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
|
#ifndef _RHEOLEF_INV_PIOLA_H
#define _RHEOLEF_INV_PIOLA_H
///
/// This file is part of Rheolef.
///
/// Copyright (C) 2000-2009 Pierre Saramito <Pierre.Saramito@imag.fr>
///
/// Rheolef 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 of the License, or
/// (at your option) any later version.
///
/// Rheolef 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 Rheolef; if not, write to the Free Software
/// Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA 02111-1307 USA
///
/// =========================================================================
//
// invert piola tranformation on nonlinear elements :
// quadrangles, high-order, etc
// by using the newton generic algorithm
//
#include "rheolef/geo.h"
#include "rheolef/piola_util.h"
namespace rheolef {
template<class T>
class inv_piola {
public:
typedef T float_type;
typedef point_basic<T> value_type;
typedef typename value_type::size_type size_type;
inv_piola();
template<class M>
void reset (const geo_basic<T,M>& omega, const reference_element& hat_K, const std::vector<size_t>& dis_inod);
void set_x (const value_type& x1) { x0 = x1; }
value_type initial() const;
value_type residue (const value_type& hat_xh) const;
void update_derivative (const value_type& hat_xh) const;
value_type derivative_solve (const value_type& r) const;
value_type derivative_trans_mult (const value_type& r) const;
float_type space_norm (const value_type& hat_xh) const;
float_type dual_space_norm (const value_type& r) const;
float_type duality_product (const value_type& r, const value_type& s) const;
protected:
size_t dim, map_dim;
basis_basic<T> b;
reference_element hat_K;
std::vector<value_type> node;
value_type x0;
mutable Eigen::Matrix<float_type,Eigen::Dynamic,1> value;
mutable Eigen::Matrix<value_type,Eigen::Dynamic,1> grad_value;
mutable tensor_basic<T> DF, inv_DF;
};
template<class T>
inv_piola<T>::inv_piola()
: dim(0),
map_dim(0),
b(),
hat_K(),
node(),
x0(),
value(),
grad_value(),
DF(),
inv_DF()
{
}
template<class T>
template<class M>
void
inv_piola<T>::reset (const geo_basic<T,M>& omega, const reference_element& hat_K1, const std::vector<size_t>& dis_inod) {
dim = omega.dimension();
b = omega.get_piola_basis();
hat_K = hat_K1;
map_dim = hat_K1.dimension();
node.resize (dis_inod.size());
for (size_t loc_inod = 0, loc_nnod = node.size(); loc_inod < loc_nnod; ++loc_inod) {
node[loc_inod] = omega.dis_node (dis_inod[loc_inod]);
}
}
template<class T>
typename inv_piola<T>::value_type
inv_piola<T>::initial() const {
switch (hat_K.variant()) {
case reference_element::e : return value_type(0.5);
case reference_element::t : return value_type(1/float_type(3),1/float_type(3));
case reference_element::q : return value_type(0,0);
case reference_element::T : return value_type(1/float_type(3),1/float_type(3),1/float_type(3));
case reference_element::P : return value_type(1/float_type(3),1/float_type(3),0);
case reference_element::H : return value_type(0,0,0);
}
return value_type(0);
}
template<class T>
typename inv_piola<T>::value_type
inv_piola<T>::residue (const value_type& hat_x) const {
b.evaluate (hat_K, hat_x, value);
value_type r;
for (size_t loc_inod = 0, loc_nnod = node.size(); loc_inod < loc_nnod; ++loc_inod) {
r = r + value[loc_inod]*node[loc_inod];
}
return r - x0;
}
template<class T>
void
inv_piola<T>::update_derivative (const value_type& hat_x) const {
b.grad_evaluate (hat_K, hat_x, grad_value);
DF.reset();
for (size_t loc_inod = 0, loc_nnod = node.size(); loc_inod < loc_nnod; ++loc_inod) {
cumul_otimes(DF, node[loc_inod], grad_value[loc_inod], dim, map_dim);
}
inv_DF = pseudo_inverse_jacobian_piola_transformation (DF, dim, map_dim);
}
template<class T>
typename inv_piola<T>::value_type
inv_piola<T>::derivative_solve (const value_type& r) const {
return inv_DF*r;
}
template<class T>
typename inv_piola<T>::float_type
inv_piola<T>::dual_space_norm (const value_type& r) const {
return norm(r);
}
template<class T>
typename inv_piola<T>::float_type
inv_piola<T>::space_norm (const value_type& hat_xh) const {
return norm(hat_xh);
}
template<class T>
typename inv_piola<T>::float_type
inv_piola<T>::duality_product (const value_type& r, const value_type& s) const {
return dot (r, s);
}
template<class T>
typename inv_piola<T>::value_type
inv_piola<T>::derivative_trans_mult (const value_type& r) const {
return DF.trans_mult(r);
}
}// namespace rheolef
#endif // _RHEOLEF_PIOLA_H
|
