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// --------------------------------------------------------------------- | ||
// | ||
// Copyright (C) 2020 - 2022 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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// Tests point-wise evaluation of higher order derivatives with | ||
// evaluate_tensor_product_higher_derivatives for a scalar function on FE_Q | ||
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#include <deal.II/base/function_lib.h> | ||
#include <deal.II/base/point.h> | ||
#include <deal.II/base/polynomial.h> | ||
#include <deal.II/base/quadrature_lib.h> | ||
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#include <deal.II/fe/fe_q.h> | ||
#include <deal.II/fe/fe_tools.h> | ||
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#include <deal.II/lac/vector.h> | ||
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#include <deal.II/matrix_free/tensor_product_kernels.h> | ||
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#include "../tests.h" | ||
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template <int dim, int derivative_order> | ||
void | ||
test(const unsigned int degree) | ||
{ | ||
FE_Q<dim> fe(degree); | ||
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// go through all monomials of degree 'derivative_order + 1' | ||
std::vector<std::array<int, 3>> exponents; | ||
for (int i2 = 0; i2 <= (dim > 2 ? derivative_order : 0); ++i2) | ||
for (int i1 = 0; i1 <= (dim > 1 ? derivative_order : 0); ++i1) | ||
for (int i0 = 0; i0 <= derivative_order; ++i0) | ||
if (i0 + i1 + i2 == derivative_order) | ||
exponents.push_back(std::array<int, 3>{{i0, i1, i2}}); | ||
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deallog << "Evaluate derivative " << derivative_order << " in " << dim | ||
<< "d with polynomial degree " << degree << std::endl; | ||
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const std::vector<unsigned int> renumbering = | ||
FETools::lexicographic_to_hierarchic_numbering<dim>(degree); | ||
const std::vector<Polynomials::Polynomial<double>> polynomials = | ||
Polynomials::generate_complete_Lagrange_basis( | ||
QGaussLobatto<1>(degree + 1).get_points()); | ||
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Point<dim> p; | ||
for (unsigned int d = 0; d < dim; ++d) | ||
p[d] = 1.; | ||
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std::vector<double> function_values(fe.dofs_per_cell); | ||
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for (const std::array<int, 3> &exponent : exponents) | ||
{ | ||
Tensor<1, dim> exp; | ||
for (unsigned int d = 0; d < dim; ++d) | ||
exp[d] = exponent[d]; | ||
Functions::Monomial<dim> monomial(exp); | ||
for (unsigned int i = 0; i < fe.dofs_per_cell; ++i) | ||
function_values[i] = monomial.value(fe.get_unit_support_points()[i]); | ||
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deallog << "Monomial ["; | ||
for (unsigned int d = 0; d < dim; ++d) | ||
deallog << exponent[d] << (d == dim - 1 ? "" : " "); | ||
deallog << "]: "; | ||
const auto derivative = | ||
internal::evaluate_tensor_product_higher_derivatives<derivative_order>( | ||
polynomials, function_values, p, renumbering); | ||
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for (unsigned int d = 0; d < derivative.dimension; ++d) | ||
deallog << (std::abs(derivative[d]) < 1e-11 ? 0. : derivative[d]) | ||
<< " "; | ||
deallog << std::endl; | ||
} | ||
deallog << std::endl; | ||
} | ||
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int | ||
main() | ||
{ | ||
initlog(); | ||
deallog << std::setprecision(3); | ||
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// test 2nd derivatives | ||
test<1, 2>(2); | ||
test<2, 2>(2); | ||
test<3, 2>(2); | ||
test<3, 2>(3); | ||
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// test 3rd derivatives | ||
test<1, 3>(3); | ||
test<2, 3>(3); | ||
test<3, 3>(3); | ||
test<3, 3>(2); | ||
test<3, 3>(4); | ||
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// test 4th derivatives | ||
test<1, 4>(4); | ||
test<2, 4>(4); | ||
test<3, 4>(4); | ||
} |
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DEAL::Evaluate derivative 2 in 1d with polynomial degree 2 | ||
DEAL::Monomial [2]: 2.00 | ||
DEAL:: | ||
DEAL::Evaluate derivative 2 in 2d with polynomial degree 2 | ||
DEAL::Monomial [2 0]: 2.00 0.00 0.00 | ||
DEAL::Monomial [1 1]: 0.00 1.00 0.00 | ||
DEAL::Monomial [0 2]: 0.00 0.00 2.00 | ||
DEAL:: | ||
DEAL::Evaluate derivative 2 in 3d with polynomial degree 2 | ||
DEAL::Monomial [2 0 0]: 2.00 0.00 0.00 0.00 0.00 0.00 | ||
DEAL::Monomial [1 1 0]: 0.00 1.00 0.00 0.00 0.00 0.00 | ||
DEAL::Monomial [0 2 0]: 0.00 0.00 2.00 0.00 0.00 0.00 | ||
DEAL::Monomial [1 0 1]: 0.00 0.00 0.00 1.00 0.00 0.00 | ||
DEAL::Monomial [0 1 1]: 0.00 0.00 0.00 0.00 1.00 0.00 | ||
DEAL::Monomial [0 0 2]: 0.00 0.00 0.00 0.00 0.00 2.00 | ||
DEAL:: | ||
DEAL::Evaluate derivative 2 in 3d with polynomial degree 3 | ||
DEAL::Monomial [2 0 0]: 2.00 0.00 0.00 0.00 0.00 0.00 | ||
DEAL::Monomial [1 1 0]: 0.00 1.00 0.00 0.00 0.00 0.00 | ||
DEAL::Monomial [0 2 0]: 0.00 0.00 2.00 0.00 0.00 0.00 | ||
DEAL::Monomial [1 0 1]: 0.00 0.00 0.00 1.00 0.00 0.00 | ||
DEAL::Monomial [0 1 1]: 0.00 0.00 0.00 0.00 1.00 0.00 | ||
DEAL::Monomial [0 0 2]: 0.00 0.00 0.00 0.00 0.00 2.00 | ||
DEAL:: | ||
DEAL::Evaluate derivative 3 in 1d with polynomial degree 3 | ||
DEAL::Monomial [3]: 6.00 | ||
DEAL:: | ||
DEAL::Evaluate derivative 3 in 2d with polynomial degree 3 | ||
DEAL::Monomial [3 0]: 6.00 0.00 0.00 0.00 | ||
DEAL::Monomial [2 1]: 0.00 2.00 0.00 0.00 | ||
DEAL::Monomial [1 2]: 0.00 0.00 2.00 0.00 | ||
DEAL::Monomial [0 3]: 0.00 0.00 0.00 6.00 | ||
DEAL:: | ||
DEAL::Evaluate derivative 3 in 3d with polynomial degree 3 | ||
DEAL::Monomial [3 0 0]: 6.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 | ||
DEAL::Monomial [2 1 0]: 0.00 2.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 | ||
DEAL::Monomial [1 2 0]: 0.00 0.00 2.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 | ||
DEAL::Monomial [0 3 0]: 0.00 0.00 0.00 6.00 0.00 0.00 0.00 0.00 0.00 0.00 | ||
DEAL::Monomial [2 0 1]: 0.00 0.00 0.00 0.00 2.00 0.00 0.00 0.00 0.00 0.00 | ||
DEAL::Monomial [1 1 1]: 0.00 0.00 0.00 0.00 0.00 1.00 0.00 0.00 0.00 0.00 | ||
DEAL::Monomial [0 2 1]: 0.00 0.00 0.00 0.00 0.00 0.00 2.00 0.00 0.00 0.00 | ||
DEAL::Monomial [1 0 2]: 0.00 0.00 0.00 0.00 0.00 0.00 0.00 2.00 0.00 0.00 | ||
DEAL::Monomial [0 1 2]: 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 2.00 0.00 | ||
DEAL::Monomial [0 0 3]: 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 6.00 | ||
DEAL:: | ||
DEAL::Evaluate derivative 3 in 3d with polynomial degree 2 | ||
DEAL::Monomial [3 0 0]: 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 | ||
DEAL::Monomial [2 1 0]: 0.00 2.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 | ||
DEAL::Monomial [1 2 0]: 0.00 0.00 2.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 | ||
DEAL::Monomial [0 3 0]: 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 | ||
DEAL::Monomial [2 0 1]: 0.00 0.00 0.00 0.00 2.00 0.00 0.00 0.00 0.00 0.00 | ||
DEAL::Monomial [1 1 1]: 0.00 0.00 0.00 0.00 0.00 1.00 0.00 0.00 0.00 0.00 | ||
DEAL::Monomial [0 2 1]: 0.00 0.00 0.00 0.00 0.00 0.00 2.00 0.00 0.00 0.00 | ||
DEAL::Monomial [1 0 2]: 0.00 0.00 0.00 0.00 0.00 0.00 0.00 2.00 0.00 0.00 | ||
DEAL::Monomial [0 1 2]: 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 2.00 0.00 | ||
DEAL::Monomial [0 0 3]: 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 | ||
DEAL:: | ||
DEAL::Evaluate derivative 3 in 3d with polynomial degree 4 | ||
DEAL::Monomial [3 0 0]: 6.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 | ||
DEAL::Monomial [2 1 0]: 0.00 2.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 | ||
DEAL::Monomial [1 2 0]: 0.00 0.00 2.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 | ||
DEAL::Monomial [0 3 0]: 0.00 0.00 0.00 6.00 0.00 0.00 0.00 0.00 0.00 0.00 | ||
DEAL::Monomial [2 0 1]: 0.00 0.00 0.00 0.00 2.00 0.00 0.00 0.00 0.00 0.00 | ||
DEAL::Monomial [1 1 1]: 0.00 0.00 0.00 0.00 0.00 1.00 0.00 0.00 0.00 0.00 | ||
DEAL::Monomial [0 2 1]: 0.00 0.00 0.00 0.00 0.00 0.00 2.00 0.00 0.00 0.00 | ||
DEAL::Monomial [1 0 2]: 0.00 0.00 0.00 0.00 0.00 0.00 0.00 2.00 0.00 0.00 | ||
DEAL::Monomial [0 1 2]: 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 2.00 0.00 | ||
DEAL::Monomial [0 0 3]: 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 6.00 | ||
DEAL:: | ||
DEAL::Evaluate derivative 4 in 1d with polynomial degree 4 | ||
DEAL::Monomial [4]: 24.0 | ||
DEAL:: | ||
DEAL::Evaluate derivative 4 in 2d with polynomial degree 4 | ||
DEAL::Monomial [4 0]: 24.0 0.00 0.00 0.00 0.00 | ||
DEAL::Monomial [3 1]: 0.00 6.00 0.00 0.00 0.00 | ||
DEAL::Monomial [2 2]: 0.00 0.00 4.00 0.00 0.00 | ||
DEAL::Monomial [1 3]: 0.00 0.00 0.00 6.00 0.00 | ||
DEAL::Monomial [0 4]: 0.00 0.00 0.00 0.00 24.0 | ||
DEAL:: | ||
DEAL::Evaluate derivative 4 in 3d with polynomial degree 4 | ||
DEAL::Monomial [4 0 0]: 24.0 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 | ||
DEAL::Monomial [3 1 0]: 0.00 6.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 | ||
DEAL::Monomial [2 2 0]: 0.00 0.00 4.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 | ||
DEAL::Monomial [1 3 0]: 0.00 0.00 0.00 6.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 | ||
DEAL::Monomial [0 4 0]: 0.00 0.00 0.00 0.00 24.0 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 | ||
DEAL::Monomial [3 0 1]: 0.00 0.00 0.00 0.00 0.00 6.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 | ||
DEAL::Monomial [2 1 1]: 0.00 0.00 0.00 0.00 0.00 0.00 2.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 | ||
DEAL::Monomial [1 2 1]: 0.00 0.00 0.00 0.00 0.00 0.00 0.00 2.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 | ||
DEAL::Monomial [0 3 1]: 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 6.00 0.00 0.00 0.00 0.00 0.00 0.00 | ||
DEAL::Monomial [2 0 2]: 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 4.00 0.00 0.00 0.00 0.00 0.00 | ||
DEAL::Monomial [1 1 2]: 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 2.00 0.00 0.00 0.00 0.00 | ||
DEAL::Monomial [0 2 2]: 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 4.00 0.00 0.00 0.00 | ||
DEAL::Monomial [1 0 3]: 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 6.00 0.00 0.00 | ||
DEAL::Monomial [0 1 3]: 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 6.00 0.00 | ||
DEAL::Monomial [0 0 4]: 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 24.0 | ||
DEAL:: |
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// --------------------------------------------------------------------- | ||
// | ||
// Copyright (C) 2020 - 2022 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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// Tests point-wise evaluation of higher order derivatives with | ||
// evaluate_tensor_product_higher_derivatives for a scalar function on FE_DGQ | ||
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#include <deal.II/base/function_lib.h> | ||
#include <deal.II/base/point.h> | ||
#include <deal.II/base/polynomial.h> | ||
#include <deal.II/base/quadrature_lib.h> | ||
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#include <deal.II/fe/fe_dgq.h> | ||
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#include <deal.II/lac/vector.h> | ||
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#include <deal.II/matrix_free/tensor_product_kernels.h> | ||
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#include "../tests.h" | ||
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template <int dim, int derivative_order> | ||
void | ||
test(const unsigned int degree) | ||
{ | ||
FE_DGQ<dim> fe(degree); | ||
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// go through all monomials of degree 'derivative_order + 1' | ||
std::vector<std::array<int, 3>> exponents; | ||
for (int i2 = 0; i2 <= (dim > 2 ? derivative_order : 0); ++i2) | ||
for (int i1 = 0; i1 <= (dim > 1 ? derivative_order : 0); ++i1) | ||
for (int i0 = 0; i0 <= derivative_order; ++i0) | ||
if (i0 + i1 + i2 == derivative_order) | ||
exponents.push_back(std::array<int, 3>{{i0, i1, i2}}); | ||
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deallog << "Evaluate derivative " << derivative_order << " in " << dim | ||
<< "d with polynomial degree " << degree << std::endl; | ||
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const std::vector<Polynomials::Polynomial<double>> polynomials = | ||
Polynomials::generate_complete_Lagrange_basis( | ||
QGaussLobatto<1>(degree + 1).get_points()); | ||
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Point<dim> p; | ||
for (unsigned int d = 0; d < dim; ++d) | ||
p[d] = 1.; | ||
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std::vector<double> function_values(fe.dofs_per_cell); | ||
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for (const std::array<int, 3> &exponent : exponents) | ||
{ | ||
Tensor<1, dim> exp; | ||
for (unsigned int d = 0; d < dim; ++d) | ||
exp[d] = exponent[d]; | ||
Functions::Monomial<dim> monomial(exp); | ||
for (unsigned int i = 0; i < fe.dofs_per_cell; ++i) | ||
function_values[i] = monomial.value(fe.get_unit_support_points()[i]); | ||
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deallog << "Monomial ["; | ||
for (unsigned int d = 0; d < dim; ++d) | ||
deallog << exponent[d] << (d == dim - 1 ? "" : " "); | ||
deallog << "]: "; | ||
const auto derivative = | ||
internal::evaluate_tensor_product_higher_derivatives<derivative_order>( | ||
polynomials, function_values, p); | ||
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for (unsigned int d = 0; d < derivative.dimension; ++d) | ||
deallog << (std::abs(derivative[d]) < 1e-11 ? 0. : derivative[d]) | ||
<< " "; | ||
deallog << std::endl; | ||
} | ||
deallog << std::endl; | ||
} | ||
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int | ||
main() | ||
{ | ||
initlog(); | ||
deallog << std::setprecision(3); | ||
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// test 2nd derivatives | ||
test<1, 2>(2); | ||
test<2, 2>(2); | ||
test<3, 2>(2); | ||
test<3, 2>(3); | ||
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// test 3rd derivatives | ||
test<1, 3>(3); | ||
test<2, 3>(3); | ||
test<3, 3>(3); | ||
test<3, 3>(2); | ||
test<3, 3>(4); | ||
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// test 4th derivatives | ||
test<1, 4>(4); | ||
test<2, 4>(4); | ||
test<3, 4>(4); | ||
} |
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