXPERIMENTAL BRICK: for midpoint scheme only !!
Adds a contact condition with or without Coulomb friction on the variable
`varname` and the mesh boundary `region`. The contact condition
is prescribed with Nitsche's method. The rigid obstacle should
be described with the data `dataname_obstacle` being a signed distance to
the obstacle (interpolated on a finite element method).
`gamma0name` is the Nitsche's method parameter.
`theta` is a scalar value which can be
positive or negative. `theta = 1` corresponds to the standard symmetric
method which is conditionnaly coercive for `gamma0` small.
`theta = -1` corresponds to the skew-symmetric method which is
inconditionnaly coercive. `theta = 0` is the simplest method
for which the second derivative of the Neumann term is not necessary.
The optional parameter `dataname_friction_coeff` is the friction
coefficient which could be constant or defined on a finite element
method.
CAUTION: This brick has to be added in the model after all the bricks
corresponding to partial differential terms having a Neumann term.
Moreover, This brick can only be applied to bricks declaring their
Neumann terms. Returns the brick index in the model.
"""
return self.set("add_Nitsche_midpoint_contact_with_rigid_obstacle_brick", mim, varname, dataname_obstacle, gamma0name, region, theta, dataname_friction_coeff, dataname_alpha, dataname_wt, option)
def add_Nitsche_fictitious_domain_contact_brick(self, mim, varname1, varname2, dataname_d1, dataname_d2, gamma0name, theta=None, *args):
"""Synopsis: ind = Model.add_Nitsche_fictitious_domain_contact_brick(self, MeshIm mim, string varname1, string varname2, string dataname_d1, string dataname_d2, string gamma0name [, scalar theta[, string dataname_friction_coeff[, string dataname_alpha, string dataname_wt1,string dataname_wt2]]])
Adds a contact condition with or without Coulomb friction between
two bodies in a fictitious domain. The contact condition is applied on
the variable `varname_u1` corresponds with the first and slave body
with Nitsche's method and on the variable `varname_u2` corresponds
with the second and master body with Nitsche's method.
The contact condition is evaluated on the fictitious slave boundary.
The first body should be described by the level-set `dataname_d1`
and the second body should be described by the level-set `dataname_d2`.
`gamma0name` is the Nitsche's method parameter.
`theta` is a scalar value which can be positive or negative.
`theta = 1` corresponds to the standard symmetric method which is
conditionnaly coercive for `gamma0` small.
`theta = -1` corresponds to the skew-symmetric method which is inconditionnaly coercive.
`theta = 0` is the simplest method for which the second derivative of
the Neumann term is not necessary. The optional parameter `dataname_friction_coeff`
is the friction coefficient which could be constant or defined on a finite element method.
CAUTION: This brick has to be added in the model after all the bricks
corresponding to partial differential terms having a Neumann term.
Moreover, This brick can only be applied to bricks declaring their
Neumann terms. Returns the brick index in the model.
"""
return self.set("add_Nitsche_fictitious_domain_contact_brick", mim, varname1, varname2, dataname_d1, dataname_d2, gamma0name, theta, *args)
def add_nodal_contact_between_nonmatching_meshes_brick(self, mim1, mim2=None, *args):
"""Synopsis: ind = Model.add_nodal_contact_between_nonmatching_meshes_brick(self, MeshIm mim1[, MeshIm mim2], string varname_u1[, string varname_u2], string multname_n[, string multname_t], string dataname_r[, string dataname_fr], int rg1, int rg2[, int slave1, int slave2, int augmented_version])
Add a contact with or without friction condition between two faces of
one or two elastic bodies. The condition is applied on the variable
`varname_u1` or the variables `varname_u1` and `varname_u2` depending
if a single or two distinct displacement fields are given. Integers
`rg1` and `rg2` represent the regions expected to come in contact with
each other. In the single displacement variable case the regions defined
in both `rg1` and `rg2` refer to the variable `varname_u1`. In the case
of two displacement variables, `rg1` refers to `varname_u1` and `rg2`
refers to `varname_u2`. `multname_n` should be a fixed size variable
whose size is the number of degrees of freedom on those regions among
the ones defined in `rg1` and `rg2` which are characterized as "slaves".
It represents the contact equivalent nodal normal forces. `multname_t`
should be a fixed size variable whose size corresponds to the size of
`multname_n` multiplied by qdim - 1 . It represents the contact
equivalent nodal tangent (frictional) forces. The augmentation parameter
`r` should be chosen in a range of acceptabe values (close to the Young
modulus of the elastic body, see Getfem user documentation). The
friction coefficient stored in the parameter `fr` is either a single
value or a vector of the same size as `multname_n`. The optional
parameters `slave1` and `slave2` declare if the regions defined in `rg1`
and `rg2` are correspondingly considered as "slaves". By default
`slave1` is true and `slave2` is false, i.e. `rg1` contains the slave
surfaces, while 'rg2' the master surfaces. Preferrably only one of
`slave1` and `slave2` is set to true. The parameter `augmented_version`
indicates the augmentation strategy : 1 for the non-symmetric
Alart-Curnier augmented Lagrangian, 2 for the symmetric one (except for
the coupling between contact and Coulomb friction),
3 for the new unsymmetric method.
Basically, this brick computes the matrices BN and BT and the vectors
gap and alpha and calls the basic contact brick. """
return self.set("add_nodal_contact_between_nonmatching_meshes_brick", mim1, mim2, *args)
def add_nonmatching_meshes_contact_brick(self, mim1, mim2=None, *args):
"""Synopsis: ind = Model.add_nonmatching_meshes_contact_brick(self, MeshIm mim1[, MeshIm mim2], string varname_u1[, string varname_u2], string multname_n[, string multname_t], string dataname_r[, string dataname_fr], int rg1, int rg2[, int slave1, int slave2, int augmented_version])
DEPRECATED FUNCTION. Use 'add nodal contact between nonmatching meshes brick' instead."""
return self.set("add_nonmatching_meshes_contact_brick", mim1, mim2, *args)
def add_integral_contact_between_nonmatching_meshes_brick(self, mim, varname_u1, varname_u2, multname, dataname_r, dataname_friction_coeff=None, *args):
"""Synopsis: ind = Model.add_integral_contact_between_nonmatching_meshes_brick(self, MeshIm mim, string varname_u1, string varname_u2, string multname, string dataname_r [, string dataname_friction_coeff], int region1, int region2 [, int option [, string dataname_alpha [, string dataname_wt1 , string dataname_wt2]]])
Add a contact with or without friction condition between nonmatching
meshes to the model. This brick adds a contact which is defined
in an integral way. It is the direct approximation of an augmented
agrangian formulation (see Getfem user documentation) defined at the
continuous level. The advantage should be a better scalability:
the number of Newton iterations should be more or less independent
of the mesh size.
The condition is applied on the variables `varname_u1` and `varname_u2`
on the boundaries corresponding to `region1` and `region2`.
`multname` should be a fem variable representing the contact stress
for the frictionless case and the contact and friction stress for the
case with friction. An inf-sup condition between `multname` and
`varname_u1` and `varname_u2` is required.
The augmentation parameter `dataname_r` should be chosen in a
range of acceptable values.
The optional parameter `dataname_friction_coeff` is the friction
coefficient which could be constant or defined on a finite element
method on the same mesh as `varname_u1`.
Possible values for `option` is 1 for the non-symmetric Alart-Curnier
augmented Lagrangian method, 2 for the symmetric one, 3 for the
non-symmetric Alart-Curnier method with an additional augmentation
and 4 for a new unsymmetric method. The default value is 1.
In case of contact with friction, `dataname_alpha`, `dataname_wt1` and
`dataname_wt2` are optional parameters to solve evolutionary friction
problems.
"""
return self.set("add_integral_contact_between_nonmatching_meshes_brick", mim, varname_u1, varname_u2, multname, dataname_r, dataname_friction_coeff, *args)
def add_penalized_contact_between_nonmatching_meshes_brick(self, mim, varname_u1, varname_u2, dataname_r, dataname_coeff=None, *args):
"""Synopsis: ind = Model.add_penalized_contact_between_nonmatching_meshes_brick(self, MeshIm mim, string varname_u1, string varname_u2, string dataname_r [, string dataname_coeff], int region1, int region2 [, int option [, string dataname_lambda, [, string dataname_alpha [, string dataname_wt1, string dataname_wt2]]]])
Add a penalized contact condition with or without friction between
nonmatching meshes to the model.
The condition is applied on the variables `varname_u1` and `varname_u2`
on the boundaries corresponding to `region1` and `region2`.
The penalization parameter `dataname_r` should be chosen
large enough to prescribe approximate non-penetration and friction
conditions but not too large not to deteriorate too much the
conditionning of the tangent system.
The optional parameter `dataname_friction_coeff` is the friction
coefficient which could be constant or defined on a finite element
method on the same mesh as `varname_u1`.
`dataname_lambda` is an optional parameter used if option
is 2. In that case, the penalization term is shifted by lambda (this
allows the use of an Uzawa algorithm on the corresponding augmented
Lagrangian formulation)
In case of contact with friction, `dataname_alpha`, `dataname_wt1` and
`dataname_wt2` are optional parameters to solve evolutionary friction
problems.
"""
return self.set("add_penalized_contact_between_nonmatching_meshes_brick", mim, varname_u1, varname_u2, dataname_r, dataname_coeff, *args)
def add_integral_large_sliding_contact_brick_raytrace(self, multi_contact, dataname_r, dataname_fr=None, *args):
"""Synopsis: ind = Model.add_integral_large_sliding_contact_brick_raytrace(self, @tmcf multi_contact, string dataname_r[, string dataname_fr[, string dataname_alpha]])
Adds a large sliding contact with friction brick to the model.
This brick is able to deal with self-contact, contact between
several deformable bodies and contact with rigid obstacles.
It takes a variable of type multi_contact_frame wich describe
the contact situation (master and slave contact boundaries,
self-contact detection or not, and a few parameter).
For each slave boundary (and also master boundaries if self-contact
is asked) a multiplier variable should be defined. """
return self.set("add_integral_large_sliding_contact_brick_raytrace", multi_contact, dataname_r, dataname_fr, *args)
def add_integral_large_sliding_contact_brick_with_field_extension(self, mim, varname_u, multname, dataname_r, dataname_fr, rg):
"""(still experimental brick)
Add a large sliding contact with friction brick to the model.
This brick is able to deal with auto-contact, contact between
several deformable bodies and contact with rigid obstacles.
The condition is applied on the variable `varname_u` on the
boundary corresponding to `region`. `dataname_r` is the augmentation
parameter of the augmented Lagrangian. `dataname_friction_coeff`
is the friction coefficient. `mim` is an integration method on the
boundary. `varname_u` is the variable on which the contact condition
will be prescribed (should be of displacement type). `multname` is
a multiplier defined on the boundary which will represent the contact
force. If no additional boundary or rigid
obstacle is added, only auto-contact will be detected. Use
`add_boundary_to_large_sliding_contact_brick` and
`add_rigid_obstacle_to_large_sliding_contact_brick` to add contact
boundaries and rigid obstacles. """
return self.set("add_integral_large_sliding_contact_brick_with_field_extension", mim, varname_u, multname, dataname_r, dataname_fr, rg)
def add_boundary_to_large_sliding_contact_brick(self, indbrick, mim, varname_u, multname, rg):
"""Add a contact boundary to an existing large sliding contact brick.
indbrick` is the brick index. """
return self.set("add_boundary_to_large_sliding_contact_brick", indbrick, mim, varname_u, multname, rg)
def add_rigid_obstacle_to_large_sliding_contact_brick(self, indbrick, obs):
"""Add a rigid obstacle to an existing large sliding contact brick.
indbrick` is the brick index, `obs` is the expression of a
unction which should be closed to a signed distance to the obstacle. """
return self.set("add_rigid_obstacle_to_large_sliding_contact_brick", indbrick, obs)
#
# GetFEM class MultiContactFrame definition.
#
class MultiContactFrame:
"""GetFEM MultiContactFrame object
This object serves for describing a multi-contact situation between
potentially several deformable bodies and eventually some rigid obstacles.
(for more details see the Getfem++ user documentation).
"""
def __init__(self, *args):
"""General constructor for MultiContactFrame objects
* ``S = MultiContactFrame(Model md, int N, scalar release_distance[, bool delaunay[, bool self_contact[, scalar cut_angle[, bool use_raytrace[, int nodes_mode[, bool ref_conf]]]]]])``
Build a new multi contact frame object linked to the model `md`.
with `N` the space dimension (typically, 2 or 3), `release_distance` is
the limit distance beyond which two points are not considered in
potential contact (should be typically comparable to element sizes).
There is several optional parameters.
If `nodes_mode=0` (default value), then contact is considered
on Gauss points, `nodes_mode=1` then contact is considered on
Gauss points for slave surfaces and on f.e.m. nodes for master surfaces
(in that case, the f.e.m. should be of Lagrange type) and
`nodes_mode=2` then contact is considered on f.e.m. nodes for
both slave and master surfaces. if `use_delaunay` is true (default value),
then contact detection is done calling
`Qhull <http://www.qhull.org>`_ package to perform a Delaunay
triangulation on potential contact points. Otherwise, contact
detection is performed by conputing some influences boxes of the element
of master surfaces. If `ref_conf` is true (default value : false),
the contact detection
is made on the reference configuration (without taking into account a
displacement) CAUTION: not fully implemented for the moment.
If `self_contact` is true (default value), the contact detection is
also made
between master surfaces and for a master surface with itself.
The parameter `cut_angle` (default value: 0.3) is an angle in radian
which is used
for the simplification of unit normal cones in the case of f.e.m.
node contact : if a contact cone has an angle less than `cut_angle`
it is reduced to a mean unit normal to simplify the contact detection.
if `use_raytrace` is set to true (default is false) raytracing is used
insted of projection.
"""
generic_constructor(self,'multi_contact_frame',*args)
def __del__(self):
generic_destructor(self, destructible=True)
def get(self, *args):
return getfem('multi_contact_frame_get',self.id, *args)
def __repr__(self):
getfem('multi_contact_frame_get',self.id, 'display')
return ''
def set(self, *args):
return getfem('multi_contact_frame_set',self.id, *args)
def __str__(self):
return self.char()
def compute_pairs(self):
"""Compute the contact pairs
"""
return self.get("compute_pairs")
def slave_points(self):
"""Get the slave points computed.
"""
return self.get("slave_points")
def master_points(self):
"""Get the master points computed.
"""
return self.get("master_points")
def char(self):
"""Output a (unique) string representation of the @tmcf.
This can be used for performing comparisons between two
different @tmcf objects.
This function is to be completed.
"""
return self.get("char")
def display(self):
"""Display a short summary for a @tmcf object."""
return self.get("display")
def add_obstacle(self, obs):
"""Add a rigid obstacle. The string `obs` is the expression of a
function which should be closed to a signed distance to the obstacle.
"""
return self.set("add_obstacle", obs)
def add_slave_boundary(self, mim, region, varname, multname=None, *args):
"""Synopsis: MultiContactFrame.add_slave_boundary(self, MeshIm mim, int region, string varname [, string multname [, string wname]])
Add a slave contact bounary.
"""
return self.set("add_slave_boundary", mim, region, varname, multname, *args)
def add_master_boundary(self, mim, region, varname, multname=None, *args):
"""Synopsis: MultiContactFrame.add_master_boundary(self, MeshIm mim, int region, string varname [, string multname [, string wname]])
Add a master contact bounary.
"""
return self.set("add_master_boundary", mim, region, varname, multname, *args)
#
# GetFEM class Precond definition.
#
class Precond:
"""GetFEM Precond object
The preconditioners may store REAL or COMPLEX values. They accept getfem
sparse matrices and Matlab sparse matrices.
"""
def __init__(self, *args):
"""General constructor for Precond objects
* ``PC = Precond('identity')``
Create a REAL identity precondioner.
* ``PC = Precond('cidentity')``
Create a COMPLEX identity precondioner.
* ``PC = Precond('diagonal', vec D)``
Create a diagonal precondioner.
* ``PC = Precond('ildlt', SpMat m)``
Create an ILDLT (Cholesky) preconditioner for the (symmetric) sparse
matrix `m`. This preconditioner has the same sparsity pattern than `m`
(no fill-in).
* ``PC = Precond('ilu', SpMat m)``
Create an ILU (Incomplete LU) preconditioner for the sparse
matrix `m`. This preconditioner has the same sparsity pattern
than `m` (no fill-in).
* ``PC = Precond('ildltt', SpMat m[, int fillin[, scalar threshold]])``
Create an ILDLTT (Cholesky with filling) preconditioner for the
(symmetric) sparse matrix `m`. The preconditioner may add at most
`fillin` additional non-zero entries on each line. The default value
for `fillin` is 10, and the default threshold is1e-7.
* ``PC = Precond('ilut', SpMat m[, int fillin[, scalar threshold]])``
Create an ILUT (Incomplete LU with filling) preconditioner for the
sparse matrix `m`. The preconditioner may add at most `fillin`
additional non-zero entries on each line. The default value for
`fillin` is 10, and the default threshold is 1e-7.
* ``PC = Precond('superlu', SpMat m)``
Uses SuperLU to build an exact factorization of the sparse matrix `m`.
This preconditioner is only available if the getfem-interface was
built with SuperLU support. Note that LU factorization is likely to
eat all your memory for 3D problems.
* ``PC = Precond('spmat', SpMat m)``
Preconditionner given explicitely by a sparse matrix.
"""
generic_constructor(self,'precond',*args)
def __del__(self):
generic_destructor(self, destructible=True)
def get(self, *args):
return getfem('precond_get',self.id, *args)
def __repr__(self):
getfem('precond_get',self.id, 'display')
return ''
def __str__(self):
return self.char()
def mult(self, V):
"""Apply the preconditioner to the supplied vector."""
return self.get("mult", V)
def tmult(self, V):
"""Apply the transposed preconditioner to the supplied vector."""
return self.get("tmult", V)
def type(self):
"""Return a string describing the type of the preconditioner ('ilu', 'ildlt',..)."""
return self.get("type")
def size(self):
"""Return the dimensions of the preconditioner."""
return self.get("size")
def is_complex(self):
"""Return 1 if the preconditioner stores complex values."""
return self.get("is_complex")
def char(self):
"""Output a (unique) string representation of the Precond.
This can be used to perform comparisons between two
different Precond objects.
This function is to be completed.
"""
return self.get("char")
def display(self):
"""displays a short summary for a Precond object."""
return self.get("display")
#
# GetFEM class Slice definition.
#
class Slice:
"""GetFEM Slice object
Creation of a mesh slice. Mesh slices are very similar to a
P1-discontinuous MeshFem on which interpolation is very fast. The slice is
built from a mesh object, and a description of the slicing operation, for
example::
sl = Slice(('planar',+1,[[0],[0]],[[0],[1]]), m, 5)
cuts the original mesh with the half space {y>0}. Each convex of the
original Mesh `m` is simplexified (for example a quadrangle is splitted
into 2 triangles), and each simplex is refined 5 times.
Slicing operations can be:
* cutting with a plane, a sphere or a cylinder
* intersection or union of slices
* isovalues surfaces/volumes
* "points", "streamlines" (see below)
If the first argument is a MeshFem `mf` instead of a Mesh, and if it is
followed by a `mf`-field `u`, then the deformation `u` will be applied to the
mesh before the slicing operation.
The first argument can also be a slice.
"""
def __init__(self, *args):
"""General constructor for Slice objects
* ``sl = Slice(sliceop, {Slice sl|{Mesh m| MeshFem mf, vec U}, int refine}[, mat CVfids])``
Create a Slice using `sliceop` operation.
`sliceop` operation is specified with Tuple
or List, do not forget the extra parentheses!. The first element is the
name of the operation, followed the slicing options:
* ('none') :
Does not cut the mesh.
* ('planar', int orient, vec p, vec n) :
Planar cut. `p` and `n` define a half-space, `p` being a point belong to
the boundary of the half-space, and `n` being its normal. If `orient` is
equal to -1 (resp. 0, +1), then the slicing operation will cut the mesh
with the "interior" (resp. "boundary", "exterior") of the half-space.
`orient` may also be set to +2 which means that the mesh will be sliced,
but both the outer and inner parts will be kept.
* ('ball', int orient, vec c, scalar r) :
Cut with a ball of center `c` and radius `r`.
* ('cylinder', int orient, vec p1, vec p2, scalar r) :
Cut with a cylinder whose axis is the line `(p1, p2)` and whose radius
is `r`.
* ('isovalues', int orient, MeshFem mf, vec U, scalar s) :
Cut using the isosurface of the field `U` (defined on the MeshFem `mf`).
The result is the set `{x such that :math:`U(x) \\leq s`}` or `{x such that
`U`(x)=`s`}` or `{x such that `U`(x) >= `s`}` depending on the value of
`orient`.
* ('boundary'[, SLICEOP]) :
Return the boundary of the result of SLICEOP, where SLICEOP is any
slicing operation. If SLICEOP is not specified, then the whole mesh is
considered (i.e. it is equivalent to ('boundary',{'none'})).
* ('explode', mat Coef) :
Build an 'exploded' view of the mesh: each convex is shrinked (:math:`0 <
\\text{Coef} \\leq 1`). In the case of 3D convexes, only their faces are kept.
* ('union', SLICEOP1, SLICEOP2) :
Returns the union of slicing operations.
* ('intersection', SLICEOP1, SLICEOP2) :
Returns the intersection of slicing operations, for example::
sl = Slice((intersection',('planar',+1,[[0],[0],[0]],[[0],[0],[1]]),
('isovalues',-1,mf2,u2,0)),mf,u,5)
* ('comp', SLICEOP) :
Returns the complementary of slicing operations.
* ('diff', SLICEOP1, SLICEOP2) :
Returns the difference of slicing operations.
* ('mesh', Mesh m) :
Build a slice which is the intersection of the sliced mesh with another
mesh. The slice is such that all of its simplexes are stricly contained
into a convex of each mesh.
* ``sl = Slice('streamlines', MeshFem mf, mat U, mat S)``
Compute streamlines of the (vector) field `U`, with seed points given
by the columns of `S`.
* ``sl = Slice('points', Mesh m, mat Pts)``
Return the "slice" composed of points given by the columns of `Pts`
(useful for interpolation on a given set of sparse points, see
``gf_compute('interpolate on',sl)``.
* ``sl = Slice('load', string filename[, Mesh m])``
Load the slice (and its linked mesh if it is not given as an argument)
from a text file.
"""
generic_constructor(self,'slice',*args)
def __del__(self):
generic_destructor(self, destructible=True)
def get(self, *args):
return getfem('slice_get',self.id, *args)
def __repr__(self):
getfem('slice_get',self.id, 'display')
return ''
def set(self, *args):
return getfem('slice_set',self.id, *args)
def __str__(self):
return self.char()
def dim(self):
"""Return the dimension of the slice (2 for a 2D mesh, etc..)."""
return self.get("dim")
def area(self):
"""Return the area of the slice."""
return self.get("area")
def cvs(self):
"""Return the list of convexes of the original mesh contained in the slice."""
return self.get("cvs")
def nbpts(self):
"""Return the number of points in the slice."""
return self.get("nbpts")
def nbsplxs(self, dim=None):
"""Return the number of simplexes in the slice.
Since the slice may contain points (simplexes of dim 0), segments
(simplexes of dimension 1), triangles etc., the result is a vector
of size Slice.dim()+1, except if the optional argument `dim`
is used."""
return self.get("nbsplxs", dim)
def pts(self):
"""Return the list of point coordinates."""
return self.get("pts")
def splxs(self, dim):
"""Return the list of simplexes of dimension `dim`.
On output, S has 'dim+1' rows, each column contains the point
numbers of a simplex. The vector `CV2S` can be used to find the
list of simplexes for any convex stored in the slice. For example
'S[:,CV2S[4]:CV2S[5]]'
gives the list of simplexes for the fourth convex."""
return self.get("splxs", dim)
def edges(self):
"""Return the edges of the linked mesh contained in the slice.
`P` contains the list of all edge vertices, `E1` contains
the indices of each mesh edge in `P`, and `E2` contains the
indices of each "edges" which is on the border of the slice.
This function is useless except for post-processing purposes."""
return self.get("edges")
def interpolate_convex_data(self, Ucv):
"""Interpolate data given on each convex of the mesh to the slice nodes.
The input array `Ucv` may have any number of dimensions, but its
last dimension should be equal to Mesh.max_cvid().
Example of use: Slice.interpolate_convex_data(Mesh.quality())."""
return self.get("interpolate_convex_data", Ucv)
def linked_mesh(self):
"""Return the mesh on which the slice was taken."""
return self.get("linked_mesh")
def mesh(self):
"""Return the mesh on which the slice was taken
(identical to 'linked mesh')"""
return self.get("mesh")
def memsize(self):
"""Return the amount of memory (in bytes) used by the slice object."""
return self.get("memsize")
def export_to_vtk(self, filename, *args):
"""Synopsis: Slice.export_to_vtk(self, string filename, ...)
Export a slice to VTK.
Following the `filename`, you may use any of the following options:
- if 'ascii' is not used, the file will contain binary data
(non portable, but fast).
- if 'edges' is used, the edges of the original mesh will be
written instead of the slice content.
More than one dataset may be written, just list them. Each dataset
consists of either:
- a field interpolated on the slice (scalar, vector or tensor),
followed by an optional name.
- a mesh_fem and a field, followed by an optional name.
Examples:
- Slice.export_to_vtk('test.vtk', Usl, 'first_dataset', mf,
U2, 'second_dataset')
- Slice.export_to_vtk('test.vtk', 'ascii', mf,U2)
- Slice.export_to_vtk('test.vtk', 'edges', 'ascii', Uslice)"""
return self.get("export_to_vtk", filename, *args)
def export_to_pov(self, filename):
"""Export a the triangles of the slice to POV-RAY."""
return self.get("export_to_pov", filename)
def export_to_dx(self, filename, *args):
"""Synopsis: Slice.export_to_dx(self, string filename, ...)
Export a slice to OpenDX.
Following the `filename`, you may use any of the following
options:
- if 'ascii' is not used, the file will contain binary data
(non portable, but fast).
- if 'edges' is used, the edges of the original mesh will be
written instead of the slice content.
- if 'append' is used, the opendx file will not be overwritten,
and the new data will be added at the end of the file.
More than one dataset may be written, just list them. Each dataset
consists of either:
- a field interpolated on the slice (scalar, vector or tensor),
followed by an optional name.
- a mesh_fem and a field, followed by an optional name."""
return self.get("export_to_dx", filename, *args)
def export_to_pos(self, filename, name=None, *args):
"""Synopsis: Slice.export_to_pos(self, string filename[, string name][[,MeshFem mf1], mat U1, string nameU1[[,MeshFem mf1], mat U2, string nameU2,...])
Export a slice to Gmsh.
More than one dataset may be written, just list them.
Each dataset consists of either:
- a field interpolated on the slice (scalar, vector or tensor).
- a mesh_fem and a field."""
return self.get("export_to_pos", filename, name, *args)
def char(self):
"""Output a (unique) string representation of the Slice.
This can be used to perform comparisons between two
different Slice objects.
This function is to be completed.
"""
return self.get("char")
def display(self):
"""displays a short summary for a Slice object."""
return self.get("display")
def set_pts(self, P):
"""Replace the points of the slice.
The new points `P` are stored in the columns the matrix. Note that
you can use the function to apply a deformation to a slice, or to
change the dimension of the slice (the number of rows of `P` is not
required to be equal to Slice.dim())."""
return self.set("pts", P)
#
# GetFEM class Spmat definition.
#
class Spmat:
"""GetFEM Spmat object
Create a new sparse matrix in getfem++ format. These sparse matrix can be stored as CSC (compressed column
sparse), which is the format used by Matlab, or they can be stored as WSC
(internal format to getfem). The CSC matrices are not writable (it would
be very inefficient), but they are optimized for multiplication with
vectors, and memory usage. The WSC are writable, they are very fast with
respect to random read/write operation. However their memory overhead is
higher than CSC matrices, and they are a little bit slower for
matrix-vector multiplications.
By default, all newly created matrices are build as WSC matrices. This can
be changed later with ``Spmat.to_csc(...)``, or may be changed
automatically by getfem (for example ``gf_linsolve()`` converts the
matrices to CSC).
The matrices may store REAL or COMPLEX values.
"""
def __init__(self, *args):
"""General constructor for Spmat objects
* ``SM = Spmat('empty', int m [, int n])``
Create a new empty (i.e. full of zeros) sparse matrix, of dimensions
`m x n`. If `n` is omitted, the matrix dimension is `m x m`.
* ``SM = Spmat('copy', mat K [, list I [, list J]])``
Duplicate a matrix `K` (which might be a SpMat). If index `I` and/or `J` are given, the matrix will
be a submatrix of `K`. For example::
m = Spmat('copy', Spmat('empty',50,50), range(40), [6, 7, 8, 3, 10])
will return a 40x5 matrix.
* ``SM = Spmat('identity', int n)``
Create a `n x n` identity matrix.
* ``SM = Spmat('mult', Spmat A, Spmat B)``
Create a sparse matrix as the product of the sparse matrices `A` and
`B`. It requires that `A` and `B` be both real or both complex, you
may have to use ``Spmat.to_complex()``
* ``SM = Spmat('add', Spmat A, Spmat B)``
Create a sparse matrix as the sum of the sparse matrices `A` and `B`.
Adding a real matrix with a complex matrix is possible.
* ``SM = Spmat('diag', mat D [, ivec E [, int n [,int m]]])``
Create a diagonal matrix. If `E` is given, `D` might be a matrix and
each column of `E` will contain the sub-diagonal number that will be
filled with the corresponding column of `D`.
* ``SM = Spmat('load','hb'|'harwell-boeing'|'mm'|'matrix-market', string filename)``
Read a sparse matrix from an Harwell-Boeing or a Matrix-Market file
.
"""
generic_constructor(self,'spmat',*args)
def __del__(self):
generic_destructor(self, destructible=True)
def get(self, *args):
return getfem('spmat_get',self.id, *args)
def __repr__(self):
getfem('spmat_get',self.id, 'display')
return ''
def set(self, *args):
return getfem('spmat_set',self.id, *args)
def __str__(self):
return self.char()
def __getitem__(self, key):
return getfem('spmat_get',self.id, 'full',*key)
def __setitem__(self, key, keyval):
getfem('spmat_set', self.id, 'assign', key[0], key[1], keyval)
def __neg__(self):
m=Spmat('copy',self)
m.scale(-1)
return m
def __add__(self, other):
return Spmat('add',self,other)
def __sub__(self, other):
return Spmat('add',self,other.__neg__())
def __mul__(self, other):
"""Multiplication of a Spmat with another Spmat or a vector or a scalar.
The result is another Spmat object.
"""
if isinstance(other,numbers.Number):
m = Spmat('copy',self)
m.set('scale',other)
elif (isinstance(other,list) or isinstance(other, numpy.ndarray)):
m = self.mult(other)
else:
m = Spmat('mult',self,other)
return m
def __rmul__(self, other):
if isinstance(other,numbers.Number):
m=Spmat('copy',self)
m.set('scale',other)
elif (isinstance(other,list) or isinstance(other, numpy.ndarray)):
m=self.tmult(other)
else:
m=Spmat('mult',other,self)
return m;
def nnz(self):
"""Return the number of non-null values stored in the sparse matrix."""
return self.get("nnz")
def full(self, I=None, *args):
"""Synopsis: Sm = Spmat.full(self[, list I[, list J]])
Return a full (sub-)matrix.
The optional arguments `I` and `J`, are the sub-intervals for the
rows and columns that are to be extracted."""
return self.get("full", I, *args)
def mult(self, V):
"""Product of the sparse matrix `M` with a vector `V`.
For matrix-matrix multiplications, see Spmat('mult')."""
return self.get("mult", V)
def tmult(self, V):
"""Product of `M` transposed (conjugated if `M` is complex) with the
vector `V`."""
return self.get("tmult", V)
def diag(self, E=None):
"""Return the diagonal of `M` as a vector.
If `E` is used, return the sub-diagonals whose ranks are given in E."""
return self.get("diag", E)
def storage(self):
"""Return the storage type currently used for the matrix.
The storage is returned as a string, either 'CSC' or 'WSC'."""
return self.get("storage")
def size(self):
"""Return a vector where `ni` and `nj` are the dimensions of the matrix."""
return self.get("size")
def is_complex(self):
"""Return 1 if the matrix contains complex values."""
return self.get("is_complex")
def csc_ind(self):
"""Return the two usual index arrays of CSC storage.
If `M` is not stored as a CSC matrix, it is converted into CSC."""
return self.get("csc_ind")
def csc_val(self):
"""Return the array of values of all non-zero entries of `M`.
If `M` is not stored as a CSC matrix, it is converted into CSC."""
return self.get("csc_val")
def dirichlet_nullspace(self, R):
"""Solve the dirichlet conditions `M.U=R`.
A solution `U0` which has a minimum L2-norm is returned, with a
sparse matrix `N` containing an orthogonal basis of the kernel of
the (assembled) constraints matrix `M` (hence, the PDE linear system
should be solved on this subspace): the initial problem
`K.U = B` with constraints `M.U = R`
is replaced by
`(N'.K.N).UU = N'.B` with `U = N.UU + U0`"""
return self.get("dirichlet_nullspace", R)
def save(self, format, filename):
"""Export the sparse matrix.
the format of the file may be 'hb' for Harwell-Boeing, or 'mm'
for Matrix-Market."""
return self.get("save", format, filename)
def char(self):
"""Output a (unique) string representation of the Spmat.
This can be used to perform comparisons between two
different Spmat objects.
This function is to be completed.
"""
return self.get("char")
def display(self):
"""displays a short summary for a Spmat object."""
return self.get("display")
def clear(self, I=None, *args):
"""Synopsis: Spmat.clear(self[, list I[, list J]])
Erase the non-zero entries of the matrix.
The optional arguments `I` and `J` may be specified to clear a
sub-matrix instead of the entire matrix."""
return self.set("clear", I, *args)
def scale(self, v):
"""Multiplies the matrix by a scalar value `v`."""
return self.set("scale", v)
def transpose(self):
"""Transpose the matrix."""
return self.set("transpose")
def conjugate(self):
"""Conjugate each element of the matrix."""
return self.set("conjugate")
def transconj(self):
"""Transpose and conjugate the matrix."""
return self.set("transconj")
def to_csc(self):
"""Convert the matrix to CSC storage.
CSC storage is recommended for matrix-vector multiplications."""
return self.set("to_csc")
def to_wsc(self):
"""Convert the matrix to WSC storage.
Read and write operation are quite fast with WSC storage."""
return self.set("to_wsc")
def to_complex(self):
"""Store complex numbers."""
return self.set("to_complex")
def set_diag(self, D, E=None):
"""Change the diagonal (or sub-diagonals) of the matrix.
If `E` is given, `D` might be a matrix and each column of `E` will
contain the sub-diagonal number that will be filled with the
corresponding column of `D`."""
return self.set("diag", D, E)
def assign(self, I, J, V):
"""Copy V into the sub-matrix 'M(I,J)'.
`V` might be a sparse matrix or a full matrix."""
return self.set("assign", I, J, V)
def add(self, I, J, V):
"""Add `V` to the sub-matrix 'M(I,J)'.
`V` might be a sparse matrix or a full matrix."""
return self.set("add", I, J, V)
#
# asm module
#
def asm_mass_matrix(mim, mf1, mf2=None, *args):
"""Synopsis: M = asm_mass_matrix(MeshIm mim, MeshFem mf1[, MeshFem mf2[, boundary_num]])
Assembly of a mass matrix.
Return a SpMat object.
"""
return getfem('asm', 'mass_matrix', mim, mf1, mf2, *args)
def asm_lsneuman_matrix(mim, mf1, mf2, ls):
"""Assembly of a level set Neuman matrix.
Return a SpMat object.
"""
return getfem('asm', 'lsneuman_matrix', mim, mf1, mf2, ls)
def asm_nlsgrad_matrix(mim, mf1, mf2, ls):
"""Assembly of a nlsgrad matrix.
Return a SpMat object.
"""
return getfem('asm', 'nlsgrad_matrix', mim, mf1, mf2, ls)
def asm_stabilization_patch_matrix(mesh, mf, mim, ratio, h):
"""Assembly of stabilization patch matrix .
Return a SpMat object.
"""
return getfem('asm', 'stabilization_patch_matrix', mesh, mf, mim, ratio, h)
def asm_laplacian(mim, mf_u, mf_d, a):
"""Assembly of the matrix for the Laplacian problem.
:math:`\\nabla\\cdot(a(x)\\nabla u)` with `a` a scalar.
Return a SpMat object.
"""
return getfem('asm', 'laplacian', mim, mf_u, mf_d, a)
def asm_linear_elasticity(mim, mf_u, mf_d, lambda_d, mu_d):
"""Assembles of the matrix for the linear (isotropic) elasticity problem.
:math:`\\nabla\\cdot(C(x):\\nabla u)`
with :math:`C` defined via `lambda_d` and `mu_d`.
Return a SpMat object.
"""
return getfem('asm', 'linear_elasticity', mim, mf_u, mf_d, lambda_d, mu_d)
def asm_nonlinear_elasticity(mim, mf_u, U, law, mf_d, params, *args):
"""Synopsis: TRHS = asm_nonlinear_elasticity(MeshIm mim, MeshFem mf_u, vec U, string law, MeshFem mf_d, mat params, {'tangent matrix'|'rhs'|'incompressible tangent matrix', MeshFem mf_p, vec P|'incompressible rhs', MeshFem mf_p, vec P})
Assembles terms (tangent matrix and right hand side) for nonlinear elasticity.
The solution `U` is required at the current time-step. The `law`
may be choosen among:
- 'SaintVenant Kirchhoff':
Linearized law, should be avoided). This law has the two usual
Lame coefficients as parameters, called lambda and mu.
- 'Mooney Rivlin':
This law has three parameters, called C1, C2 and D1.
Can be preceded with the words 'compressible' or 'incompressible' to force
a specific version. By default, the incompressible version is considered
which requires only the first two material coefficients.
- 'neo Hookean':
A special case of the 'Mooney Rivlin' law that requires one material
coefficient less (C2 = 0). By default, its compressible version is used.
- 'Ciarlet Geymonat':
This law has 3 parameters, called lambda, mu and gamma, with
gamma chosen such that gamma is in ]-lambda/2-mu, -mu[.
Te parameters of the material law are described on the MeshFem `mf_d`.
Te matrix `params` should have `nbdof(mf_d)` columns, each row
crrespounds to a parameter.
Te last argument selects what is to be built: either the tangent
mtrix, or the right hand side. If the incompressibility is
cnsidered, it should be followed by a MeshFem `mf_p`, for the
pession.
Rturn a SpMat object (tangent matrix), vec object (right hand
sde), tuple of SpMat objects (incompressible tangent matrix), or
tple of vec objects (incompressible right hand side).
"""
return getfem('asm', 'nonlinear_elasticity', mim, mf_u, U, law, mf_d, params, *args)
def asm_stokes(mim, mf_u, mf_p, mf_d, nu):
"""Assembly of matrices for the Stokes problem.
:math:`-\\nu(x)\\Delta u + \\nabla p = 0`
:math:`\\nabla\\cdot u = 0`
with :math:`\\nu` (`nu`), the fluid's dynamic viscosity.
On output, `K` is the usual linear elasticity stiffness matrix with
:math:`\\lambda = 0` and
:math:`2\\mu = \\nu`. `B` is a matrix
corresponding to :math:`\\int p\\nabla\\cdot\\phi`.
`K` and `B` are SpMat object's.
"""
return getfem('asm', 'stokes', mim, mf_u, mf_p, mf_d, nu)
def asm_helmholtz(mim, mf_u, mf_d, k):
"""Assembly of the matrix for the Helmholtz problem.
:math:`\\Delta u + k^2 u` = 0, with `k` complex scalar.
Return a SpMat object.
"""
return getfem('asm', 'helmholtz', mim, mf_u, mf_d, k)
def asm_bilaplacian(mim, mf_u, mf_d, a):
"""Assembly of the matrix for the Bilaplacian problem.
:math:`\\Delta(a(x)\\Delta u) = 0` with `a` scalar.
Return a SpMat object.
"""
return getfem('asm', 'bilaplacian', mim, mf_u, mf_d, a)
def asm_bilaplacian_KL(mim, mf_u, mf_d, a, nu):
"""Assembly of the matrix for the Bilaplacian problem with Kirchoff-Love formulation.
:math:`\\Delta(a(x)\\Delta u) = 0` with `a` scalar.
Return a SpMat object.
"""
return getfem('asm', 'bilaplacian_KL', mim, mf_u, mf_d, a, nu)
def asm_volumic_source(mim, mf_u, mf_d, fd):
"""Assembly of a volumic source term.
Output a vector `V`, assembled on the MeshFem `mf_u`, using the data
vector `fd` defined on the data MeshFem `mf_d`. `fd` may be real or
complex-valued.
Return a vec object.
"""
return getfem('asm', 'volumic_source', mim, mf_u, mf_d, fd)
def asm_boundary_source(bnum, mim, mf_u, mf_d, G):
"""Assembly of a boundary source term.
`G` should be a [Qdim x N] matrix, where N is the number of dof
of `mf_d`, and Qdim is the dimension of the unkown u (that is set
when creating the MeshFem).
Return a vec object.
"""
return getfem('asm', 'boundary_source', bnum, mim, mf_u, mf_d, G)
def asm_dirichlet(bnum, mim, mf_u, mf_d, H, R, threshold=None):
"""Assembly of Dirichlet conditions of type `h.u = r`.
Handle `h.u = r` where h is a square matrix (of any rank) whose
size is equal to the dimension of the unkown u. This matrix is
stored in `H`, one column per dof in `mf_d`, each column containing
the values of the matrix h stored in fortran order:
.. math::
`H(:,j) = [h11(x_j) h21(x_j) h12(x_j) h22(x_j)]`
if u is a 2D vector field.
Of course, if the unknown is a scalar field, you just have to set
`H = ones(1, N)`, where N is the number of dof of `mf_d`.
This is basically the same than calling gf_asm('boundary qu term')
for `H` and calling gf_asm('neumann') for `R`, except that this
function tries to produce a 'better' (more diagonal) constraints
matrix (when possible).
See also Spmat.Dirichlet_nullspace()."""
return getfem('asm', 'dirichlet', bnum, mim, mf_u, mf_d, H, R, threshold)
def asm_boundary_qu_term(boundary_num, mim, mf_u, mf_d, q):
"""Assembly of a boundary qu term.
`q` should be be a [Qdim x Qdim x N] array, where N is the number
of dof of `mf_d`, and Qdim is the dimension of the unkown u (that
is set when creating the MeshFem).
Return a SpMat object.
"""
return getfem('asm', 'boundary_qu_term', boundary_num, mim, mf_u, mf_d, q)
def asm_define_function(name, nb_args, expression, expression_derivative_t=None, *args):
"""Synopsis: asm_define_function(string name, int nb_args, string expression[, string expression_derivative_t[, string expression_derivative_u]])
Define a new function `name` which can be used in high level
generic assembly. The function can have one or two parameters.
In `expression` all available predefined function or operation
of the generic assembly can be used. However, no reference to
some variables or data can be specified. The argument of the
function is `t` for a one parameter function and `t` and `u`
for a two parameter function. For instance 'sin(pi*t)+2*t*t'
is a valid expression for a one parameter function and
'sin(max(t,u)*pi)' is a valid expression for a two parameters
function. `expression_derivative_t` and `expression_derivative_u`
are optional expressions for the derivatives with respect
to `t` and `u`. If they are not furnished, a symbolic derivation
is used. """
return getfem('asm', 'define_function', name, nb_args, expression, expression_derivative_t, *args)
def asm_undefine_function(name):
"""Cancel the definition of a previously defined function `name`
for the high level generic assembly. """
return getfem('asm', 'undefine_function', name)
def asm_generic(mim, order, expression, region, varname=None, is_variable=None, *args):
"""Synopsis: (...) = asm_generic(MeshIm mim, int order, string expression, int region, [string varname, int is_variable[, MeshFem mesh_fem], value], ...)
High-level generic assembly procedure for volumic assembly.
Performs the generic assembly of `expression` with the integration
method `mim` on the mesh region of index `region' (-1 means all
the element of the mesh). The smae mesh should be shared by
the integration method and all the finite element methods
corresponding to the variables.
`order` indicates either that the (scalar) potential
(order = 0) or the (vector) residual (order = 1) or the
tangent (matrix) (order = 2) is to be computed.
The variables and constant (data) are listed after the
region number. For each variable/constant, first the variable/constant
name should be given (as it is referred in the assembly string), then
1 if it is a variable or 0 for a constant, then the finite element
method if it is a fem variable/constant, and the vector representing
the value of the variable/constant. It is possible to give an arbitrary
number of variable/constant. The difference between a variable and a
constant is that automatic differentiation is done with respect to
variables only (see Getfem++ user documentation). Test functions are
only available for variables, not for constants.
Note that if several variables are given, the assembly of the
tangent matrix/residual vector will be done considering the order
in the call of the function (the degrees of freedom of the first
variable, then of the second, and so on).
For example, the L2 norm of a vector field "u" can be computed with::
gf_compute('L2 norm') or with the square root of:
gf_asm('generic', mim, 0, 'u.u', -1, 'u', 1, mf, U);
The nonhomogeneous Laplacian stiffness matrix of a scalar field can be evaluated with::
gf_asm('laplacian', mim, mf, mf_data, A) or equivalently with:
gf_asm('generic', mim, 2, 'A*Grad_Test2_u.Grad_Test_u', -1, 'u', 1, mf, U, 'A', 0, mf_data, A);
"""
return getfem('asm', 'generic', mim, order, expression, region, varname, is_variable, *args)
def asm_volumic(CVLST=None, *args):
"""Synopsis: (...) = asm_volumic(,CVLST], expr [, mesh_ims, mesh_fems, data...])
Low-level generic assembly procedure for volumic assembly.
The expression `expr` is evaluated over the MeshFem's listed in the
arguments (with optional data) and assigned to the output arguments.
For details about the syntax of assembly expressions, please refer
to the getfem user manual (or look at the file getfem_assembling.h
in the getfem++ sources).
For example, the L2 norm of a field can be computed with::
gf_compute('L2 norm') or with the square root of:
gf_asm('volumic','u=data(#1); V()+=u(i).u(j).comp(Base(#1).Base(#1))(i,j)',mim,mf,U)
The Laplacian stiffness matrix can be evaluated with::
gf_asm('laplacian',mim, mf, mf_data, A) or equivalently with:
gf_asm('volumic','a=data(#2);M(#1,#1)+=sym(comp(Grad(#1).Grad(#1).Base(#2))(:,i,:,i,j).a(j))', mim,mf,mf_data,A);"""
return getfem('asm', 'volumic', CVLST, *args)
def asm_boundary(bnum, expr, mim=None, mf=None, data=None, *args):
"""Synopsis: (...) = asm_boundary(int bnum, string expr [, MeshIm mim, MeshFem mf, data...])
Low-level generic boundary assembly.
See the help for gf_asm('volumic')."""
return getfem('asm', 'boundary', bnum, expr, mim, mf, data, *args)
def asm_interpolation_matrix(mf, mfi):
"""Build the interpolation matrix from a MeshFem onto another MeshFem.
Return a matrix `Mi`, such that `V = Mi.U` is equal to
gf_compute('interpolate_on',mfi). Useful for repeated interpolations.
Note that this is just interpolation, no elementary integrations
are involved here, and `mfi` has to be lagrangian. In the more
general case, you would have to do a L2 projection via the mass
matrix.
`Mi` is a SpMat object.
"""
return getfem('asm', 'interpolation_matrix', mf, mfi)
def asm_extrapolation_matrix(mf, mfe):
"""Build the extrapolation matrix from a MeshFem onto another MeshFem.
Return a matrix `Me`, such that `V = Me.U` is equal to
gf_compute('extrapolate_on',mfe). Useful for repeated
extrapolations.
`Me` is a SpMat object.
"""
return getfem('asm', 'extrapolation_matrix', mf, mfe)
def asm_integral_contact_Uzawa_projection(bnum, mim, mf_u, U, mf_lambda, vec_lambda, mf_obstacle, obstacle, r, *args):
"""Synopsis: B = asm_integral_contact_Uzawa_projection(int bnum, MeshIm mim, MeshFem mf_u, vec U, MeshFem mf_lambda, vec vec_lambda, MeshFem mf_obstacle, vec obstacle, scalar r [, {scalar coeff | MeshFem mf_coeff, vec coeff} [, int option[, scalar alpha, vec W]]])
Specific assembly procedure for the use of an Uzawa algorithm to solve
contact problems. Projects the term $-(\\lambda - r (u_N-g))_-$ on the
finite element space of $\\lambda$.
Return a vec object.
"""
return getfem('asm', 'integral_contact_Uzawa_projection', bnum, mim, mf_u, U, mf_lambda, vec_lambda, mf_obstacle, obstacle, r, *args)
def asm_level_set_normal_source_term(bnum, mim, mf_u, mf_lambda, vec_lambda, mf_levelset, levelset):
"""Performs an assembly of the source term represented by `vec_lambda`
on `mf_lambda` considered to be a component in the direction of the
gradient of a levelset function (normal to the levelset) of a vector
field defined on `mf_u` on the boundary `bnum`.
Return a vec object.
"""
return getfem('asm', 'level_set_normal_source_term', bnum, mim, mf_u, mf_lambda, vec_lambda, mf_levelset, levelset)
#
# compute module
#
def compute_L2_norm(MF, U, mim, CVids=None):
"""Compute the L2 norm of the (real or complex) field `U`.
If `CVids` is given, the norm will be computed only on the listed
convexes."""
return getfem('compute', MF, U, 'L2_norm', mim, CVids)
def compute_L2_dist(MF, U, mim, mf2, U2, CVids=None):
"""Compute the L2 distance between `U` and `U2`.
If `CVids` is given, the norm will be computed only on the listed
convexes."""
return getfem('compute', MF, U, 'L2_dist', mim, mf2, U2, CVids)
def compute_H1_semi_norm(MF, U, mim, CVids=None):
"""Compute the L2 norm of grad(`U`).
If `CVids` is given, the norm will be computed only on the listed
convexes."""
return getfem('compute', MF, U, 'H1_semi_norm', mim, CVids)
def compute_H1_semi_dist(MF, U, mim, mf2, U2, CVids=None):
"""Compute the semi H1 distance between `U` and `U2`.
If `CVids` is given, the norm will be computed only on the listed
convexes."""
return getfem('compute', MF, U, 'H1_semi_dist', mim, mf2, U2, CVids)
def compute_H1_norm(MF, U, mim, CVids=None):
"""Compute the H1 norm of `U`.
If `CVids` is given, the norm will be computed only on the listed
convexes."""
return getfem('compute', MF, U, 'H1_norm', mim, CVids)
def compute_H2_semi_norm(MF, U, mim, CVids=None):
"""Compute the L2 norm of D^2(`U`).
If `CVids` is given, the norm will be computed only on the listed
convexes."""
return getfem('compute', MF, U, 'H2_semi_norm', mim, CVids)
def compute_H2_norm(MF, U, mim, CVids=None):
"""Compute the H2 norm of `U`.
If `CVids` is given, the norm will be computed only on the listed
convexes."""
return getfem('compute', MF, U, 'H2_norm', mim, CVids)
def compute_gradient(MF, U, mf_du):
"""Compute the gradient of the field `U` defined on MeshFem `mf_du`.
The gradient is interpolated on the MeshFem `mf_du`, and returned in
`DU`. For example, if `U` is defined on a P2 MeshFem, `DU` should be
evaluated on a P1-discontinuous MeshFem. `mf` and `mf_du` should
share the same mesh.
`U` may have any number of dimensions (i.e. this function is not
restricted to the gradient of scalar fields, but may also be used
for tensor fields). However the last dimension of `U` has to be
equal to the number of dof of `mf`. For example, if `U` is a
[3x3xNmf] array (where Nmf is the number of dof of `mf`), `DU` will
be a [Nx3x3[xQ]xNmf_du] array, where N is the dimension of the mesh,
Nmf_du is the number of dof of `mf_du`, and the optional Q dimension
is inserted if `Qdim_mf != Qdim_mf_du`, where Qdim_mf is the Qdim of
`mf` and Qdim_mf_du is the Qdim of `mf_du`."""
return getfem('compute', MF, U, 'gradient', mf_du)
def compute_hessian(MF, U, mf_h):
"""Compute the hessian of the field `U` defined on MeshFem `mf_h`.
See also gf_compute('gradient', MeshFem mf_du)."""
return getfem('compute', MF, U, 'hessian', mf_h)
def compute_eval_on_triangulated_surface(MF, U, Nrefine, CVLIST=None):
"""[OBSOLETE FUNCTION! will be removed in a future release]
Utility function designed for 2D triangular meshes : returns a list
of triangles coordinates with interpolated U values. This can be
used for the accurate visualization of data defined on a
discontinous high order element. On output, the six first rows of UP
contains the triangle coordinates, and the others rows contain the
interpolated values of U (one for each triangle vertex) CVLIST may
indicate the list of convex number that should be consider, if not
used then all the mesh convexes will be used. U should be a row
vector.
"""
return getfem('compute', MF, U, 'eval_on_triangulated_surface', Nrefine, CVLIST)
def compute_interpolate_on(MF, U, *args):
"""Synopsis: Ui = compute_interpolate_on(MeshFem MF, vec U, {MeshFem mfi | Slice sli | vec pts})
Interpolate a field on another MeshFem or a Slice or a list of points.
- Interpolation on another MeshFem `mfi`:
`mfi` has to be Lagrangian. If `mf` and `mfi` share the same
mesh object, the interpolation will be much faster.
- Interpolation on a Slice `sli`:
this is similar to interpolation on a refined P1-discontinuous
mesh, but it is much faster. This can also be used with
Slice('points') to obtain field values at a given set of
points.
- Interpolation on a set of points `pts`
See also gf_asm('interpolation matrix')
"""
return getfem('compute', MF, U, 'interpolate_on', *args)
def compute_extrapolate_on(MF, U, mfe):
"""Extrapolate a field on another MeshFem.
If the mesh of `mfe` is stricly included in the mesh of `mf`, this
function does stricly the same job as gf_compute('interpolate_on').
However, if the mesh of `mfe` is not exactly included in `mf`
(imagine interpolation between a curved refined mesh and a coarse
mesh), then values which are outside `mf` will be
extrapolated.
See also gf_asm('extrapolation matrix')"""
return getfem('compute', MF, U, 'extrapolate_on', mfe)
def compute_error_estimate(MF, U, mim):
"""Compute an a posteriori error estimate.
Currently there is only one which is available: for each convex,
the jump of the normal derivative is integrated on its faces."""
return getfem('compute', MF, U, 'error_estimate', mim)
def compute_error_estimate_nitsche(MF, U, mim, GAMMAC, GAMMAN, lambda_, mu_, gamma0, f_coeff):
"""Compute an a posteriori error estimate in the case of Nitsche method.
Currently there is only one which is available: for each convex,
the jump of the normal derivative is integrated on its faces."""
return getfem('compute', MF, U, 'error_estimate_nitsche', mim, GAMMAC, GAMMAN, lambda_, mu_, gamma0, f_coeff)
def compute_convect(MF, U, mf_v, V, dt, nt, option=None, *args):
"""Synopsis: E = compute_convect(MeshFem MF, vec U, MeshFem mf_v, vec V, scalar dt, int nt[, string option[, vec per_min, vec per_max]])
Compute a convection of `U` with regards to a steady state velocity
field `V` with a Characteristic-Galerkin method. This
method is restricted to pure Lagrange fems for U. `mf_v` should represent
a continuous finite element method. `dt` is the integration time and `nt`
is the number of integration step on the caracteristics. `option` is an
option for the part of the boundary where there is a re-entrant convection.
`option = 'extrapolation'` for an extrapolation on the nearest element,
`option = 'unchanged'` for a constant value on that boundary or
`option = 'periodicity'` for a peridiodic boundary. For this latter option
the two vectors per_min, per_max has to be given and represent the limits
of the periodic domain (on components where per_max[k] < per_min[k]
no operation is done).
This method is rather dissipative, but stable.
"""
return getfem('compute', MF, U, 'convect', mf_v, V, dt, nt, option, *args)
#
# delete module
#
def delete(I, J=None, K=None, *args):
"""Synopsis: delete(I[, J, K,...])
I should be a descriptor given by gf_mesh(),
gf_mesh_im(), gf_slice() etc.
Note that if another object uses I, then object I will be deleted only
when both have been asked for deletion.
Only objects listed in the output of gf_workspace('stats') can be
deleted (for example gf_fem objects cannot be destroyed).
You may also use gf_workspace('clear all') to erase everything at
once.
"""
return getfem('delete', I, J, K, *args)
#
# linsolve module
#
def linsolve_gmres(M, b, restart=None, *args):
"""Synopsis: X = linsolve_gmres(SpMat M, vec b[, int restart][, Mrecond P][,'noisy'][,'res', r][,'maxiter', n])
Solve `M.X = b` with the generalized minimum residuals method.
Optionally using `P` as preconditioner. The default value of the
restart parameter is 50."""
return getfem('linsolve', 'gmres', M, b, restart, *args)
def linsolve_cg(M, b, P=None, *args):
"""Synopsis: X = linsolve_cg(SpMat M, vec b [, Mrecond P][,'noisy'][,'res', r][,'maxiter', n])
Solve `M.X = b` with the conjugated gradient method.
Optionally using `P` as preconditioner."""
return getfem('linsolve', 'cg', M, b, P, *args)
def linsolve_bicgstab(M, b, P=None, *args):
"""Synopsis: X = linsolve_bicgstab(SpMat M, vec b [, Mrecond P][,'noisy'][,'res', r][,'maxiter', n])
Solve `M.X = b` with the bi-conjugated gradient stabilized method.
Optionally using `P` as a preconditioner."""
return getfem('linsolve', 'bicgstab', M, b, P, *args)
def linsolve_lu(M, b):
"""Alias for gf_linsolve('superlu',...)"""
return getfem('linsolve', 'lu', M, b)
def linsolve_superlu(M, b):
"""Solve `M.U = b` apply the SuperLU solver (sparse LU factorization).
The condition number estimate `cond` is returned with the solution `U`."""
return getfem('linsolve', 'superlu', M, b)
#
# poly module
#
def poly_print(P):
"""Prints the content of P.
"""
return getfem('poly', P, 'print')
def poly_product(P):
"""To be done ... !
"""
return getfem('poly', P, 'product')
#
# undelete module
#
def undelete(I, J=None, K=None, *args):
"""Synopsis: undelete(I[, J, K,...])
I should be a descriptor given by gf_mesh(), gf_mesh_im(),
gf_slice() etc.
"""
return getfem('undelete', I, J, K, *args)
#
# util module
#
def util_save_matrix(FMT, FILENAME, A):
"""Exports a sparse matrix into the file named FILENAME, using
Harwell-Boeing (FMT='hb') or Matrix-Market (FMT='mm') formatting. """
return getfem('util', 'save_matrix', FMT, FILENAME, A)
def util_load_matrix(FMT, FILENAME):
"""Imports a sparse matrix from a file."""
return getfem('util', 'load_matrix', FMT, FILENAME)
def util_trace_level(level=None):
"""Set the verbosity of some getfem++ routines.
Typically the messages printed by the model bricks, 0 means no
trace message (default is 3). if no level is given,
the current trace level is returned. """
return getfem('util', 'trace_level', level)
def util_warning_level(level):
"""Filter the less important warnings displayed by getfem.
0 means no warnings, default level is 3. if no level is given,
the current warning level is returned. """
return getfem('util', 'warning_level', level)
def memstats():
print "*** Getfem view of the workspace:"
getfem('workspace','stats')
print "*** Python view of the workspace:"
for id,c in obj_count.iteritems():
if (c):
name=str(factory(id).__class__)
print "%s class %d, id %d : instances=%d" % (name,id.classid,id.objid,c)
def linsolve(what, *args):
return getfem('linsolve', what, *args)
def compute(mf, U, what, *args):
return getfem('compute', mf, U, what, *args)
def asm(what, *args):
return getfem('asm', what, *args)
def util(what, *args):
return getfem('util', what, *args)
def factory(id):
t = ( ContStruct,
CvStruct,
Eltm,
Fem,
GeoTrans,
GlobalFunction,
Integ,
LevelSet,
MdBrick,
MdState,
Mesh,
MeshFem,
MeshIm,
MeshLevelSet,
MesherObject,
Model,
MultiContactFrame,
Precond,
Slice,
Spmat)[id.classid]
return t(id)
register_python_factory(factory)
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