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Merge pull request #13158 from harmonj/FE_NEDELEC_EMBEDDING_DOFS
Add get_embedding_dofs() to FE_Nedelec (2-D)
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New: FE_Nedelec<2> now includes the function get_embedding_dofs(), | ||
which permits direct identification of DoF indices between two | ||
realizations of the FE_Nedelec cell. | ||
<br> | ||
(Jake Harmon, 2022/01/25) |
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// --------------------------------------------------------------------- | ||
// | ||
// Copyright (C) 2017 - 2021 by the deal.II authors | ||
// | ||
// This file is part of the deal.II library. | ||
// | ||
// The deal.II library is free software; you can use it, redistribute | ||
// it, and/or modify it under the terms of the GNU Lesser General | ||
// Public License as published by the Free Software Foundation; either | ||
// version 2.1 of the License, or (at your option) any later version. | ||
// The full text of the license can be found in the file LICENSE.md at | ||
// the top level directory of deal.II. | ||
// | ||
// --------------------------------------------------------------------- | ||
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// Checks if get_embedding_dofs() correctly maps the local DoF indices | ||
// of an FE_Nedelec element of sub_degree to an element of sup_degree, | ||
// where sub_degree <= sup_degree | ||
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#include <deal.II/base/quadrature_lib.h> | ||
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#include <deal.II/fe/fe_nedelec.h> | ||
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#include "interpolate_common.h" | ||
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template <int dim> | ||
void | ||
check_nedelec_embed(const unsigned int sub_degree, | ||
const unsigned int sup_degree) | ||
{ | ||
Assert((sub_degree > 0) && (sub_degree <= sup_degree), | ||
ExcIndexRange(sub_degree, 1, sup_degree)); | ||
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const FE_Nedelec<dim> fe_sub(sub_degree - 1); | ||
const FE_Nedelec<dim> fe_sup(sup_degree - 1); | ||
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deallog << fe_sub.get_name() << ' ' << fe_sup.get_name() << ' ' | ||
<< fe_sub.dofs_per_cell << ' ' << fe_sup.dofs_per_cell; | ||
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// Set the quadrature sufficiently high for the enriched finite element space | ||
const QGauss<dim> quadrature(fe_sup.degree + 1); | ||
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std::vector<double> dofs_sub(fe_sub.dofs_per_cell, 0.); | ||
std::vector<double> dofs_sup(fe_sup.dofs_per_cell, 0.); | ||
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// Assign arbitrary values to dofs_sub | ||
for (unsigned int i = 0; i < dofs_sub.size(); ++i) | ||
dofs_sub[i] = std::sin(i + 0.5); | ||
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// Map the DoFs from fe_sub to fe_sup | ||
const std::vector<unsigned int> embedding_dofs = | ||
fe_sup.get_embedding_dofs(fe_sub.degree); | ||
for (unsigned int i = 0; i < dofs_sub.size(); ++i) | ||
dofs_sup[embedding_dofs[i]] = dofs_sub[i]; | ||
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// Compare the values at each quadrature point | ||
double result = 0.; | ||
for (unsigned int k = 0; k < quadrature.size(); ++k) | ||
for (unsigned int comp = 0; comp < fe_sup.n_components(); ++comp) | ||
{ | ||
double eval_sub = 0., eval_sup = 0.; | ||
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for (unsigned int i = 0; i < dofs_sub.size(); ++i) | ||
eval_sub += | ||
dofs_sub[i] * | ||
fe_sub.shape_value_component(i, quadrature.point(k), comp); | ||
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for (unsigned int i = 0; i < dofs_sup.size(); ++i) | ||
eval_sup += | ||
dofs_sup[i] * | ||
fe_sup.shape_value_component(i, quadrature.point(k), comp); | ||
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const double diff = std::abs(eval_sub - eval_sup); | ||
result = std::max(result, diff); | ||
} | ||
deallog << " max diff " << result << std::endl; | ||
} | ||
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int | ||
main() | ||
{ | ||
initlog(); | ||
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// For 2-D | ||
{ | ||
for (unsigned int low_deg = 1; low_deg <= 5; ++low_deg) | ||
for (unsigned int high_deg = low_deg; high_deg <= 10; ++high_deg) | ||
check_nedelec_embed<2>(low_deg, high_deg); | ||
} | ||
} |
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DEAL::FE_Nedelec<2>(0) FE_Nedelec<2>(0) 4 4 max diff 0.00000 | ||
DEAL::FE_Nedelec<2>(0) FE_Nedelec<2>(1) 4 12 max diff 0.00000 | ||
DEAL::FE_Nedelec<2>(0) FE_Nedelec<2>(2) 4 24 max diff 0.00000 | ||
DEAL::FE_Nedelec<2>(0) FE_Nedelec<2>(3) 4 40 max diff 0.00000 | ||
DEAL::FE_Nedelec<2>(0) FE_Nedelec<2>(4) 4 60 max diff 0.00000 | ||
DEAL::FE_Nedelec<2>(0) FE_Nedelec<2>(5) 4 84 max diff 0.00000 | ||
DEAL::FE_Nedelec<2>(0) FE_Nedelec<2>(6) 4 112 max diff 0.00000 | ||
DEAL::FE_Nedelec<2>(0) FE_Nedelec<2>(7) 4 144 max diff 0.00000 | ||
DEAL::FE_Nedelec<2>(0) FE_Nedelec<2>(8) 4 180 max diff 0.00000 | ||
DEAL::FE_Nedelec<2>(0) FE_Nedelec<2>(9) 4 220 max diff 0.00000 | ||
DEAL::FE_Nedelec<2>(1) FE_Nedelec<2>(1) 12 12 max diff 0.00000 | ||
DEAL::FE_Nedelec<2>(1) FE_Nedelec<2>(2) 12 24 max diff 0.00000 | ||
DEAL::FE_Nedelec<2>(1) FE_Nedelec<2>(3) 12 40 max diff 0.00000 | ||
DEAL::FE_Nedelec<2>(1) FE_Nedelec<2>(4) 12 60 max diff 0.00000 | ||
DEAL::FE_Nedelec<2>(1) FE_Nedelec<2>(5) 12 84 max diff 0.00000 | ||
DEAL::FE_Nedelec<2>(1) FE_Nedelec<2>(6) 12 112 max diff 0.00000 | ||
DEAL::FE_Nedelec<2>(1) FE_Nedelec<2>(7) 12 144 max diff 0.00000 | ||
DEAL::FE_Nedelec<2>(1) FE_Nedelec<2>(8) 12 180 max diff 0.00000 | ||
DEAL::FE_Nedelec<2>(1) FE_Nedelec<2>(9) 12 220 max diff 0.00000 | ||
DEAL::FE_Nedelec<2>(2) FE_Nedelec<2>(2) 24 24 max diff 0.00000 | ||
DEAL::FE_Nedelec<2>(2) FE_Nedelec<2>(3) 24 40 max diff 0.00000 | ||
DEAL::FE_Nedelec<2>(2) FE_Nedelec<2>(4) 24 60 max diff 0.00000 | ||
DEAL::FE_Nedelec<2>(2) FE_Nedelec<2>(5) 24 84 max diff 0.00000 | ||
DEAL::FE_Nedelec<2>(2) FE_Nedelec<2>(6) 24 112 max diff 0.00000 | ||
DEAL::FE_Nedelec<2>(2) FE_Nedelec<2>(7) 24 144 max diff 0.00000 | ||
DEAL::FE_Nedelec<2>(2) FE_Nedelec<2>(8) 24 180 max diff 0.00000 | ||
DEAL::FE_Nedelec<2>(2) FE_Nedelec<2>(9) 24 220 max diff 0.00000 | ||
DEAL::FE_Nedelec<2>(3) FE_Nedelec<2>(3) 40 40 max diff 0.00000 | ||
DEAL::FE_Nedelec<2>(3) FE_Nedelec<2>(4) 40 60 max diff 0.00000 | ||
DEAL::FE_Nedelec<2>(3) FE_Nedelec<2>(5) 40 84 max diff 0.00000 | ||
DEAL::FE_Nedelec<2>(3) FE_Nedelec<2>(6) 40 112 max diff 0.00000 | ||
DEAL::FE_Nedelec<2>(3) FE_Nedelec<2>(7) 40 144 max diff 0.00000 | ||
DEAL::FE_Nedelec<2>(3) FE_Nedelec<2>(8) 40 180 max diff 0.00000 | ||
DEAL::FE_Nedelec<2>(3) FE_Nedelec<2>(9) 40 220 max diff 0.00000 | ||
DEAL::FE_Nedelec<2>(4) FE_Nedelec<2>(4) 60 60 max diff 0.00000 | ||
DEAL::FE_Nedelec<2>(4) FE_Nedelec<2>(5) 60 84 max diff 0.00000 | ||
DEAL::FE_Nedelec<2>(4) FE_Nedelec<2>(6) 60 112 max diff 0.00000 | ||
DEAL::FE_Nedelec<2>(4) FE_Nedelec<2>(7) 60 144 max diff 0.00000 | ||
DEAL::FE_Nedelec<2>(4) FE_Nedelec<2>(8) 60 180 max diff 0.00000 | ||
DEAL::FE_Nedelec<2>(4) FE_Nedelec<2>(9) 60 220 max diff 0.00000 |