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// ------------------------------------------------------------------------
//
// SPDX-License-Identifier: LGPL-2.1-or-later
// Copyright (C) 2004 - 2024 by the deal.II authors
//
// This file is part of the deal.II library.
//
// Part of the source code is dual licensed under Apache-2.0 WITH
// LLVM-exception OR LGPL-2.1-or-later. Detailed license information
// governing the source code and code contributions can be found in
// LICENSE.md and CONTRIBUTING.md at the top level directory of deal.II.
//
// ------------------------------------------------------------------------
#include <deal.II/base/geometry_info.h>
#include <deal.II/base/polynomial_space.h>
#include <deal.II/base/polynomials_bdm.h>
#include <deal.II/base/quadrature_lib.h>
#include <iomanip>
#include <iostream>
#include <memory>
DEAL_II_NAMESPACE_OPEN
template <int dim>
PolynomialsBDM<dim>::PolynomialsBDM(const unsigned int k)
: TensorPolynomialsBase<dim>(k + 1, n_polynomials(k))
, polynomial_space(Polynomials::Legendre::generate_complete_basis(k))
, monomials((dim == 2) ? (1) : (k + 2))
, p_values(polynomial_space.n())
, p_grads(polynomial_space.n())
, p_grad_grads(polynomial_space.n())
{
switch (dim)
{
case 2:
monomials[0] = Polynomials::Monomial<double>(k + 1);
break;
case 3:
for (unsigned int i = 0; i < monomials.size(); ++i)
monomials[i] = Polynomials::Monomial<double>(i);
break;
default:
DEAL_II_NOT_IMPLEMENTED();
}
}
template <int dim>
void
PolynomialsBDM<dim>::evaluate(
const Point<dim> &unit_point,
std::vector<Tensor<1, dim>> &values,
std::vector<Tensor<2, dim>> &grads,
std::vector<Tensor<3, dim>> &grad_grads,
std::vector<Tensor<4, dim>> &third_derivatives,
std::vector<Tensor<5, dim>> &fourth_derivatives) const
{
Assert(values.size() == this->n() || values.empty(),
ExcDimensionMismatch(values.size(), this->n()));
Assert(grads.size() == this->n() || grads.empty(),
ExcDimensionMismatch(grads.size(), this->n()));
Assert(grad_grads.size() == this->n() || grad_grads.empty(),
ExcDimensionMismatch(grad_grads.size(), this->n()));
Assert(third_derivatives.size() == this->n() || third_derivatives.empty(),
ExcDimensionMismatch(third_derivatives.size(), this->n()));
Assert(fourth_derivatives.size() == this->n() || fourth_derivatives.empty(),
ExcDimensionMismatch(fourth_derivatives.size(), this->n()));
// third and fourth derivatives not implemented
(void)third_derivatives;
Assert(third_derivatives.empty(), ExcNotImplemented());
(void)fourth_derivatives;
Assert(fourth_derivatives.empty(), ExcNotImplemented());
const unsigned int n_sub = polynomial_space.n();
// guard access to the scratch arrays in the following block using a
// mutex to make sure they are not used by multiple threads at once
{
std::lock_guard<std::mutex> lock(mutex);
p_values.resize((values.empty()) ? 0 : n_sub);
p_grads.resize((grads.empty()) ? 0 : n_sub);
p_grad_grads.resize((grad_grads.empty()) ? 0 : n_sub);
// Compute values of complete space and insert into tensors. Result
// will have first all polynomials in the x-component, then y and z.
polynomial_space.evaluate(unit_point,
p_values,
p_grads,
p_grad_grads,
p_third_derivatives,
p_fourth_derivatives);
std::fill(values.begin(), values.end(), Tensor<1, dim>());
for (unsigned int i = 0; i < p_values.size(); ++i)
for (unsigned int j = 0; j < dim; ++j)
values[i + j * n_sub][j] = p_values[i];
std::fill(grads.begin(), grads.end(), Tensor<2, dim>());
for (unsigned int i = 0; i < p_grads.size(); ++i)
for (unsigned int j = 0; j < dim; ++j)
grads[i + j * n_sub][j] = p_grads[i];
std::fill(grad_grads.begin(), grad_grads.end(), Tensor<3, dim>());
for (unsigned int i = 0; i < p_grad_grads.size(); ++i)
for (unsigned int j = 0; j < dim; ++j)
grad_grads[i + j * n_sub][j] = p_grad_grads[i];
}
// This is the first polynomial not covered by the P_k subspace
unsigned int start = dim * n_sub;
// Store values of auxiliary polynomials and their three derivatives
std::vector<std::vector<double>> monovali(dim, std::vector<double>(4));
std::vector<std::vector<double>> monovalk(dim, std::vector<double>(4));
if (dim == 1)
{
// Despite the fact that we are instantiating this class for 1, 2 and
// 3 space dimensions we only support dimension 2 and 3.
Assert(false,
dealii::ExcMessage("PolynomialsBDF::evaluate is only "
"available for dim == 2, or dim == 3"));
}
else if (dim == 2)
{
for (unsigned int d = 0; d < dim; ++d)
monomials[0].value(unit_point[d], monovali[d]);
if (values.size() != 0)
{
values[start][0] = monovali[0][0];
values[start][1] = -unit_point[1] * monovali[0][1];
values[start + 1][0] = unit_point[0] * monovali[1][1];
values[start + 1][1] = -monovali[1][0];
}
if (grads.size() != 0)
{
grads[start][0][0] = monovali[0][1];
grads[start][0][1] = 0.;
grads[start][1][0] = -unit_point[1] * monovali[0][2];
grads[start][1][1] = -monovali[0][1];
grads[start + 1][0][0] = monovali[1][1];
grads[start + 1][0][1] = unit_point[0] * monovali[1][2];
grads[start + 1][1][0] = 0.;
grads[start + 1][1][1] = -monovali[1][1];
}
if (grad_grads.size() != 0)
{
grad_grads[start][0][0][0] = monovali[0][2];
grad_grads[start][0][0][1] = 0.;
grad_grads[start][0][1][0] = 0.;
grad_grads[start][0][1][1] = 0.;
grad_grads[start][1][0][0] = -unit_point[1] * monovali[0][3];
grad_grads[start][1][0][1] = -monovali[0][2];
grad_grads[start][1][1][0] = -monovali[0][2];
grad_grads[start][1][1][1] = 0.;
grad_grads[start + 1][0][0][0] = 0;
grad_grads[start + 1][0][0][1] = monovali[1][2];
grad_grads[start + 1][0][1][0] = monovali[1][2];
grad_grads[start + 1][0][1][1] = unit_point[0] * monovali[1][3];
grad_grads[start + 1][1][0][0] = 0.;
grad_grads[start + 1][1][0][1] = 0.;
grad_grads[start + 1][1][1][0] = 0.;
grad_grads[start + 1][1][1][1] = -monovali[1][2];
}
}
else if (dim == 3)
{
// The number of curls in each component. Note that the table in
// BrezziFortin91 has a typo, but the text has the right basis
// Note that the next basis function is always obtained from the
// previous by cyclic rotation of the coordinates
const unsigned int n_curls = monomials.size() - 1;
for (unsigned int i = 0; i < n_curls; ++i, start += dim)
{
for (unsigned int d = 0; d < dim; ++d)
{
// p(t) = t^(i+1)
monomials[i + 1].value(unit_point[d], monovali[d]);
// q(t) = t^(k-i)
monomials[this->degree() - 1 - i].value(unit_point[d],
monovalk[d]);
}
if (values.size() != 0)
{
// x p'(y) q(z)
values[start][0] =
unit_point[0] * monovali[1][1] * monovalk[2][0];
// - p(y) q(z)
values[start][1] = -monovali[1][0] * monovalk[2][0];
values[start][2] = 0.;
// y p'(z) q(x)
values[start + 1][1] =
unit_point[1] * monovali[2][1] * monovalk[0][0];
// - p(z) q(x)
values[start + 1][2] = -monovali[2][0] * monovalk[0][0];
values[start + 1][0] = 0.;
// z p'(x) q(y)
values[start + 2][2] =
unit_point[2] * monovali[0][1] * monovalk[1][0];
// -p(x) q(y)
values[start + 2][0] = -monovali[0][0] * monovalk[1][0];
values[start + 2][1] = 0.;
}
if (grads.size() != 0)
{
grads[start][0][0] = monovali[1][1] * monovalk[2][0];
grads[start][0][1] =
unit_point[0] * monovali[1][2] * monovalk[2][0];
grads[start][0][2] =
unit_point[0] * monovali[1][1] * monovalk[2][1];
grads[start][1][0] = 0.;
grads[start][1][1] = -monovali[1][1] * monovalk[2][0];
grads[start][1][2] = -monovali[1][0] * monovalk[2][1];
grads[start][2][0] = 0.;
grads[start][2][1] = 0.;
grads[start][2][2] = 0.;
grads[start + 1][1][1] = monovali[2][1] * monovalk[0][0];
grads[start + 1][1][2] =
unit_point[1] * monovali[2][2] * monovalk[0][0];
grads[start + 1][1][0] =
unit_point[1] * monovali[2][1] * monovalk[0][1];
grads[start + 1][2][1] = 0.;
grads[start + 1][2][2] = -monovali[2][1] * monovalk[0][0];
grads[start + 1][2][0] = -monovali[2][0] * monovalk[0][1];
grads[start + 1][0][1] = 0.;
grads[start + 1][0][2] = 0.;
grads[start + 1][0][0] = 0.;
grads[start + 2][2][2] = monovali[0][1] * monovalk[1][0];
grads[start + 2][2][0] =
unit_point[2] * monovali[0][2] * monovalk[1][0];
grads[start + 2][2][1] =
unit_point[2] * monovali[0][1] * monovalk[1][1];
grads[start + 2][0][2] = 0.;
grads[start + 2][0][0] = -monovali[0][1] * monovalk[1][0];
grads[start + 2][0][1] = -monovali[0][0] * monovalk[1][1];
grads[start + 2][1][2] = 0.;
grads[start + 2][1][0] = 0.;
grads[start + 2][1][1] = 0.;
}
if (grad_grads.size() != 0)
{
grad_grads[start][0][0][0] = 0.;
grad_grads[start][0][0][1] = monovali[1][2] * monovalk[2][0];
grad_grads[start][0][0][2] = monovali[1][1] * monovalk[2][1];
grad_grads[start][0][1][0] = monovali[1][2] * monovalk[2][0];
grad_grads[start][0][1][1] =
unit_point[0] * monovali[1][3] * monovalk[2][0];
grad_grads[start][0][1][2] =
unit_point[0] * monovali[1][2] * monovalk[2][1];
grad_grads[start][0][2][0] = monovali[1][1] * monovalk[2][1];
grad_grads[start][0][2][1] =
unit_point[0] * monovali[1][2] * monovalk[2][1];
grad_grads[start][0][2][2] =
unit_point[0] * monovali[1][1] * monovalk[2][2];
grad_grads[start][1][0][0] = 0.;
grad_grads[start][1][0][1] = 0.;
grad_grads[start][1][0][2] = 0.;
grad_grads[start][1][1][0] = 0.;
grad_grads[start][1][1][1] = -monovali[1][2] * monovalk[2][0];
grad_grads[start][1][1][2] = -monovali[1][1] * monovalk[2][1];
grad_grads[start][1][2][0] = 0.;
grad_grads[start][1][2][1] = -monovali[1][1] * monovalk[2][1];
grad_grads[start][1][2][2] = -monovali[1][0] * monovalk[2][2];
grad_grads[start][2][0][0] = 0.;
grad_grads[start][2][0][1] = 0.;
grad_grads[start][2][0][2] = 0.;
grad_grads[start][2][1][0] = 0.;
grad_grads[start][2][1][1] = 0.;
grad_grads[start][2][1][2] = 0.;
grad_grads[start][2][2][0] = 0.;
grad_grads[start][2][2][1] = 0.;
grad_grads[start][2][2][2] = 0.;
grad_grads[start + 1][0][0][0] = 0.;
grad_grads[start + 1][0][0][1] = 0.;
grad_grads[start + 1][0][0][2] = 0.;
grad_grads[start + 1][0][1][0] = 0.;
grad_grads[start + 1][0][1][1] = 0.;
grad_grads[start + 1][0][1][2] = 0.;
grad_grads[start + 1][0][2][0] = 0.;
grad_grads[start + 1][0][2][1] = 0.;
grad_grads[start + 1][0][2][2] = 0.;
grad_grads[start + 1][1][0][0] =
unit_point[1] * monovali[2][1] * monovalk[0][2];
grad_grads[start + 1][1][0][1] = monovali[2][1] * monovalk[0][1];
grad_grads[start + 1][1][0][2] =
unit_point[1] * monovali[2][2] * monovalk[0][1];
grad_grads[start + 1][1][1][0] = monovalk[0][1] * monovali[2][1];
grad_grads[start + 1][1][1][1] = 0.;
grad_grads[start + 1][1][1][2] = monovalk[0][0] * monovali[2][2];
grad_grads[start + 1][1][2][0] =
unit_point[1] * monovalk[0][1] * monovali[2][2];
grad_grads[start + 1][1][2][1] = monovalk[0][0] * monovali[2][2];
grad_grads[start + 1][1][2][2] =
unit_point[1] * monovalk[0][0] * monovali[2][3];
grad_grads[start + 1][2][0][0] = -monovalk[0][2] * monovali[2][0];
grad_grads[start + 1][2][0][1] = 0.;
grad_grads[start + 1][2][0][2] = -monovalk[0][1] * monovali[2][1];
grad_grads[start + 1][2][1][0] = 0.;
grad_grads[start + 1][2][1][1] = 0.;
grad_grads[start + 1][2][1][2] = 0.;
grad_grads[start + 1][2][2][0] = -monovalk[0][1] * monovali[2][1];
grad_grads[start + 1][2][2][1] = 0.;
grad_grads[start + 1][2][2][2] = -monovalk[0][0] * monovali[2][2];
grad_grads[start + 2][0][0][0] = -monovali[0][2] * monovalk[1][0];
grad_grads[start + 2][0][0][1] = -monovali[0][1] * monovalk[1][1];
grad_grads[start + 2][0][0][2] = 0.;
grad_grads[start + 2][0][1][0] = -monovali[0][1] * monovalk[1][1];
grad_grads[start + 2][0][1][1] = -monovali[0][0] * monovalk[1][2];
grad_grads[start + 2][0][1][2] = 0.;
grad_grads[start + 2][0][2][0] = 0.;
grad_grads[start + 2][0][2][1] = 0.;
grad_grads[start + 2][0][2][2] = 0.;
grad_grads[start + 2][1][0][0] = 0.;
grad_grads[start + 2][1][0][1] = 0.;
grad_grads[start + 2][1][0][2] = 0.;
grad_grads[start + 2][1][1][0] = 0.;
grad_grads[start + 2][1][1][1] = 0.;
grad_grads[start + 2][1][1][2] = 0.;
grad_grads[start + 2][1][2][0] = 0.;
grad_grads[start + 2][1][2][1] = 0.;
grad_grads[start + 2][1][2][2] = 0.;
grad_grads[start + 2][2][0][0] =
unit_point[2] * monovali[0][3] * monovalk[1][0];
grad_grads[start + 2][2][0][1] =
unit_point[2] * monovali[0][2] * monovalk[1][1];
grad_grads[start + 2][2][0][2] = monovali[0][2] * monovalk[1][0];
grad_grads[start + 2][2][1][0] =
unit_point[2] * monovali[0][2] * monovalk[1][1];
grad_grads[start + 2][2][1][1] =
unit_point[2] * monovali[0][1] * monovalk[1][2];
grad_grads[start + 2][2][1][2] = monovali[0][1] * monovalk[1][1];
grad_grads[start + 2][2][2][0] = monovali[0][2] * monovalk[1][0];
grad_grads[start + 2][2][2][1] = monovali[0][1] * monovalk[1][1];
grad_grads[start + 2][2][2][2] = 0.;
}
}
Assert(start == this->n(), ExcInternalError());
}
}
template <int dim>
unsigned int
PolynomialsBDM<dim>::n_polynomials(const unsigned int k)
{
if (dim == 1)
return k + 1;
if (dim == 2)
return (k + 1) * (k + 2) + 2;
if (dim == 3)
return ((k + 1) * (k + 2) * (k + 3)) / 2 + 3 * (k + 1);
DEAL_II_NOT_IMPLEMENTED();
return 0;
}
template <int dim>
std::unique_ptr<TensorPolynomialsBase<dim>>
PolynomialsBDM<dim>::clone() const
{
return std::make_unique<PolynomialsBDM<dim>>(*this);
}
template class PolynomialsBDM<1>;
template class PolynomialsBDM<2>;
template class PolynomialsBDM<3>;
DEAL_II_NAMESPACE_CLOSE
|
