Reference documentation for deal.II version 9.4.1
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1// ---------------------------------------------------------------------
2//
3// Copyright (C) 2000 - 2020 by the deal.II authors
4//
5// This file is part of the deal.II library.
6//
7// The deal.II library is free software; you can use it, redistribute
8// it, and/or modify it under the terms of the GNU Lesser General
9// Public License as published by the Free Software Foundation; either
10// version 2.1 of the License, or (at your option) any later version.
11// The full text of the license can be found in the file LICENSE.md at
12// the top level directory of deal.II.
13//
14// ---------------------------------------------------------------------
15
18
19#include <memory>
20
21#define ENTER_COEFFICIENTS( \
22 koefs, z, a0, a1, a2, a3, a4, a5, a6, a7, a8, a9, a10, a11) \
23 koefs(0, z) = a0; \
24 koefs(1, z) = a1; \
25 koefs(2, z) = a2; \
26 koefs(3, z) = a3; \
27 koefs(4, z) = a4; \
28 koefs(5, z) = a5; \
29 koefs(6, z) = a6; \
30 koefs(7, z) = a7; \
31 koefs(8, z) = a8; \
32 koefs(9, z) = a9; \
33 koefs(10, z) = a10; \
34 koefs(11, z) = a11;
35
36
38
39
40
41template <int dim>
43 : ScalarPolynomialsBase<dim>(3, 12)
44 , coef(12, 12)
45 , dx(12, 12)
46 , dy(12, 12)
47 , dxx(12, 12)
48 , dyy(12, 12)
49 , dxy(12, 12)
50{
51 Assert(dim == 2, ExcNotImplemented());
52
53 // 1 x y xx yy xy 3x 3y xyy xxy 3xy x3y
54 // 0 1 2 3 4 5 6 7 8 9 10 11
55 ENTER_COEFFICIENTS(coef, 0, 1, 0, 0, -3, -3, -1, 2, 2, 3, 3, -2, -2);
56 ENTER_COEFFICIENTS(coef, 1, 0, 1, 0, -2, 0, -1, 1, 0, 0, 2, -1, 0);
57 ENTER_COEFFICIENTS(coef, 2, 0, 0, 1, 0, -2, -1, 0, 1, 2, 0, 0, -1);
58 ENTER_COEFFICIENTS(coef, 3, 0, 0, 0, 3, 0, 1, -2, 0, -3, -3, 2, 2);
59 ENTER_COEFFICIENTS(coef, 4, 0, 0, 0, -1, 0, 0, 1, 0, 0, 1, -1, 0);
60 ENTER_COEFFICIENTS(coef, 5, 0, 0, 0, 0, 0, 1, 0, 0, -2, 0, 0, 1);
61 ENTER_COEFFICIENTS(coef, 6, 0, 0, 0, 0, 3, 1, 0, -2, -3, -3, 2, 2);
62 ENTER_COEFFICIENTS(coef, 7, 0, 0, 0, 0, 0, 1, 0, 0, 0, -2, 1, 0);
63 ENTER_COEFFICIENTS(coef, 8, 0, 0, 0, 0, -1, 0, 0, 1, 1, 0, 0, -1);
64 ENTER_COEFFICIENTS(coef, 9, 0, 0, 0, 0, 0, -1, 0, 0, 3, 3, -2, -2);
65 ENTER_COEFFICIENTS(coef, 10, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 1, 0);
66 ENTER_COEFFICIENTS(coef, 11, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 1);
67
68 ENTER_COEFFICIENTS(dx, 0, 0, -6, -1, 6, 3, 6, 0, -2, 0, -6, 0, 0);
69 ENTER_COEFFICIENTS(dx, 1, 1, -4, -1, 3, 0, 4, 0, 0, 0, -3, 0, 0);
70 ENTER_COEFFICIENTS(dx, 2, 0, 0, -1, 0, 2, 0, 0, -1, 0, 0, 0, 0);
71 ENTER_COEFFICIENTS(dx, 3, 0, 6, 1, -6, -3, -6, 0, 2, 0, 6, 0, 0);
72 ENTER_COEFFICIENTS(dx, 4, 0, -2, 0, 3, 0, 2, 0, 0, 0, -3, 0, 0);
73 ENTER_COEFFICIENTS(dx, 5, 0, 0, 1, 0, -2, 0, 0, 1, 0, 0, 0, 0);
74 ENTER_COEFFICIENTS(dx, 6, 0, 0, 1, 0, -3, -6, 0, 2, 0, 6, 0, 0);
75 ENTER_COEFFICIENTS(dx, 7, 0, 0, 1, 0, 0, -4, 0, 0, 0, 3, 0, 0);
76 ENTER_COEFFICIENTS(dx, 8, 0, 0, 0, 0, 1, 0, 0, -1, 0, 0, 0, 0);
77 ENTER_COEFFICIENTS(dx, 9, 0, 0, -1, 0, 3, 6, 0, -2, 0, -6, 0, 0);
78 ENTER_COEFFICIENTS(dx, 10, 0, 0, 0, 0, 0, -2, 0, 0, 0, 3, 0, 0);
79 ENTER_COEFFICIENTS(dx, 11, 0, 0, 0, 0, -1, 0, 0, 1, 0, 0, 0, 0);
80
81 ENTER_COEFFICIENTS(dy, 0, 0, -1, -6, 3, 6, 6, -2, 0, -6, 0, 0, 0);
82 ENTER_COEFFICIENTS(dy, 1, 0, -1, 0, 2, 0, 0, -1, 0, 0, 0, 0, 0);
83 ENTER_COEFFICIENTS(dy, 2, 1, -1, -4, 0, 3, 4, 0, 0, -3, 0, 0, 0);
84 ENTER_COEFFICIENTS(dy, 3, 0, 1, 0, -3, 0, -6, 2, 0, 6, 0, 0, 0);
85 ENTER_COEFFICIENTS(dy, 4, 0, 0, 0, 1, 0, 0, -1, 0, 0, 0, 0, 0);
86 ENTER_COEFFICIENTS(dy, 5, 0, 1, 0, 0, 0, -4, 0, 0, 3, 0, 0, 0);
87 ENTER_COEFFICIENTS(dy, 6, 0, 1, 6, -3, -6, -6, 2, 0, 6, 0, 0, 0);
88 ENTER_COEFFICIENTS(dy, 7, 0, 1, 0, -2, 0, 0, 1, 0, 0, 0, 0, 0);
89 ENTER_COEFFICIENTS(dy, 8, 0, 0, -2, 0, 3, 2, 0, 0, -3, 0, 0, 0);
90 ENTER_COEFFICIENTS(dy, 9, 0, -1, 0, 3, 0, 6, -2, 0, -6, 0, 0, 0);
91 ENTER_COEFFICIENTS(dy, 10, 0, 0, 0, -1, 0, 0, 1, 0, 0, 0, 0, 0);
92 ENTER_COEFFICIENTS(dy, 11, 0, 0, 0, 0, 0, -2, 0, 0, 3, 0, 0, 0);
93
94 ENTER_COEFFICIENTS(dxx, 0, -6, 12, 6, 0, 0, -12, 0, 0, 0, 0, 0, 0);
95 ENTER_COEFFICIENTS(dxx, 1, -4, 6, 4, 0, 0, -6, 0, 0, 0, 0, 0, 0);
96 ENTER_COEFFICIENTS(dxx, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0);
97 ENTER_COEFFICIENTS(dxx, 3, 6, -12, -6, 0, 0, 12, 0, 0, 0, 0, 0, 0);
98 ENTER_COEFFICIENTS(dxx, 4, -2, 6, 2, 0, 0, -6, 0, 0, 0, 0, 0, 0);
99 ENTER_COEFFICIENTS(dxx, 5, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0);
100 ENTER_COEFFICIENTS(dxx, 6, 0, 0, -6, 0, 0, 12, 0, 0, 0, 0, 0, 0);
101 ENTER_COEFFICIENTS(dxx, 7, 0, 0, -4, 0, 0, 6, 0, 0, 0, 0, 0, 0);
102 ENTER_COEFFICIENTS(dxx, 8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0);
103 ENTER_COEFFICIENTS(dxx, 9, 0, 0, 6, 0, 0, -12, 0, 0, 0, 0, 0, 0);
104 ENTER_COEFFICIENTS(dxx, 10, 0, 0, -2, 0, 0, 6, 0, 0, 0, 0, 0, 0);
105 ENTER_COEFFICIENTS(dxx, 11, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0);
106
107 ENTER_COEFFICIENTS(dyy, 0, -6, 6, 12, 0, 0, -12, 0, 0, 0, 0, 0, 0);
108 ENTER_COEFFICIENTS(dyy, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0);
109 ENTER_COEFFICIENTS(dyy, 2, -4, 4, 6, 0, 0, -6, 0, 0, 0, 0, 0, 0);
110 ENTER_COEFFICIENTS(dyy, 3, 0, -6, 0, 0, 0, 12, 0, 0, 0, 0, 0, 0);
111 ENTER_COEFFICIENTS(dyy, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0);
112 ENTER_COEFFICIENTS(dyy, 5, 0, -4, 0, 0, 0, 6, 0, 0, 0, 0, 0, 0);
113 ENTER_COEFFICIENTS(dyy, 6, 6, -6, -12, 0, 0, 12, 0, 0, 0, 0, 0, 0);
114 ENTER_COEFFICIENTS(dyy, 7, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0);
115 ENTER_COEFFICIENTS(dyy, 8, -2, 2, 6, 0, 0, -6, 0, -0, 0, 0, 0, 0);
116 ENTER_COEFFICIENTS(dyy, 9, 0, 6, 0, 0, 0, -12, 0, 0, 0, 0, 0, 0);
117 ENTER_COEFFICIENTS(dyy, 10, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0);
118 ENTER_COEFFICIENTS(dyy, 11, 0, -2, 0, 0, 0, 6, 0, 0, 0, 0, 0, 0);
119
120 ENTER_COEFFICIENTS(dxy, 0, -1, 6, 6, -6, -6, 0, 0, 0, 0, 0, 0, 0);
121 ENTER_COEFFICIENTS(dxy, 1, -1, 4, 0, -3, 0, 0, 0, 0, 0, 0, 0, 0);
122 ENTER_COEFFICIENTS(dxy, 2, -1, 0, 4, 0, -3, 0, 0, 0, 0, 0, 0, 0);
123 ENTER_COEFFICIENTS(dxy, 3, 1, -6, -6, 6, 6, 0, 0, 0, 0, 0, 0, 0);
124 ENTER_COEFFICIENTS(dxy, 4, 0, 2, 0, -3, 0, 0, 0, 0, 0, 0, 0, 0);
125 ENTER_COEFFICIENTS(dxy, 5, 1, 0, -4, 0, 3, 0, 0, 0, 0, 0, 0, 0);
126 ENTER_COEFFICIENTS(dxy, 6, 1, -6, -6, 6, 6, 0, 0, 0, 0, 0, 0, 0);
127 ENTER_COEFFICIENTS(dxy, 7, 1, -4, 0, 3, 0, 0, 0, 0, 0, 0, 0, 0);
128 ENTER_COEFFICIENTS(dxy, 8, 0, 0, 2, 0, -3, 0, 0, 0, 0, 0, 0, 0);
129 ENTER_COEFFICIENTS(dxy, 9, -1, 6, 6, -6, -6, 0, 0, 0, 0, 0, 0, 0);
130 ENTER_COEFFICIENTS(dxy, 10, 0, -2, 0, 3, 0, 0, 0, 0, 0, 0, 0, 0);
131 ENTER_COEFFICIENTS(dxy, 11, 0, 0, -2, 0, 3, 0, 0, 0, 0, 0, 0, 0);
132}
133
134
135
136template <int dim>
137void
139 const Point<dim> & unit_point,
140 std::vector<double> & values,
141 std::vector<Tensor<1, dim>> &grads,
143 std::vector<Tensor<3, dim>> &third_derivatives,
144 std::vector<Tensor<4, dim>> &fourth_derivatives) const
145{
146 const unsigned int n_pols = this->n();
147 (void)n_pols;
148
149 Assert(values.size() == n_pols || values.size() == 0,
150 ExcDimensionMismatch(values.size(), n_pols));
151 Assert(grads.size() == n_pols || grads.size() == 0,
155 (void)third_derivatives;
156 Assert(third_derivatives.size() == n_pols || third_derivatives.size() == 0,
157 ExcDimensionMismatch(third_derivatives.size(), n_pols));
158 (void)fourth_derivatives;
159 Assert(fourth_derivatives.size() == n_pols || fourth_derivatives.size() == 0,
160 ExcDimensionMismatch(fourth_derivatives.size(), n_pols));
161
162 if (values.empty() == false) // do not bother if empty
163 {
164 for (unsigned int i = 0; i < values.size(); ++i)
165 {
166 values[i] = compute_value(i, unit_point);
167 }
168 }
169
170 if (grads.empty() == false) // do not bother if empty
171 {
172 for (unsigned int i = 0; i < grads.size(); ++i)
173 {
175 }
176 }
177
178 if (grad_grads.empty() == false) // do not bother if empty
179 {
180 for (unsigned int i = 0; i < grad_grads.size(); ++i)
181 {
183 }
184 }
185
186 return;
187}
188
189
190
191template <int dim>
192double
194 const Point<dim> & p) const
195{
196 const double x = p(0);
197 const double y = p(1);
198 return coef(0, i) + coef(1, i) * x + coef(2, i) * y + coef(3, i) * x * x +
199 coef(4, i) * y * y + coef(5, i) * x * y + coef(6, i) * x * x * x +
200 coef(7, i) * y * y * y + coef(8, i) * x * y * y +
201 coef(9, i) * x * x * y + coef(10, i) * x * x * x * y +
202 coef(11, i) * x * y * y * y;
203}
204
205
206
207template <int dim>
210 const Point<dim> & p) const
211{
212 const double x = p(0);
213 const double y = p(1);
214 Tensor<1, dim> tensor;
215 tensor[0] = dx(0, i) + dx(1, i) * x + dx(2, i) * y + dx(3, i) * x * x +
216 dx(4, i) * y * y + dx(5, i) * x * y + dx(6, i) * x * x * x +
217 dx(7, i) * y * y * y + dx(8, i) * x * y * y +
218 dx(9, i) * x * x * y + dx(10, i) * x * x * x * y +
219 dx(11, i) * x * y * y * y;
220
221 tensor[1] = dy(0, i) + dy(1, i) * x + dy(2, i) * y + dy(3, i) * x * x +
222 dy(4, i) * y * y + dy(5, i) * x * y + dy(6, i) * x * x * x +
223 dy(7, i) * y * y * y + dy(8, i) * x * y * y +
224 dy(9, i) * x * x * y + dy(10, i) * x * x * x * y +
225 dy(11, i) * x * y * y * y;
226 return tensor;
227}
228
229
230
231template <int dim>
234 const Point<dim> & p) const
235{
236 const double x = p(0);
237 const double y = p(1);
238 Tensor<2, dim> tensor;
239 tensor[0][0] = dxx(0, i) + dxx(1, i) * x + dxx(2, i) * y + dxx(3, i) * x * x +
240 dxx(4, i) * y * y + dxx(5, i) * x * y + dxx(6, i) * x * x * x +
241 dxx(7, i) * y * y * y + dxx(8, i) * x * y * y +
242 dxx(9, i) * x * x * y + dxx(10, i) * x * x * x * y +
243 dxx(11, i) * x * y * y * y;
244 tensor[0][1] = dxy(0, i) + dxy(1, i) * x + dxy(2, i) * y + dxy(3, i) * x * x +
245 dxy(4, i) * y * y + dxy(5, i) * x * y + dxy(6, i) * x * x * x +
246 dxy(7, i) * y * y * y + dxy(8, i) * x * y * y +
247 dxy(9, i) * x * x * y + dxy(10, i) * x * x * x * y +
248 dxy(11, i) * x * y * y * y;
249 tensor[1][0] = tensor[0][1];
250 tensor[1][1] = dyy(0, i) + dyy(1, i) * x + dyy(2, i) * y + dyy(3, i) * x * x +
251 dyy(4, i) * y * y + dyy(5, i) * x * y + dyy(6, i) * x * x * x +
252 dyy(7, i) * y * y * y + dyy(8, i) * x * y * y +
253 dyy(9, i) * x * x * y + dyy(10, i) * x * x * x * y +
254 dyy(11, i) * x * y * y * y;
255 return tensor;
256}
257
258
259
260template <int dim>
261std::unique_ptr<ScalarPolynomialsBase<dim>>
263{
265}
266
267
268
273
Definition: point.h:111
virtual std::unique_ptr< ScalarPolynomialsBase< dim > > clone() const override
Table< 2, double > dyy
Table< 2, double > dy
double compute_value(const unsigned int i, const Point< dim > &p) const override
void evaluate(const Point< dim > &unit_point, std::vector< double > &values, std::vector< Tensor< 1, dim > > &grads, std::vector< Tensor< 2, dim > > &grad_grads, std::vector< Tensor< 3, dim > > &third_derivatives, std::vector< Tensor< 4, dim > > &fourth_derivatives) const override
Tensor< 2, dim > compute_grad_grad(const unsigned int i, const Point< dim > &p) const override
Table< 2, double > dxy
Table< 2, double > dx
Table< 2, double > coef
Table< 2, double > dxx
Tensor< 1, dim > compute_grad(const unsigned int i, const Point< dim > &p) const override
Definition: tensor.h:503
#define DEAL_II_NAMESPACE_OPEN
Definition: config.h:442
#define DEAL_II_NAMESPACE_CLOSE
Definition: config.h:443
static ::ExceptionBase & ExcNotImplemented()
#define Assert(cond, exc)
Definition: exceptions.h:1473
static ::ExceptionBase & ExcDimensionMismatch(std::size_t arg1, std::size_t arg2)
#define ENTER_COEFFICIENTS( koefs, z, a0, a1, a2, a3, a4, a5, a6, a7, a8, a9, a10, a11)