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)