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Mesh Oriented datABase
(version 5.5.1)
An array-based unstructured mesh library
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Mesh Oriented datABase
(version 5.5.1)
An array-based unstructured mesh library
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#include <quadratic_hex_map.hpp>
Inheritance diagram for moab::element_utility::Quadratic_hex_map< _Matrix >:Public Types | |
| typedef _Matrix | Matrix |
Public Member Functions | |
| Quadratic_hex_map () | |
| Quadratic_hex_map (const Self &f) | |
| template<typename Moab , typename Entity_handle , typename Points , typename Point > | |
| std::pair< bool, Point > | operator() (const Moab &, const Entity_handle &, const Points &v, const Point &p, const double tol=1.e-6) const |
Private Types | |
| typedef Quadratic_hex_map< Matrix > | Self |
Private Member Functions | |
| double | reference_points (const std::size_t &i, const std::size_t &j) const |
| template<typename Point > | |
| bool | is_contained (const Point &p, const double tol) const |
| template<typename Point , typename Points > | |
| bool | solve_inverse (const Point &x, Point &xi, const Points &points, const double tol=1.e-6) const |
| template<typename Point , typename Points > | |
| Point & | evaluate (const Point &p, const Points &points, Point &f) const |
| template<typename Point , typename Field > | |
| double | evaluate_scalar_field (const Point &p, const Field &field) const |
| template<typename Field , typename Points > | |
| double | integrate_scalar_field (const Points &p, const Field &field_values) const |
| template<typename Point , typename Points > | |
| Matrix & | jacobian (const Point &p, const Points &, Matrix &J) const |
Definition at line 51 of file quadratic_hex_map.hpp.
| typedef _Matrix moab::element_utility::Quadratic_hex_map< _Matrix >::Matrix |
Definition at line 54 of file quadratic_hex_map.hpp.
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private |
Definition at line 57 of file quadratic_hex_map.hpp.
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inline |
Definition at line 61 of file quadratic_hex_map.hpp.
61 {}
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inline |
Definition at line 63 of file quadratic_hex_map.hpp.
63 {}
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inlineprivate |
Definition at line 169 of file quadratic_hex_map.hpp.
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 }
References moab::element_utility::Quadratic_hex_map< _Matrix >::reference_points(), and moab::Element::SH().
Referenced by moab::element_utility::Quadratic_hex_map< _Matrix >::solve_inverse().
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inlineprivate |
Definition at line 190 of file quadratic_hex_map.hpp.
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 }
References moab::element_utility::Quadratic_hex_map< _Matrix >::reference_points(), and moab::Element::SH().
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inlineprivate |
Definition at line 202 of file quadratic_hex_map.hpp.
203 {
204 // TODO: gaussian integration , probably 2x2x2
205 return 0.;
206 }
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inlineprivate |
Definition at line 110 of file quadratic_hex_map.hpp.
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 }
Referenced by moab::element_utility::Quadratic_hex_map< _Matrix >::operator()().
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inlineprivate |
Definition at line 209 of file quadratic_hex_map.hpp.
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 }
References moab::Element::DSH(), moab::element_utility::Quadratic_hex_map< _Matrix >::reference_points(), and moab::Element::SH().
Referenced by moab::element_utility::Quadratic_hex_map< _Matrix >::solve_inverse().
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inline |
Definition at line 68 of file quadratic_hex_map.hpp.
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 }
References moab::element_utility::Quadratic_hex_map< _Matrix >::is_contained(), and moab::element_utility::Quadratic_hex_map< _Matrix >::solve_inverse().
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inlineprivate |
Definition at line 83 of file quadratic_hex_map.hpp.
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 }
Referenced by moab::element_utility::Quadratic_hex_map< _Matrix >::evaluate(), moab::element_utility::Quadratic_hex_map< _Matrix >::evaluate_scalar_field(), and moab::element_utility::Quadratic_hex_map< _Matrix >::jacobian().
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inlineprivate |
Definition at line 118 of file quadratic_hex_map.hpp.
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 }
References moab::element_utility::Quadratic_hex_map< _Matrix >::evaluate(), moab::Matrix::inverse(), and moab::element_utility::Quadratic_hex_map< _Matrix >::jacobian().
Referenced by moab::element_utility::Quadratic_hex_map< _Matrix >::operator()().
1.9.1.