Source code for ufl.finiteelement.finiteelement

# -*- 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 Anders Logg 2014
# Modified by Massimiliano Leoni, 2016

from ufl.log import error
from ufl.utils.formatting import istr
from ufl.cell import as_cell

from ufl.cell import TensorProductCell
from ufl.finiteelement.elementlist import canonical_element_description, simplices
from ufl.finiteelement.finiteelementbase import FiniteElementBase


[docs]class FiniteElement(FiniteElementBase): "The basic finite element class for all simple finite elements." # TODO: Move these to base? __slots__ = ("_short_name", "_sobolev_space", "_mapping", "_variant") def __new__(cls, family, cell=None, degree=None, form_degree=None, quad_scheme=None, variant=None): """Intercepts construction to expand CG, DG, RTCE and RTCF spaces on TensorProductCells.""" if cell is not None: cell = as_cell(cell) if isinstance(cell, TensorProductCell): # Delay import to avoid circular dependency at module load time from ufl.finiteelement.tensorproductelement import TensorProductElement from ufl.finiteelement.enrichedelement import EnrichedElement from ufl.finiteelement.hdivcurl import HDivElement as HDiv, HCurlElement as HCurl family, short_name, degree, value_shape, reference_value_shape, sobolev_space, mapping = \ canonical_element_description(family, cell, degree, form_degree) if family in ["RTCF", "RTCE"]: cell_h, cell_v = cell.sub_cells() if cell_h.cellname() != "interval": error("%s is available on TensorProductCell(interval, interval) only." % family) if cell_v.cellname() != "interval": error("%s is available on TensorProductCell(interval, interval) only." % family) C_elt = FiniteElement("CG", "interval", degree, variant=variant) D_elt = FiniteElement("DG", "interval", degree - 1, variant=variant) CxD_elt = TensorProductElement(C_elt, D_elt, cell=cell) DxC_elt = TensorProductElement(D_elt, C_elt, cell=cell) if family == "RTCF": return EnrichedElement(HDiv(CxD_elt), HDiv(DxC_elt)) if family == "RTCE": return EnrichedElement(HCurl(CxD_elt), HCurl(DxC_elt)) elif family == "NCF": cell_h, cell_v = cell.sub_cells() if cell_h.cellname() != "quadrilateral": error("%s is available on TensorProductCell(quadrilateral, interval) only." % family) if cell_v.cellname() != "interval": error("%s is available on TensorProductCell(quadrilateral, interval) only." % family) Qc_elt = FiniteElement("RTCF", "quadrilateral", degree, variant=variant) Qd_elt = FiniteElement("DQ", "quadrilateral", degree - 1, variant=variant) Id_elt = FiniteElement("DG", "interval", degree - 1, variant=variant) Ic_elt = FiniteElement("CG", "interval", degree, variant=variant) return EnrichedElement(HDiv(TensorProductElement(Qc_elt, Id_elt, cell=cell)), HDiv(TensorProductElement(Qd_elt, Ic_elt, cell=cell))) elif family == "NCE": cell_h, cell_v = cell.sub_cells() if cell_h.cellname() != "quadrilateral": error("%s is available on TensorProductCell(quadrilateral, interval) only." % family) if cell_v.cellname() != "interval": error("%s is available on TensorProductCell(quadrilateral, interval) only." % family) Qc_elt = FiniteElement("Q", "quadrilateral", degree, variant=variant) Qd_elt = FiniteElement("RTCE", "quadrilateral", degree, variant=variant) Id_elt = FiniteElement("DG", "interval", degree - 1, variant=variant) Ic_elt = FiniteElement("CG", "interval", degree, variant=variant) return EnrichedElement(HCurl(TensorProductElement(Qc_elt, Id_elt, cell=cell)), HCurl(TensorProductElement(Qd_elt, Ic_elt, cell=cell))) elif family == "Q": return TensorProductElement(*[FiniteElement("CG", c, degree, variant=variant) for c in cell.sub_cells()], cell=cell) elif family == "DQ": def dq_family(cell): return "DG" if cell.cellname() in simplices else "DQ" return TensorProductElement(*[FiniteElement(dq_family(c), c, degree, variant=variant) for c in cell.sub_cells()], cell=cell) elif family == "DQ L2": def dq_family_l2(cell): return "DG L2" if cell.cellname() in simplices else "DQ L2" return TensorProductElement(*[FiniteElement(dq_family_l2(c), c, degree, variant=variant) for c in cell.sub_cells()], cell=cell) return super(FiniteElement, cls).__new__(cls) def __init__(self, family, cell=None, degree=None, form_degree=None, quad_scheme=None, variant=None): """Create finite element. *Arguments* family (string) The finite element family cell The geometric cell degree (int) The polynomial degree (optional) form_degree (int) The form degree (FEEC notation, used when field is viewed as k-form) quad_scheme The quadrature scheme (optional) variant Hint for the local basis function variant (optional) """ # Note: Unfortunately, dolfin sometimes passes None for # cell. Until this is fixed, allow it: if cell is not None: cell = as_cell(cell) family, short_name, degree, value_shape, reference_value_shape, sobolev_space, mapping = canonical_element_description(family, cell, degree, form_degree) # TODO: Move these to base? Might be better to instead # simplify base though. self._sobolev_space = sobolev_space self._mapping = mapping self._short_name = short_name self._variant = variant # Finite elements on quadrilaterals and hexahedrons have an IrreducibleInt as degree if cell is not None: if cell.cellname() in ["quadrilateral", "hexahedron"]: from ufl.algorithms.estimate_degrees import IrreducibleInt degree = IrreducibleInt(degree) # Type check variant if variant is not None and not isinstance(variant, str): raise ValueError("Illegal variant: must be string or None") # Initialize element data FiniteElementBase.__init__(self, family, cell, degree, quad_scheme, value_shape, reference_value_shape) # Cache repr string qs = self.quadrature_scheme() if qs is None: quad_str = "" else: quad_str = ", quad_scheme=%s" % repr(qs) v = self.variant() if v is None: var_str = "" else: var_str = ", variant=%s" % repr(v) self._repr = "FiniteElement(%s, %s, %s%s%s)" % ( repr(self.family()), repr(self.cell()), repr(self.degree()), quad_str, var_str) assert '"' not in self._repr
[docs] def mapping(self): return self._mapping
[docs] def sobolev_space(self): "Return the underlying Sobolev space." return self._sobolev_space
[docs] def variant(self): """Return the variant used to initialise the element.""" return self._variant
[docs] def reconstruct(self, family=None, cell=None, degree=None, quad_scheme=None, variant=None): """Construct a new FiniteElement object with some properties replaced with new values.""" if family is None: family = self.family() if cell is None: cell = self.cell() if degree is None: degree = self.degree() if quad_scheme is None: quad_scheme = self.quadrature_scheme() if variant is None: variant = self.variant() return FiniteElement(family, cell, degree, quad_scheme=quad_scheme, variant=variant)
def __str__(self): "Format as string for pretty printing." qs = self.quadrature_scheme() qs = "" if qs is None else "(%s)" % qs v = self.variant() v = "" if v is None else "(%s)" % v return "<%s%s%s%s on a %s>" % (self._short_name, istr(self.degree()), qs, v, self.cell())
[docs] def shortstr(self): "Format as string for pretty printing." return "%s%s(%s,%s)" % (self._short_name, istr(self.degree()), istr(self.quadrature_scheme()), istr(self.variant()))
def __getnewargs__(self): """Return the arguments which pickle needs to recreate the object.""" return (self.family(), self.cell(), self.degree(), None, self.quadrature_scheme(), self.variant())