 |
Mesh Oriented datABase
(version 5.5.1)
An array-based unstructured mesh library
|
|
Mesh Oriented datABase
(version 5.5.1)
An array-based unstructured mesh library
|
1 #ifndef MOAB_QUADRATIC_HEX_HPP
2 #define MOAB_QUADRATIC_HEX_HPP
3
4 #include "moab/Matrix3.hpp"
5 #include "moab/CartVect.hpp"
6 #include <sstream>
7 #include <iomanip>
8 #include <iostream>
9
10 namespace moab
11 {
12
13 namespace element_utility
14 {
15
16 namespace
17 {
18
19 double SH( const int i, const double xi )
20 {
21 switch( i )
22 {
23 case -1:
24 return ( xi * xi - xi ) / 2;
25 case 0:
26 return 1 - xi * xi;
27 case 1:
28 return ( xi * xi + xi ) / 2;
29 default:
30 return 0.;
31 }
32 }
33 double DSH( const int i, const double xi )
34 {
35 switch( i )
36 {
37 case -1:
38 return xi - 0.5;
39 case 0:
40 return -2 * xi;
41 case 1:
42 return xi + 0.5;
43 default:
44 return 0.;
45 }
46 }
47
48 } // namespace
49
50 template < typename _Matrix >
51 class Quadratic_hex_map
52 {
53 public:
54 typedef _Matrix Matrix;
55
56 private:
57 typedef Quadratic_hex_map< Matrix > Self;
58
59 public:
60 // Constructor
61 Quadratic_hex_map() {}
62 // Copy constructor
63 Quadratic_hex_map( const Self& f ) {}
64
65 public:
66 // Natural coordinates
67 template < typename Moab, typename Entity_handle, typename Points, typename Point >
68 std::pair< bool, Point > operator()( const Moab& /* moab */,
69 const Entity_handle& /* h */,
70 const Points& v,
71 const Point& p,
72 const double tol = 1.e-6 ) const
73 {
74 Point result( 3, 0.0 );
75 bool point_found = solve_inverse( p, result, v, tol ) && is_contained( result, tol );
76 return std::make_pair( point_found, result );
77 }
78
79 private:
80 // This is a hack to avoid a .cpp file and C++11
81 // reference_points(i,j) will be a 1 or -1;
82 // This should unroll..
83 inline double reference_points( const std::size_t& i, const std::size_t& j ) const
84 {
85 const double rpts[27][3] = { { -1, -1, -1 }, { 1, -1, -1 }, { 1, 1, -1 }, // reference_points nodes: 0-7
86 { -1, 1, -1 }, // mid-edge nodes: 8-19
87 { -1, -1, 1 }, // center-face nodes 20-25 center node 26
88 { 1, -1, 1 }, //
89 { 1, 1, 1 }, { -1, 1, 1 }, // 4 ----- 19 ----- 7
90 { 0, -1, -1 }, // . | . |
91 { 1, 0, -1 }, // 16 25 18 |
92 { 0, 1, -1 }, // . | . |
93 { -1, 0, -1 }, // 5 ----- 17 ----- 6 |
94 { -1, -1, 0 }, // | 12 | 23 15
95 { 1, -1, 0 }, // | | |
96 { 1, 1, 0 }, // | 20 | 26 | 22 |
97 { -1, 1, 0 }, // | | |
98 { 0, -1, 1 }, // 13 21 | 14 |
99 { 1, 0, 1 }, // | 0 ----- 11 ----- 3
100 { 0, 1, 1 }, // | . | .
101 { -1, 0, 1 }, // | 8 24 | 10
102 { 0, -1, 0 }, // | . | .
103 { 1, 0, 0 }, // 1 ----- 9 ----- 2
104 { 0, 1, 0 }, //
105 { -1, 0, 0 }, { 0, 0, -1 }, { 0, 0, 1 }, { 0, 0, 0 } };
106 return rpts[i][j];
107 }
108
109 template < typename Point >
110 bool is_contained( const Point& p, const double tol ) const
111 {
112 // just look at the box+tol here
113 return ( p[0] >= -1. - tol ) && ( p[0] <= 1. + tol ) && ( p[1] >= -1. - tol ) && ( p[1] <= 1. + tol ) &&
114 ( p[2] >= -1. - tol ) && ( p[2] <= 1. + tol );
115 }
116
117 template < typename Point, typename Points >
118 bool solve_inverse( const Point& x, Point& xi, const Points& points, const double tol = 1.e-6 ) const
119 {
120 const double error_tol_sqr = tol * tol;
121 Point delta( 3, 0.0 );
122 xi = delta;
123 evaluate( xi, points, delta );
124 vec_subtract( delta, x );
125 std::size_t num_iterations = 0;
126 #ifdef QUADRATIC_HEX_DEBUG
127 std::stringstream ss;
128 ss << "Point: ";
129 ss << x[0] << ", " << x[1] << ", " << x[2] << std::endl;
130 ss << "Hex: ";
131 for( int i = 0; i < 8; ++i )
132 {
133 ss << points[i][0] << ", " << points[i][1] << ", " << points[i][2] << std::endl;
134 }
135 ss << std::endl;
136 #endif
137 while( normsq( delta ) > error_tol_sqr )
138 {
139 #ifdef QUADRATIC_HEX_DEBUG
140 ss << "Iter #: " << num_iterations << " Err: " << sqrt( normsq( delta ) ) << " Iterate: ";
141 ss << xi[0] << ", " << xi[1] << ", " << xi[2] << std::endl;
142 #endif
143 if( ++num_iterations >= 5 )
144 {
145 return false;
146 }
147 Matrix J;
148 jacobian( xi, points, J );
149 double det = moab::Matrix::determinant3( J );
150 if( fabs( det ) < 1.e-10 )
151 {
152 #ifdef QUADRATIC_HEX_DEBUG
153 std::cerr << ss.str();
154 #endif
155 #ifndef QUADRATIC_HEX_DEBUG
156 std::cerr << x[0] << ", " << x[1] << ", " << x[2] << std::endl;
157 #endif
158 std::cerr << "inverse solve failure: det: " << det << std::endl;
159 exit( -1 );
160 }
161 vec_subtract( xi, moab::Matrix::inverse( J, 1.0 / det ) * delta );
162 evaluate( xi, points, delta );
163 vec_subtract( delta, x );
164 }
165 return true;
166 }
167
168 template < typename Point, typename Points >
169 Point& evaluate( const Point& p, const Points& points, Point& f ) const
170 {
171 typedef typename Points::value_type Vector;
172 Vector result;
173 for( int i = 0; i < 3; ++i )
174 {
175 result[i] = 0;
176 }
177 for( unsigned i = 0; i < 27; ++i )
178 {
179 const double sh = SH( reference_points( i, 0 ), p[0] ) * SH( reference_points( i, 1 ), p[1] ) *
180 SH( reference_points( i, 2 ), p[2] );
181 result += sh * points[i];
182 }
183 for( int i = 0; i < 3; ++i )
184 {
185 f[i] = result[i];
186 }
187 return f;
188 }
189 template < typename Point, typename Field >
190 double evaluate_scalar_field( const Point& p, const Field& field ) const
191 {
192 double x = 0.0;
193 for( int i = 0; i < 27; i++ )
194 {
195 const double sh = SH( reference_points( i, 0 ), p[0] ) * SH( reference_points( i, 1 ), p[1] ) *
196 SH( reference_points( i, 2 ), p[2] );
197 x += sh * field[i];
198 }
199 return x;
200 }
201 template < typename Field, typename Points >
202 double integrate_scalar_field( const Points& p, const Field& field_values ) const
203 {
204 // TODO: gaussian integration , probably 2x2x2
205 return 0.;
206 }
207
208 template < typename Point, typename Points >
209 Matrix& jacobian( const Point& p, const Points& /* points */, Matrix& J ) const
210 {
211 J = Matrix( 0.0 );
212 for( int i = 0; i < 27; i++ )
213 {
214 const double sh[3] = { SH( reference_points( i, 0 ), p[0] ), SH( reference_points( i, 1 ), p[1] ),
215 SH( reference_points( i, 2 ), p[2] ) };
216 const double dsh[3] = { DSH( reference_points( i, 0 ), p[0] ), DSH( reference_points( i, 1 ), p[1] ),
217 DSH( reference_points( i, 2 ), p[2] ) };
218 for( int j = 0; j < 3; j++ )
219 {
220 // dxj/dr first column
221 J( j, 0 ) += dsh[0] * sh[1] * sh[2] * reference_points( i, j );
222 J( j, 1 ) += sh[0] * dsh[1] * sh[2] * reference_points( i, j ); // dxj/ds
223 J( j, 2 ) += sh[0] * sh[1] * dsh[2] * reference_points( i, j ); // dxj/dt
224 }
225 }
226 return J;
227 }
228
229 private:
230 }; // Class Quadratic_hex_map
231
232 } // namespace element_utility
233
234 } // namespace moab
235 #endif // MOAB_QUADRATIC_HEX_nPP
1.9.1.