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
|
// This file is part of ff3d - http://www.freefem.org/ff3d
// Copyright (C) 2001, 2002, 2003 Stphane Del Pino
// This program is free software; you can redistribute it and/or modify
// it under the terms of the GNU General Public License as published by
// the Free Software Foundation; either version 2, or (at your option)
// any later version.
// This program is distributed in the hope that it will be useful,
// but WITHOUT ANY WARRANTY; without even the implied warranty of
// MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
// GNU General Public License for more details.
// You should have received a copy of the GNU General Public License
// along with this program; if not, write to the Free Software Foundation,
// Inc., 59 Temple Place - Suite 330, Boston, MA 02111-1307, USA.
// $Id: ConformTransformation.cpp,v 1.17 2007/06/09 10:37:07 delpinux Exp $
#include <Domain.hpp>
#include <ConformTransformation.hpp>
#include <ScalarFunctionBase.hpp>
real_t
ConformTransformationQ1Hexahedron::integrate(const ScalarFunctionBase& f) const
{
throw ErrorHandler(__FILE__,__LINE__,
"not implemented",
ErrorHandler::unexpected);
return 0;
}
bool
ConformTransformationQ1Hexahedron::
__inside(const real_t& x,
const real_t& y,
const real_t& z,
TinyVector<6, bool>& faces) const
{
bool inside = true;
faces = false;
for (size_t i = 0 ; i<Hexahedron::NumberOfFaces; ++i) {
TinyVector<3, real_t> faceMassCenter(0,0,0);
TinyVector<Hexahedron::FaceType::NumberOfVertices, Vertex*> face;
for (size_t n=0; n<Hexahedron::FaceType::NumberOfVertices; ++n) {
const Vertex& v = __H(Hexahedron::faces[i][n]);
faceMassCenter += v;
face[n] = const_cast<Vertex*>(&v);
}
Quadrangle Q(face);
faceMassCenter *= (1./Hexahedron::FaceType::NumberOfVertices);
TinyVector<3,real_t> normal = Q.normal();
TinyVector<3, real_t> X(x,y,z);
X -= faceMassCenter;
if (X*normal > 0) { // must look in that direction
faces[i] = true;
inside = false;
}
}
return inside;
}
//! Computes Xhat, the point which transformed is (x,y,z)
bool ConformTransformationQ1Hexahedron::
invertT(const real_t& x,
const real_t& y,
const real_t& z,
TinyVector<3,real_t>& Xhat) const
{
// initialization
for(size_t i=0; i<3; ++i)
Xhat[i] = 0.5;
TinyVector<3,real_t> X;
TinyVector<3,real_t> f;
TinyVector<3,real_t> delta;
const size_t maxiter = 100;
size_t niter = 0;
do {
niter++;
//! Computing F(Xhat) - (x,y,z).
value(Xhat,f);
f[0] -= x;
f[1] -= y;
f[2] -= z;
// Evaluation of the Jacobian
TinyMatrix<3,3,real_t> J;
dx(Xhat,X);
for (size_t i=0; i<3; ++i)
J(i,0) = X[i];
dy(Xhat,X);
for (size_t i=0; i<3; ++i)
J(i,1) = X[i];
dz(Xhat,X);
for (size_t i=0; i<3; ++i)
J(i,2) = X[i];
delta = f/J;
// Uses relaxation to help convergence (the functional is not convexe)
Xhat -= delta;
if (niter>maxiter) { // or(Norm(f)>10)) {
return false;
}
} while(Norm(f)>1E-3);
for (size_t i = 0; i<Xhat.size(); ++i) {
if ((Xhat[i]<1E-3) or (Xhat[i]>1.001)) {
return false;
}
}
return true;
}
real_t
ConformTransformationP1Tetrahedron::integrate(const ScalarFunctionBase& f) const
{
throw ErrorHandler(__FILE__,__LINE__,
"not implemented",
ErrorHandler::unexpected);
return 0;
}
real_t
ConformTransformationQ1CartesianHexahedron::
integrateCharacteristic(const Domain& d) const
{
return 1;
// Here we use order 4 Lobatto quadrature
TinyVector<4, real_t> x;
x[0] = 0.;
x[1] = .27639320225002103036; //(1-sqrt(5)/5)/2.;
x[2] = .72360679774997896964; //(1+sqrt(5)/5)/2.;
x[3] = 1.;
TinyVector<4, real_t> w;
w[0] = 1./12.;
w[1] = 5./12.;
w[2] = 5./12.;
w[3] = 1./12.;
real_t sum = 0;
TinyVector<3, real_t> X_hat;
TinyVector<3, real_t> X;
for (unsigned i=0; i<4; ++i) {
X_hat[0] = x[i];
for (unsigned j=0; j<4; ++j) {
X_hat[1] = x[j];
for (unsigned k=0; k<4; ++k) {
X_hat[2] = x[k];
this->value(X_hat, X);
sum += w[i]*w[j]*w[k] * (d.inside(X) ? 1 : 0);
}
}
}
return sum;
}
real_t
ConformTransformationP1Triangle::integrate(const ScalarFunctionBase& f) const
{
throw ErrorHandler(__FILE__,__LINE__,
"not implemented",
ErrorHandler::unexpected);
return 0.;
}
real_t
ConformTransformationQ1Quadrangle::integrate(const ScalarFunctionBase& f) const
{
throw ErrorHandler(__FILE__,__LINE__,
"not implemented",
ErrorHandler::unexpected);
return 0.;
}
|
