1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
|
// ------------------------------------------------------------------------
//
// SPDX-License-Identifier: LGPL-2.1-or-later
// Copyright (C) 2005 - 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/polynomials_abf.h>
#include <deal.II/base/quadrature_lib.h>
#include <iomanip>
#include <iostream>
#include <memory>
DEAL_II_NAMESPACE_OPEN
namespace
{
template <int dim>
std::vector<std::vector<Polynomials::Polynomial<double>>>
get_abf_polynomials(const unsigned int k)
{
std::vector<std::vector<Polynomials::Polynomial<double>>> pols(dim);
pols[0] = Polynomials::LagrangeEquidistant::generate_complete_basis(k + 2);
if (k == 0)
for (unsigned int d = 1; d < dim; ++d)
pols[d] = Polynomials::Legendre::generate_complete_basis(0);
else
for (unsigned int d = 1; d < dim; ++d)
pols[d] = Polynomials::LagrangeEquidistant::generate_complete_basis(k);
return pols;
}
} // namespace
template <int dim>
PolynomialsABF<dim>::PolynomialsABF(const unsigned int k)
: TensorPolynomialsBase<dim>(k, n_polynomials(k))
, polynomial_space(get_abf_polynomials<dim>(k))
{
// check that the dimensions match. we only store one of the 'dim'
// anisotropic polynomials that make up the vector-valued space, so
// multiply by 'dim'
Assert(dim * polynomial_space.n() == n_polynomials(k), ExcInternalError());
}
template <int dim>
void
PolynomialsABF<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()));
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);
p_third_derivatives.resize((third_derivatives.empty()) ? 0 : n_sub);
p_fourth_derivatives.resize((fourth_derivatives.empty()) ? 0 : n_sub);
for (unsigned int d = 0; d < dim; ++d)
{
// First we copy the point. The
// polynomial space for
// component d consists of
// polynomials of degree k+1 in
// x_d and degree k in the
// other variables. in order to
// simplify this, we use the
// same AnisotropicPolynomial
// space and simply rotate the
// coordinates through all
// directions.
Point<dim> p;
for (unsigned int c = 0; c < dim; ++c)
p[c] = unit_point[(c + d) % dim];
polynomial_space.evaluate(p,
p_values,
p_grads,
p_grad_grads,
p_third_derivatives,
p_fourth_derivatives);
for (unsigned int i = 0; i < p_values.size(); ++i)
values[i + d * n_sub][d] = p_values[i];
for (unsigned int i = 0; i < p_grads.size(); ++i)
for (unsigned int d1 = 0; d1 < dim; ++d1)
grads[i + d * n_sub][d][(d1 + d) % dim] = p_grads[i][d1];
for (unsigned int i = 0; i < p_grad_grads.size(); ++i)
for (unsigned int d1 = 0; d1 < dim; ++d1)
for (unsigned int d2 = 0; d2 < dim; ++d2)
grad_grads[i + d * n_sub][d][(d1 + d) % dim][(d2 + d) % dim] =
p_grad_grads[i][d1][d2];
for (unsigned int i = 0; i < p_third_derivatives.size(); ++i)
for (unsigned int d1 = 0; d1 < dim; ++d1)
for (unsigned int d2 = 0; d2 < dim; ++d2)
for (unsigned int d3 = 0; d3 < dim; ++d3)
third_derivatives[i + d * n_sub][d][(d1 + d) % dim]
[(d2 + d) % dim][(d3 + d) % dim] =
p_third_derivatives[i][d1][d2][d3];
for (unsigned int i = 0; i < p_fourth_derivatives.size(); ++i)
for (unsigned int d1 = 0; d1 < dim; ++d1)
for (unsigned int d2 = 0; d2 < dim; ++d2)
for (unsigned int d3 = 0; d3 < dim; ++d3)
for (unsigned int d4 = 0; d4 < dim; ++d4)
fourth_derivatives[i + d * n_sub][d][(d1 + d) % dim]
[(d2 + d) % dim][(d3 + d) % dim]
[(d4 + d) % dim] =
p_fourth_derivatives[i][d1][d2][d3][d4];
}
}
template <int dim>
unsigned int
PolynomialsABF<dim>::n_polynomials(const unsigned int k)
{
switch (dim)
{
case 1:
// in 1d, we simply have Q_{k+2}, which has dimension k+3
return k + 3;
case 2:
// the polynomial space is Q_{k+2,k} \times Q_{k,k+2}, which has
// 2(k+3)(k+1) DoFs
return 2 * (k + 3) * (k + 1);
case 3:
// the polynomial space is Q_{k+2,k,k} \times Q_{k,k+2,k} \times
// Q_{k,k,k+2}, which has 3(k+3)(k+1)(k+1) DoFs
return 3 * (k + 3) * (k + 1) * (k + 1);
default:
DEAL_II_NOT_IMPLEMENTED();
}
return 0;
}
template <int dim>
std::unique_ptr<TensorPolynomialsBase<dim>>
PolynomialsABF<dim>::clone() const
{
return std::make_unique<PolynomialsABF<dim>>(*this);
}
template class PolynomialsABF<1>;
template class PolynomialsABF<2>;
template class PolynomialsABF<3>;
DEAL_II_NAMESPACE_CLOSE
|
