Source code for FIAT.gauss_lobatto_legendre

# Copyright (C) 2015 Imperial College London and others.
#
# This file is part of FIAT (https://www.fenicsproject.org)
#
# SPDX-License-Identifier:    LGPL-3.0-or-later
#
# Written by David A. Ham (david.ham@imperial.ac.uk), 2015
#
# Modified by Pablo D. Brubeck (brubeck@protonmail.com), 2021

import numpy

from FIAT import finite_element, polynomial_set, dual_set, functional, quadrature
from FIAT.reference_element import LINE
from FIAT.barycentric_interpolation import barycentric_interpolation


[docs] class GaussLobattoLegendreDualSet(dual_set.DualSet): """The dual basis for 1D continuous elements with nodes at the Gauss-Lobatto points.""" def __init__(self, ref_el, degree): entity_ids = {0: {0: [0], 1: [degree]}, 1: {0: list(range(1, degree))}} lr = quadrature.GaussLobattoLegendreQuadratureLineRule(ref_el, degree+1) nodes = [functional.PointEvaluation(ref_el, x) for x in lr.pts] super(GaussLobattoLegendreDualSet, self).__init__(nodes, ref_el, entity_ids)
[docs] class GaussLobattoLegendre(finite_element.CiarletElement): """1D continuous element with nodes at the Gauss-Lobatto points.""" def __init__(self, ref_el, degree): if ref_el.shape != LINE: raise ValueError("Gauss-Lobatto-Legendre elements are only defined in one dimension.") poly_set = polynomial_set.ONPolynomialSet(ref_el, degree) dual = GaussLobattoLegendreDualSet(ref_el, degree) formdegree = 0 # 0-form super(GaussLobattoLegendre, self).__init__(poly_set, dual, degree, formdegree)
[docs] def tabulate(self, order, points, entity=None): # This overrides the default with a more numerically stable algorithm if entity is None: entity = (self.ref_el.get_dimension(), 0) entity_dim, entity_id = entity transform = self.ref_el.get_entity_transform(entity_dim, entity_id) xsrc = [] for node in self.dual.nodes: # Assert singleton point for each node. (pt,), = node.get_point_dict().keys() xsrc.append(pt) xsrc = numpy.asarray(xsrc) xdst = numpy.array(list(map(transform, points))).flatten() return barycentric_interpolation(xsrc, xdst, order=order)