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
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
216
217
218
219
220
221
222
223
224
225
226
227
228
229
230
231
232
233
234
235
236
237
238
239
240
241
242
243
244
245
246
|
// ------------------------------------------------------------------------
//
// SPDX-License-Identifier: LGPL-2.1-or-later
// Copyright (C) 2000 - 2025 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/function_derivative.h>
#include <deal.II/base/point.h>
#include <deal.II/lac/vector.h>
#include <cmath>
#include <vector>
DEAL_II_NAMESPACE_OPEN
template <int dim>
FunctionDerivative<dim>::FunctionDerivative(const Function<dim> &f,
const Point<dim> &dir,
const double h)
: AutoDerivativeFunction<dim>(h, f.n_components, f.get_time())
, f(f)
, h(h)
, incr(1, h * dir)
{
set_formula();
}
template <int dim>
FunctionDerivative<dim>::FunctionDerivative(const Function<dim> &f,
const std::vector<Point<dim>> &dir,
const double h)
: AutoDerivativeFunction<dim>(h, f.n_components, f.get_time())
, f(f)
, h(h)
, incr(dir.size())
{
for (unsigned int i = 0; i < incr.size(); ++i)
incr[i] = h * dir[i];
set_formula();
}
template <int dim>
void
FunctionDerivative<dim>::set_formula(
typename AutoDerivativeFunction<dim>::DifferenceFormula form)
{
// go through all known formulas, reject ones we don't know about
// and don't handle in the member functions of this class
switch (form)
{
case AutoDerivativeFunction<dim>::Euler:
case AutoDerivativeFunction<dim>::UpwindEuler:
case AutoDerivativeFunction<dim>::FourthOrder:
break;
default:
Assert(false,
ExcMessage("The argument passed to this function does not "
"match any known difference formula."));
}
formula = form;
}
template <int dim>
void
FunctionDerivative<dim>::set_h(const double new_h)
{
for (unsigned int i = 0; i < incr.size(); ++i)
incr[i] *= new_h / h;
h = new_h;
}
template <int dim>
double
FunctionDerivative<dim>::value(const Point<dim> &p,
const unsigned int component) const
{
Assert(incr.size() == 1,
ExcMessage(
"FunctionDerivative was not initialized for constant direction"));
switch (formula)
{
case AutoDerivativeFunction<dim>::Euler:
return (f.value(p + incr[0], component) -
f.value(p - incr[0], component)) /
(2 * h);
case AutoDerivativeFunction<dim>::UpwindEuler:
return (f.value(p, component) - f.value(p - incr[0], component)) / h;
case AutoDerivativeFunction<dim>::FourthOrder:
return (-f.value(p + 2 * incr[0], component) +
8 * f.value(p + incr[0], component) -
8 * f.value(p - incr[0], component) +
f.value(p - 2 * incr[0], component)) /
(12 * h);
default:
DEAL_II_NOT_IMPLEMENTED();
}
return 0.;
}
template <int dim>
void
FunctionDerivative<dim>::vector_value(const Point<dim> &p,
Vector<double> &result) const
{
Assert(incr.size() == 1,
ExcMessage(
"FunctionDerivative was not initialized for constant direction"));
Vector<double> aux(result.size());
// Formulas are the same as in
// value, but here we have to use
// Vector arithmetic
switch (formula)
{
case AutoDerivativeFunction<dim>::Euler:
f.vector_value(p + incr[0], result);
f.vector_value(p - incr[0], aux);
result.sadd(1. / (2 * h), -1. / (2 * h), aux);
return;
case AutoDerivativeFunction<dim>::UpwindEuler:
f.vector_value(p, result);
f.vector_value(p - incr[0], aux);
result.sadd(1. / h, -1. / h, aux);
return;
case AutoDerivativeFunction<dim>::FourthOrder:
f.vector_value(p - 2 * incr[0], result);
f.vector_value(p + 2 * incr[0], aux);
result.add(-1., aux);
f.vector_value(p - incr[0], aux);
result.add(-8., aux);
f.vector_value(p + incr[0], aux);
result.add(8., aux);
result /= (12. * h);
return;
default:
DEAL_II_NOT_IMPLEMENTED();
}
}
template <int dim>
void
FunctionDerivative<dim>::value_list(const std::vector<Point<dim>> &points,
std::vector<double> &values,
const unsigned int component) const
{
const unsigned int n = points.size();
const bool variable_direction = (incr.size() == 1) ? false : true;
if (variable_direction)
Assert(incr.size() == points.size(),
ExcDimensionMismatch(incr.size(), points.size()));
// Vector of auxiliary values
std::vector<double> aux(n);
// Vector of auxiliary points
std::vector<Point<dim>> paux(n);
// Use the same formulas as in
// value, but with vector
// arithmetic
switch (formula)
{
case AutoDerivativeFunction<dim>::Euler:
for (unsigned int i = 0; i < n; ++i)
paux[i] = points[i] + incr[(variable_direction) ? i : 0U];
f.value_list(paux, values, component);
for (unsigned int i = 0; i < n; ++i)
paux[i] = points[i] - incr[(variable_direction) ? i : 0U];
f.value_list(paux, aux, component);
for (unsigned int i = 0; i < n; ++i)
values[i] = (values[i] - aux[i]) / (2 * h);
return;
case AutoDerivativeFunction<dim>::UpwindEuler:
f.value_list(points, values, component);
for (unsigned int i = 0; i < n; ++i)
paux[i] = points[i] - incr[(variable_direction) ? i : 0U];
f.value_list(paux, aux, component);
for (unsigned int i = 0; i < n; ++i)
values[i] = (values[i] - aux[i]) / h;
return;
case AutoDerivativeFunction<dim>::FourthOrder:
for (unsigned int i = 0; i < n; ++i)
paux[i] = points[i] - 2 * incr[(variable_direction) ? i : 0U];
f.value_list(paux, values, component);
for (unsigned int i = 0; i < n; ++i)
paux[i] = points[i] + 2 * incr[(variable_direction) ? i : 0U];
f.value_list(paux, aux, component);
for (unsigned int i = 0; i < n; ++i)
values[i] -= aux[i];
for (unsigned int i = 0; i < n; ++i)
paux[i] = points[i] + incr[(variable_direction) ? i : 0U];
f.value_list(paux, aux, component);
for (unsigned int i = 0; i < n; ++i)
values[i] += 8. * aux[i];
for (unsigned int i = 0; i < n; ++i)
paux[i] = points[i] - incr[(variable_direction) ? i : 0U];
f.value_list(paux, aux, component);
for (unsigned int i = 0; i < n; ++i)
values[i] = (values[i] - 8. * aux[i]) / (12 * h);
return;
default:
DEAL_II_NOT_IMPLEMENTED();
}
}
template <int dim>
std::size_t
FunctionDerivative<dim>::memory_consumption() const
{
// only simple data elements, so
// use sizeof operator
return sizeof(*this);
}
// explicit instantiations
template class FunctionDerivative<1>;
template class FunctionDerivative<2>;
template class FunctionDerivative<3>;
DEAL_II_NAMESPACE_CLOSE
|
