Source code for ufl.finiteelement.tensorproductelement

# -*- coding: utf-8 -*-
"This module defines the UFL finite element classes."

# Copyright (C) 2008-2016 Martin Sandve Aln├Žs
#
# This file is part of UFL (https://www.fenicsproject.org)
#
# SPDX-License-Identifier:    LGPL-3.0-or-later
#
# Modified by Kristian B. Oelgaard
# Modified by Marie E. Rognes 2010, 2012
# Modified by Massimiliano Leoni, 2016

from itertools import chain

from ufl.log import error
from ufl.cell import TensorProductCell, as_cell
from ufl.sobolevspace import DirectionalSobolevSpace

from ufl.finiteelement.finiteelementbase import FiniteElementBase


[docs]class TensorProductElement(FiniteElementBase): r"""The tensor product of :math:`d` element spaces: .. math:: V = V_1 \otimes V_2 \otimes ... \otimes V_d Given bases :math:`\{\phi_{j_i}\}` of the spaces :math:`V_i` for :math:`i = 1, ...., d`, :math:`\{ \phi_{j_1} \otimes \phi_{j_2} \otimes \cdots \otimes \phi_{j_d} \}` forms a basis for :math:`V`. """ __slots__ = ("_sub_elements", "_cell") def __init__(self, *elements, **kwargs): "Create TensorProductElement from a given list of elements." if not elements: error("Cannot create TensorProductElement from empty list.") keywords = list(kwargs.keys()) if keywords and keywords != ["cell"]: raise ValueError("TensorProductElement got an unexpected keyword argument '%s'" % keywords[0]) cell = kwargs.get("cell") family = "TensorProductElement" if cell is None: # Define cell as the product of each elements cell cell = TensorProductCell(*[e.cell() for e in elements]) else: cell = as_cell(cell) # Define polynomial degree as a tuple of sub-degrees degree = tuple(e.degree() for e in elements) # No quadrature scheme defined quad_scheme = None # match FIAT implementation value_shape = tuple(chain(*[e.value_shape() for e in elements])) reference_value_shape = tuple(chain(*[e.reference_value_shape() for e in elements])) if len(value_shape) > 1: error("Product of vector-valued elements not supported") if len(reference_value_shape) > 1: error("Product of vector-valued elements not supported") FiniteElementBase.__init__(self, family, cell, degree, quad_scheme, value_shape, reference_value_shape) self._sub_elements = elements self._cell = cell self._repr = "TensorProductElement(%s, cell=%s)" % ( ", ".join(repr(e) for e in elements), repr(cell))
[docs] def mapping(self): if all(e.mapping() == "identity" for e in self._sub_elements): return "identity" elif all(e.mapping() == "L2 Piola" for e in self._sub_elements): return "L2 Piola" else: return "undefined"
[docs] def sobolev_space(self): "Return the underlying Sobolev space of the TensorProductElement." elements = self._sub_elements if all(e.sobolev_space() == elements[0].sobolev_space() for e in elements): return elements[0].sobolev_space() else: # Generate a DirectionalSobolevSpace which contains # continuity information parametrized by spatial index orders = [] for e in elements: e_dim = e.cell().geometric_dimension() e_order = (e.sobolev_space()._order,) * e_dim orders.extend(e_order) return DirectionalSobolevSpace(orders)
[docs] def num_sub_elements(self): "Return number of subelements." return len(self._sub_elements)
[docs] def sub_elements(self): "Return subelements (factors)." return self._sub_elements
[docs] def reconstruct(self, **kwargs): cell = kwargs.pop("cell", self.cell()) return TensorProductElement(*[e.reconstruct(**kwargs) for e in self.sub_elements()], cell=cell)
def __str__(self): "Pretty-print." return "TensorProductElement(%s, cell=%s)" \ % (', '.join([str(e) for e in self._sub_elements]), str(self._cell))
[docs] def shortstr(self): "Short pretty-print." return "TensorProductElement(%s, cell=%s)" \ % (', '.join([e.shortstr() for e in self._sub_elements]), str(self._cell))