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
|
// Gmsh - Copyright (C) 1997-2021 C. Geuzaine, J.-F. Remacle
//
// See the LICENSE.txt file for license information. Please report all
// issues on https://gitlab.onelab.info/gmsh/gmsh/issues.
//
// Contributor(s):
// Amaury Johnen
//
#include "incompleteBasis.h"
#include "BasisFactory.h"
#include "ElementType.h"
void incompleteBasis::_computeCoefficientsTriangle()
{
if(order < 3) {
coefficients.resize(0, 0);
return;
}
int szInc = getNumShapeFunctions();
int szComp = completeBasis->getNumShapeFunctions();
coefficients.resize(szComp - szInc, szInc, true);
std::map<std::pair<int, int>, int> coord2idx;
for(int i = 0; i < szInc; ++i) {
int u = static_cast<int>(points(i, 0) * order + .5);
int v = static_cast<int>(points(i, 1) * order + .5);
coord2idx[std::make_pair(u, v)] = i;
}
int &n = order;
fullMatrix<double> pts = completeBasis->getReferenceNodes();
for(int i = 0; i < szComp - szInc; ++i) {
double xi = pts(szInc + i, 0);
double eta = pts(szInc + i, 1);
int u = static_cast<int>(xi * order + .5);
int v = static_cast<int>(eta * order + .5);
coefficients(i, coord2idx[std::make_pair(u + v, 0)]) = xi;
coefficients(i, coord2idx[std::make_pair(n, 0)]) = -xi;
coefficients(i, coord2idx[std::make_pair(n - v, v)]) = xi;
coefficients(i, coord2idx[std::make_pair(u, n - u)]) = eta;
coefficients(i, coord2idx[std::make_pair(0, n)]) = -eta;
coefficients(i, coord2idx[std::make_pair(0, u + v)]) = eta;
coefficients(i, coord2idx[std::make_pair(0, v)]) = 1 - xi - eta;
coefficients(i, coord2idx[std::make_pair(0, 0)]) = -(1 - xi - eta);
coefficients(i, coord2idx[std::make_pair(u, 0)]) = 1 - xi - eta;
}
coefficients.print("coefficients");
}
incompleteBasis::incompleteBasis(int tag)
// If the element is complete, compute the incomplete basis anyway
: nodalBasis(ElementType::getType(ElementType::getParentType(tag),
ElementType::getOrder(tag), true)),
completeBasis(nullptr), polyBasis(nullptr)
{
int tagComplete = ElementType::getType(parentType, order, false);
switch(parentType) {
case TYPE_LIN:
case TYPE_PNT:
case TYPE_QUA:
case TYPE_HEX: polyBasis = new polynomialBasis(type); break;
case TYPE_TET:
case TYPE_PRI:
case TYPE_PYR:
completeBasis = BasisFactory::getNodalBasis(tagComplete);
break;
case TYPE_TRI:
completeBasis = BasisFactory::getNodalBasis(tagComplete);
_computeCoefficientsTriangle();
break;
}
}
incompleteBasis::~incompleteBasis() { delete polyBasis; }
void incompleteBasis::f(double u, double v, double w, double *sf) const
{
if(polyBasis)
polyBasis->f(u, v, w, sf);
else {
double csf[1331];
completeBasis->f(u, v, w, csf);
int szInc = getNumShapeFunctions();
for(int i = 0; i < szInc; ++i) {
sf[i] = csf[i];
for(int j = 0; j < coefficients.size1(); ++j) {
sf[i] += csf[szInc + j] * coefficients(j, i);
}
}
}
}
void incompleteBasis::f(const fullMatrix<double> &coord,
fullMatrix<double> &sf) const
{
if(polyBasis)
polyBasis->f(coord, sf);
else {
completeBasis->f(coord, sf);
int szInc = getNumShapeFunctions();
for(int k = 0; k < sf.size1(); ++k) {
for(int i = 0; i < szInc; ++i) {
for(int j = 0; j < coefficients.size1(); ++j) {
sf(k, i) += sf(k, szInc + j) * coefficients(j, i);
}
}
}
sf.resize(sf.size1(), szInc, false);
}
}
void incompleteBasis::df(const fullMatrix<double> &coord,
fullMatrix<double> &dfm) const
{
if(polyBasis)
polyBasis->df(coord, dfm);
else {
completeBasis->df(coord, dfm);
int szInc = getNumShapeFunctions();
for(int k = 0; k < dfm.size1(); ++k) {
for(int i = 0; i < szInc; ++i) {
for(int j = 0; j < coefficients.size1(); ++j) {
dfm(k, i) += dfm(k, szInc + j) * coefficients(j, i);
}
}
}
dfm.resize(dfm.size1(), szInc, false);
}
}
void incompleteBasis::df(double u, double v, double w, double grads[][3]) const
{
if(polyBasis)
polyBasis->df(u, v, w, grads);
else {
double cgrads[1331][3];
completeBasis->df(u, v, w, cgrads);
int szInc = getNumShapeFunctions();
for(int i = 0; i < szInc; ++i) {
grads[i][0] = cgrads[i][0];
grads[i][1] = cgrads[i][1];
grads[i][2] = cgrads[i][2];
for(int j = 0; j < coefficients.size1(); ++j) {
grads[i][0] = cgrads[szInc + j][0] * coefficients(j, i);
grads[i][1] = cgrads[szInc + j][1] * coefficients(j, i);
grads[i][2] = cgrads[szInc + j][2] * coefficients(j, i);
}
}
}
}
void incompleteBasis::ddf(double u, double v, double w,
double hess[][3][3]) const
{
if(polyBasis)
polyBasis->ddf(u, v, w, hess);
else {
double chess[1331][3][3];
completeBasis->ddf(u, v, w, chess);
int szInc = getNumShapeFunctions();
for(int i = 0; i < szInc; ++i) {
for(int k = 0; k < 3; ++k) {
for(int l = 0; l < 3; ++l) { hess[i][k][l] = chess[i][k][l]; }
}
for(int j = 0; j < coefficients.size1(); ++j) {
for(int k = 0; k < 3; ++k) {
for(int l = 0; l < 3; ++l) {
hess[i][k][l] = chess[szInc + j][k][l] * coefficients(j, i);
}
}
}
}
}
}
void incompleteBasis::dddf(double u, double v, double w,
double third[][3][3][3]) const
{
if(polyBasis)
polyBasis->dddf(u, v, w, third);
else {
double cthird[1331][3][3][3];
completeBasis->dddf(u, v, w, cthird);
int szInc = getNumShapeFunctions();
for(int i = 0; i < szInc; ++i) {
for(int k = 0; k < 3; ++k) {
for(int l = 0; l < 3; ++l) {
for(int m = 0; m < 3; ++m) { third[i][k][l][m] = cthird[i][k][l][m]; }
}
}
for(int j = 0; j < coefficients.size1(); ++j) {
for(int k = 0; k < 3; ++k) {
for(int l = 0; l < 3; ++l) {
for(int m = 0; m < 3; ++m) {
third[i][k][l][m] =
cthird[szInc + j][k][l][m] * coefficients(j, i);
}
}
}
}
}
}
}
|
