Source code for FIAT.mixed

# -*- coding: utf-8 -*-
#
# Copyright (C) 2005-2010 Anders Logg
#
# This file is part of FIAT (https://www.fenicsproject.org)
#
# SPDX-License-Identifier:    LGPL-3.0-or-later

import numpy

from operator import add
from functools import partial

from FIAT.dual_set import DualSet
from FIAT.finite_element import FiniteElement


[docs]class MixedElement(FiniteElement): """A FIAT-like representation of a mixed element. :arg elements: An iterable of FIAT elements. :arg ref_el: The reference element (optional). This object offers tabulation of the concatenated basis function tables along with an entity_dofs dict.""" def __init__(self, elements, ref_el=None): elements = tuple(elements) cells = set(e.get_reference_element() for e in elements) if ref_el is not None: cells.add(ref_el) ref_el, = cells # These functionals are absolutely wrong, they all map from # functions of the wrong shape, and potentially of different # shapes. However, they are wrong precisely as FFC hacks # expect them to be. :( nodes = [L for e in elements for L in e.dual_basis()] entity_dofs = concatenate_entity_dofs(ref_el, elements) dual = DualSet(nodes, ref_el, entity_dofs) super(MixedElement, self).__init__(ref_el, dual, None, mapping=None) self._elements = elements
[docs] def elements(self): return self._elements
[docs] def num_sub_elements(self): return len(self._elements)
[docs] def value_shape(self): return (sum(numpy.prod(e.value_shape(), dtype=int) for e in self.elements()), )
[docs] def mapping(self): return [m for e in self._elements for m in e.mapping()]
[docs] def get_nodal_basis(self): raise NotImplementedError("get_nodal_basis not implemented")
[docs] def tabulate(self, order, points, entity=None): """Tabulate a mixed element by appropriately splatting together the tabulation of the individual elements. """ shape = (self.space_dimension(),) + self.value_shape() + (len(points),) output = {} sub_dims = [0] + list(e.space_dimension() for e in self.elements()) sub_cmps = [0] + list(numpy.prod(e.value_shape(), dtype=int) for e in self.elements()) irange = numpy.cumsum(sub_dims) crange = numpy.cumsum(sub_cmps) for i, e in enumerate(self.elements()): table = e.tabulate(order, points, entity) for d, tab in table.items(): try: arr = output[d] except KeyError: arr = numpy.zeros(shape, dtype=tab.dtype) output[d] = arr ir = irange[i:i+2] cr = crange[i:i+2] tab = tab.reshape(ir[1] - ir[0], cr[1] - cr[0], -1) arr[slice(*ir), slice(*cr)] = tab return output
[docs] def is_nodal(self): """True if primal and dual bases are orthogonal.""" return all(e.is_nodal() for e in self._elements)
[docs]def concatenate_entity_dofs(ref_el, elements): """Combine the entity_dofs from a list of elements into a combined entity_dof containing the information for the concatenated DoFs of all the elements.""" entity_dofs = {dim: {i: [] for i in entities} for dim, entities in ref_el.get_topology().items()} offsets = numpy.cumsum([0] + list(e.space_dimension() for e in elements), dtype=int) for i, d in enumerate(e.entity_dofs() for e in elements): for dim, dofs in d.items(): for ent, off in dofs.items(): entity_dofs[dim][ent] += list(map(partial(add, offsets[i]), off)) return entity_dofs