/usr/lib/python2.7/dist-packages/FIAT/regge.py is in python-fiat 2016.2.0-2.
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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 | # -*- coding: utf-8 -*-
"""Implementation of the generalized Regge finite elements."""
# Copyright (C) 2015-2018 Lizao Li
#
# This file is part of FIAT.
#
# FIAT 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.
#
# FIAT 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 FIAT. If not, see <http://www.gnu.org/licenses/>.
from __future__ import absolute_import, print_function, division
from FIAT.finite_element import CiarletElement
from FIAT.dual_set import DualSet
from FIAT.polynomial_set import ONSymTensorPolynomialSet
from FIAT.functional import PointwiseInnerProductEvaluation as InnerProduct
class ReggeDual(DualSet):
"""Degrees of freedom for generalized Regge finite elements."""
def __init__(self, cell, degree):
dim = cell.get_spatial_dimension()
if (dim < 2) or (dim > 3):
raise ValueError("Generalized Regge elements are implemented only "
"for dimension 2--3. For 1D, it is just DG(r).")
# construct the degrees of freedoms
dofs = [] # list of functionals
# dof_ids[i][j] contains the indices of dofs that are associated with
# entity j in dim i
dof_ids = {}
# no vertex dof
dof_ids[0] = {i: [] for i in range(dim + 1)}
# edge dofs
(_dofs, _dof_ids) = self._generate_dofs(cell, 1, degree, 0)
dofs.extend(_dofs)
dof_ids[1] = _dof_ids
# facet dofs for 3D
if dim == 3:
(_dofs, _dof_ids) = self._generate_dofs(cell, 2, degree, len(dofs))
dofs.extend(_dofs)
dof_ids[2] = _dof_ids
# cell dofs
(_dofs, _dof_ids) = self._generate_dofs(cell, dim, degree, len(dofs))
dofs.extend(_dofs)
dof_ids[dim] = _dof_ids
super(ReggeDual, self).__init__(dofs, cell, dof_ids)
@staticmethod
def _generate_dofs(cell, entity_dim, degree, offset):
"""generate degrees of freedom for enetities of dimension entity_dim
Input: all obvious except
offset -- the current first available dof id.
Output:
dofs -- an array of dofs associated to entities in that dim
dof_ids -- a dict mapping entity_id to the range of indices of dofs
associated to it.
On a k-face for degree r, the dofs are given by the value of
t^T u t
evaluated at points enough to control P(r-k+1) for all the edge
tangents of the face.
`cell.make_points(entity_dim, entity_id, degree + 2)` happens to
generate exactly those points needed.
"""
dofs = []
dof_ids = {}
num_entities = len(cell.get_topology()[entity_dim])
for entity_id in range(num_entities):
pts = cell.make_points(entity_dim, entity_id, degree + 2)
tangents = cell.compute_face_edge_tangents(entity_dim, entity_id)
dofs += [InnerProduct(cell, t, t, pt)
for pt in pts
for t in tangents]
num_new_dofs = len(pts) * len(tangents)
dof_ids[entity_id] = list(range(offset, offset + num_new_dofs))
offset += num_new_dofs
return (dofs, dof_ids)
class Regge(CiarletElement):
"""The generalized Regge elements for symmetric-matrix-valued functions.
REG(r) in dimension n is the space of polynomial symmetric-matrix-valued
functions of degree r or less with tangential-tangential continuity.
"""
def __init__(self, cell, degree):
assert degree >= 0, "Regge start at degree 0!"
# shape functions
Ps = ONSymTensorPolynomialSet(cell, degree)
# degrees of freedom
Ls = ReggeDual(cell, degree)
# mapping under affine transformation
mapping = "double covariant piola"
super(Regge, self).__init__(Ps, Ls, degree, mapping=mapping)
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