/usr/lib/python2.7/dist-packages/dolfin/fem/projection.py is in python-dolfin 1.3.0+dfsg-2.
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1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 | """This module provides a simple way to compute the projection of a
:py:class:`Function <dolfin.functions.function.Function>` or an
:py:class:`Expression <dolfin.functions.expression.Expression>` onto a
finite element space."""
# Copyright (C) 2008-2011 Anders Logg
#
# This file is part of DOLFIN.
#
# DOLFIN 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.
#
# DOLFIN 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 for more details.
#
# You should have received a copy of the GNU Lesser General Public License
# along with DOLFIN. If not, see <http://www.gnu.org/licenses/>.
#
# First added: 2008-07-13
# Last changed: 2011-11-15
__all__ = ['project']
# Import UFL and SWIG-generated extension module (DOLFIN C++)
import ufl
import dolfin.cpp as cpp
# Local imports
from dolfin.functions.function import *
from dolfin.functions.expression import *
from dolfin.functions.functionspace import *
from dolfin.fem.assembling import *
def project(v, V=None, bcs=None, mesh=None,
solver_type="cg",
preconditioner_type="default",
form_compiler_parameters=None):
"""
Return projection of given expression *v* onto the finite element space *V*.
*Arguments*
v
a :py:class:`Function <dolfin.functions.function.Function>` or
an :py:class:`Expression <dolfin.functions.expression.Expression>`
bcs
Optional argument :py:class:`list of DirichletBC
<dolfin.fem.bcs.DirichletBC>`
V
Optional argument :py:class:`FunctionSpace
<dolfin.functions.functionspace.FunctionSpace>`
mesh
Optional argument :py:class:`mesh <dolfin.cpp.Mesh>`.
solver_type
see :py:func:`solve <dolfin.fem.solving.solve>` for options.
preconditioner_type
see :py:func:`solve <dolfin.fem.solving.solve>` for options.
form_compiler_parameters
see :py:class:`Parameters <dolfin.cpp.Parameters>` for more
information.
*Example of usage*
.. code-block:: python
v = Expression("sin(pi*x[0])")
V = FunctionSpace(mesh, "Lagrange", 1)
Pv = project(v, V)
This is useful for post-processing functions or expressions
which are not readily handled by visualization tools (such as
for example discontinuous functions).
"""
# If trying to project an Expression
if V is None and isinstance(v, Expression):
if mesh is not None and isinstance(mesh, cpp.Mesh):
V = FunctionSpaceBase(mesh, v.ufl_element())
else:
raise TypeError, "expected a mesh when projecting an Expression"
# Try extracting function space if not specified
if V is None:
V = _extract_function_space(v, mesh)
# Check arguments
if not isinstance(V, FunctionSpaceBase):
cpp.dolfin_error("projection.py",
"compute projection",
"Illegal function space for projection, not a FunctionSpace: " + str(v))
# Define variational problem for projection
w = TestFunction(V)
Pv = TrialFunction(V)
a = ufl.inner(w, Pv)*ufl.dx()
L = ufl.inner(w, v)*ufl.dx()
# Assemble linear system
A, b = assemble_system(a, L, bcs=bcs,
form_compiler_parameters=form_compiler_parameters)
# Solve linear system for projection
Pv = Function(V)
cpp.la_solve(A, Pv.vector(), b, solver_type, preconditioner_type)
return Pv
def _extract_function_space(expression, mesh):
"""Try to extract a suitable function space for projection of
given expression."""
# Extract functions
functions = ufl.algorithms.extract_coefficients(expression)
# Extract mesh from functions
if mesh is None:
for f in functions:
if isinstance(f, Function):
mesh = f.function_space().mesh()
if mesh is not None:
break
if mesh is None:
raise RuntimeError, "Unable to project expression, can't find a suitable mesh."
# Create function space
shape = expression.shape()
if shape == ():
V = FunctionSpace(mesh, "CG", 1)
elif len(shape) == 1:
V = VectorFunctionSpace(mesh, "CG", 1, dim=shape[0])
elif len(shape) == 2:
V = TensorFunctionSpace(mesh, "CG", 1, shape=shape)
else:
raise RuntimeError, "Unable to project expression, unhandled rank, shape is %s." % (shape,)
return V
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