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fem_tools.h
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1/** \file fem_tools.h
2 * \brief Loose implementation of some useful functions
3 *
4 * FIXME: Implementation here is very unstructured, need cleaning and pruning
5 *
6 */
7
8#ifndef __FEM_H__
9#define __FEM_H__
10
11#include <petscsys.h>
12
13#ifdef __cplusplus
14extern "C" {
15#endif
16#include <cblas.h>
17#include <lapack_wrap.h>
18#ifdef __cplusplus
19}
20#endif
21
22#define LAMBDA(E, NU) (E * NU / ((1. + NU) * (1. - 2. * NU)))
23#define MU(E, NU) (0.5 * E / (1. + NU))
24#define DELTA(NU_P, NU_PZ, E_P, E_Z) \
25 (((1 + NU_P) * (1 - NU_P - 2 * NU_PZ * (NU_PZ * E_Z / E_P))) / \
26 (E_P * E_P * E_Z))
27
28#define N_MBTET0(x, y, z) (1. - x - y - z) ///< tetrahedral shape function
29#define N_MBTET1(x, y, z) (x) ///< tetrahedral shape function
30#define N_MBTET2(x, y, z) (y) ///< tetrahedral shape function
31#define N_MBTET3(x, y, z) (z) ///< tetrahedral shape function
32#define diffN_MBTET0x (-1.) ///< derivative of tetrahedral shape function
33#define diffN_MBTET0y (-1.) ///< derivative of tetrahedral shape function
34#define diffN_MBTET0z (-1.) ///< derivative of tetrahedral shape function
35#define diffN_MBTET1x (1.) ///< derivative of tetrahedral shape function
36#define diffN_MBTET1y (0.) ///< derivative of tetrahedral shape function
37#define diffN_MBTET1z (0.) ///< derivative of tetrahedral shape function
38#define diffN_MBTET2x (0.) ///< derivative of tetrahedral shape function
39#define diffN_MBTET2y (1.) ///< derivative of tetrahedral shape function
40#define diffN_MBTET2z (0.) ///< derivative of tetrahedral shape function
41#define diffN_MBTET3x (0.) ///< derivative of tetrahedral shape function
42#define diffN_MBTET3y (0.) ///< derivative of tetrahedral shape function
43#define diffN_MBTET3z (1.) ///< derivative of tetrahedral shape function
44
45// MBTRI
46#define N_MBTRI0(x, y) (1. - x - y) ///< triangle shape function
47#define N_MBTRI1(x, y) (x) ///< triangle shape function
48#define N_MBTRI2(x, y) (y) ///< triangle shape function
49#define diffN_MBTRI0x (-1.) ///< derivative of triangle shape function
50#define diffN_MBTRI0y (-1.) ///< derivative of triangle shape function
51#define diffN_MBTRI1x (1.) ///< derivative of triangle shape function
52#define diffN_MBTRI1y (0.) ///< derivative of triangle shape function
53#define diffN_MBTRI2x (0.) ///< derivative of triangle shape function
54#define diffN_MBTRI2y (1.) ///< derivative of triangle shape function
55
56// MBQUAD
57#define N_MBQUAD0(x, y) ((1. - x) * (1. - y)) ///< quad shape function
58#define N_MBQUAD1(x, y) ((x) * (1. - y)) ///< quad shape function
59#define N_MBQUAD2(x, y) ((x) * (y)) ///< quad shape function
60#define N_MBQUAD3(x, y) ((1. - x) * (y)) ///< quad shape function
61#define diffN_MBQUAD0x(y) (-(1. - y))
62#define diffN_MBQUAD0y(x) (-(1. - x))
63#define diffN_MBQUAD1x(y) ((1. - y))
64#define diffN_MBQUAD1y(x) (-x)
65#define diffN_MBQUAD2x(y) (y)
66#define diffN_MBQUAD2y(x) (x)
67#define diffN_MBQUAD3x(y) (-y)
68#define diffN_MBQUAD3y(x) ((1. - x))
69
70// MBHEX
71#define N_MBHEX0(x, y, z) (N_MBQUAD0(x, y) * (1 - z))
72#define N_MBHEX1(x, y, z) (N_MBQUAD1(x, y) * (1 - z))
73#define N_MBHEX2(x, y, z) (N_MBQUAD2(x, y) * (1 - z))
74#define N_MBHEX3(x, y, z) (N_MBQUAD3(x, y) * (1 - z))
75#define N_MBHEX4(x, y, z) (N_MBQUAD0(x, y) * (z))
76#define N_MBHEX5(x, y, z) (N_MBQUAD1(x, y) * (z))
77#define N_MBHEX6(x, y, z) (N_MBQUAD2(x, y) * (z))
78#define N_MBHEX7(x, y, z) (N_MBQUAD3(x, y) * (z))
79#define diffN_MBHEX0x(y, z) (diffN_MBQUAD0x(y) * (1 - z))
80#define diffN_MBHEX1x(y, z) (diffN_MBQUAD1x(y) * (1 - z))
81#define diffN_MBHEX2x(y, z) (diffN_MBQUAD2x(y) * (1 - z))
82#define diffN_MBHEX3x(y, z) (diffN_MBQUAD3x(y) * (1 - z))
83#define diffN_MBHEX4x(y, z) (diffN_MBQUAD0x(y) * (z))
84#define diffN_MBHEX5x(y, z) (diffN_MBQUAD1x(y) * (z))
85#define diffN_MBHEX6x(y, z) (diffN_MBQUAD2x(y) * (z))
86#define diffN_MBHEX7x(y, z) (diffN_MBQUAD3x(y) * (z))
87#define diffN_MBHEX0y(x, z) (diffN_MBQUAD0y(x) * (1 - z))
88#define diffN_MBHEX1y(x, z) (diffN_MBQUAD1y(x) * (1 - z))
89#define diffN_MBHEX2y(x, z) (diffN_MBQUAD2y(x) * (1 - z))
90#define diffN_MBHEX3y(x, z) (diffN_MBQUAD3y(x) * (1 - z))
91#define diffN_MBHEX4y(x, z) (diffN_MBQUAD0y(x) * (z))
92#define diffN_MBHEX5y(x, z) (diffN_MBQUAD1y(x) * (z))
93#define diffN_MBHEX6y(x, z) (diffN_MBQUAD2y(x) * (z))
94#define diffN_MBHEX7y(x, z) (diffN_MBQUAD3y(x) * (z))
95#define diffN_MBHEX0z(x, y) (-N_MBQUAD0(x, y))
96#define diffN_MBHEX1z(x, y) (-N_MBQUAD1(x, y))
97#define diffN_MBHEX2z(x, y) (-N_MBQUAD2(x, y))
98#define diffN_MBHEX3z(x, y) (-N_MBQUAD3(x, y))
99#define diffN_MBHEX4z(x, y) (N_MBQUAD0(x, y))
100#define diffN_MBHEX5z(x, y) (N_MBQUAD1(x, y))
101#define diffN_MBHEX6z(x, y) (N_MBQUAD2(x, y))
102#define diffN_MBHEX7z(x, y) (N_MBQUAD3(x, y))
103
104// MBEDGE
105#define N_MBEDGE0(x) (1. - (x)) ///< edge shape function
106#define N_MBEDGE1(x) (x) ///< edge shape function
107#define diffN_MBEDGE0 (-1.) ///< derivative of edge shape function
108#define diffN_MBEDGE1 (1.) ///< derivative of edge shape function
109
110// MBTRIQ
111#define N_MBTRIQ0(x, y) ((1. - x - y) * (2 * (1. - x - y) - 1.))
112#define N_MBTRIQ1(x, y) (x * (2. * x - 1.))
113#define N_MBTRIQ2(x, y) (y * (2. * y - 1.))
114#define N_MBTRIQ3(x, y) (4. * (1. - x - y) * x)
115#define N_MBTRIQ4(x, y) (4. * x * y)
116#define N_MBTRIQ5(x, y) (4. * (1. - x - y) * y)
117#define diffN_MBTRIQ0x(x, y) (x + y - 3. * (1. - x - y))
118#define diffN_MBTRIQ0y(x, y) (x + y - 3. * (1. - x - y))
119#define diffN_MBTRIQ1x(x, y) (-1. + 4. * x)
120#define diffN_MBTRIQ1y(x, y) (0.)
121#define diffN_MBTRIQ2x(x, y) (0.)
122#define diffN_MBTRIQ2y(x, y) (-1. + 4. * y)
123#define diffN_MBTRIQ3x(x, y) (4. * ((1. - x - y) - x))
124#define diffN_MBTRIQ3y(x, y) (-4. * x)
125#define diffN_MBTRIQ4x(x, y) (4. * y)
126#define diffN_MBTRIQ4y(x, y) (4. * x)
127#define diffN_MBTRIQ5x(x, y) (-4. * y)
128#define diffN_MBTRIQ5y(x, y) (4. * ((1. - x - y) - y))
129
130#ifdef __cplusplus
131extern "C" {
132#endif
133
134/// print matric M
135void print_mat(double *M, int m, int n);
136/// print upper part of the symmetric matrix
137void print_mat_sym_upper(double *M, int m, int n);
138/// priint complex matrix
139void print_mat_complex(__CLPK_doublecomplex *M, int m, int n);
140
141/// \brief calculate shape functions on triangle
142/// \param N shape function array
143/// \param X array of Gauss X coordinates
144/// \param Y array of Gauss Y coordinates
145/// \param G_DIM number of Gauss points
146PetscErrorCode ShapeMBTRI(double *N, const double *X, const double *Y,
147 const int G_DIM);
148/// calculate derivatives of shape functions
149PetscErrorCode ShapeDiffMBTRI(double *diffN);
150
151/// calculate face normal
152/// \param diffN derivatives of shape functions
153/// \param coords is position of the nodes
154/// \param normal vector
155PetscErrorCode ShapeFaceNormalMBTRI(double *diffN, const double *coords,
156 double *normal);
157PetscErrorCode ShapeFaceBaseMBTRI(double *diffN, const double *coords,
158 double *normal, double *s1, double *s2);
159
160/// calculate derivative of normal in respect to nodal positions
161PetscErrorCode ShapeFaceDiffNormalMBTRI(double *diffN, const double *coords,
162 double *diff_normal);
163/// calculate jacobioan
164void ShapeJacMBTRI(double *diffN, const double *coords, double *Jac);
165/// calculate derivatives of shape functions in space
166void ShapeDiffMBTRIinvJ(double *diffN, double *invJac, double *diffNinvJac);
167/// calculate shape functions
168PetscErrorCode ShapeMBTET(double *N, const double *G_X, const double *G_Y,
169 const double *G_Z, int DIM);
170/// calculate derivatives of shape functions
171PetscErrorCode ShapeDiffMBTET(double *diffN);
172/// determined of jacobian
173double ShapeDetJacVolume(double *jac);
174/// calculate jacobian
175PetscErrorCode ShapeJacMBTET(double *diffN, const double *coords, double *jac);
176// calculate inverse of jacobian
177PetscErrorCode ShapeInvJacVolume(double *jac);
178/// calculate TET volume
179double ShapeVolumeMBTET(double *diffN, const double *coords);
180/// calculate shape functions derivatives in space
181PetscErrorCode ShapeDiffMBTETinvJ(double *diffN, double *invJac,
182 double *diffNinvJac);
183
184/// calculate spin matrix from vector
185// \param spinOmega is a spin matrix
186// \param vecOmega is a spin vector
187PetscErrorCode Spin(double *spinOmega, double *vecOmega);
188
189/// Compose complex matrix (3x3) from two real matrices
190PetscErrorCode make_complex_matrix(double *reA, double *imA,
191 __CLPK_doublecomplex *xA);
192/// Complex normal
193PetscErrorCode
194Normal_hierarchical(int order_approx, int *order_edge_approx, int order,
195 int *order_edge, double *diffN, double *diffN_face,
196 double *diffN_edge[], double *dofs, double *dofs_edge[],
197 double *dofs_face, double *idofs, double *idofs_edge[],
198 double *idofs_face, __CLPK_doublecomplex *xnormal,
199 __CLPK_doublecomplex *s1, __CLPK_doublecomplex *s2, int gg);
200PetscErrorCode Base_scale(__CLPK_doublecomplex *xnormal,
201 __CLPK_doublecomplex *xs1, __CLPK_doublecomplex *xs2);
202
203/**
204 * \brief calculate local coordinates for given global coordinates
205 *
206 * new version for multiple points need to be implemented
207 */
208PetscErrorCode ShapeMBTET_inverse(double *N, double *diffN,
209 const double *elem_coords,
210 const double *glob_coords,
211 double *loc_coords);
212
213/**
214 * \brief calculate local coordinates of triangle element for given global
215coordinates in 2D (Assume e.g. z=0) \f[ \left[\begin{array}{cc}
216\frac{\partial N_{1}}{\partial\xi}x_{N_{1}}+\frac{\partial
217N_{2}}{\partial\xi}x_{N_{2}}+\frac{\partial N_{3}}{\partial\xi}x_{N_{3}} &
218\frac{\partial N_{1}}{\partial\eta}x_{N_{1}}+\frac{\partial
219N_{2}}{\partial\eta}x_{N_{2}}+\frac{\partial N_{3}}{\partial\eta}x_{N_{3}}\\
220\frac{\partial N_{1}}{\partial\xi}y_{N_{1}}+\frac{\partial
221N_{2}}{\partial\xi}y_{N_{2}}+\frac{\partial N_{3}}{\partial\xi}y_{N_{3}} &
222\frac{\partial N_{1}}{\partial\eta}y_{N_{1}}+\frac{\partial
223N_{2}}{\partial\eta}y_{N_{2}}+\frac{\partial N_{3}}{\partial\eta}y_{N_{3}}
224\end{array}\right]\left\{ \begin{array}{c}
225\xi\\
226\eta
227\end{array}\right\} =\left\{ \begin{array}{c}
228x_{gp}-\left(N_{1}x_{N_{1}}+N_{2}x_{N_{2}}+N_{3}x_{N_{3}}\right)\\
229y_{gp}-\left(N_{1}y_{N_{1}}+N_{2}y_{N_{2}}+N_{3}y_{N_{3}}\right)
230\end{array}\right\}
231 \f]
232
233 /// \param N shape function array
234 /// \param diffN array of shape function derivative w.r.t to local coordinates
235 /// \param elem_coords global coordinates of element
236 /// \param glob_coords global coordinates of required point
237 /// \param loc_coords local coordinates of required point
238 */
239PetscErrorCode ShapeMBTRI_inverse(double *N, double *diffN,
240 const double *elem_coords,
241 const double *glob_coords,
242 double *loc_coords);
243
244/// calculate gradient of deformation
245PetscErrorCode GradientOfDeformation(double *diffN, double *dofs, double *F);
246
247// 2 Node edge
248PetscErrorCode ShapeMBEDGE(double *N, const double *G_X, int DIM);
249PetscErrorCode ShapeDiffMBEDGE(double *diffN);
250
251// 10 Node Tet
252PetscErrorCode ShapeMBTRIQ(double *N, const double *X, const double *Y,
253 const int G_DIM);
254PetscErrorCode ShapeDiffMBTRIQ(double *diffN, const double *X, const double *Y,
255 const int G_DIM);
256PetscErrorCode ShapeMBTETQ(double *N, const double x, const double y,
257 const double z);
258PetscErrorCode ShapeDiffMBTETQ(double *diffN, const double x, const double y,
259 const double z);
260PetscErrorCode ShapeMBTETQ_GAUSS(double *N, const double *X, const double *Y,
261 const double *Z, const int G_DIM);
262PetscErrorCode ShapeDiffMBTETQ_GAUSS(double *diffN, const double *X,
263 const double *Y, const double *Z,
264 const int G_DIM);
265PetscErrorCode ShapeJacMBTETQ(const double *diffN, const double *coords,
266 double *Jac);
267PetscErrorCode
268ShapeMBTETQ_detJac_at_Gauss_Points(double *detJac_at_Gauss_Points,
269 const double *diffN, const double *coords,
270 int G_DIM);
271double ShapeVolumeMBTETQ(const double *diffN, const double *coords, int G_DIM,
272 double *G_TET_W);
273PetscErrorCode ShapeMBTETQ_inverse(double *N, double *diffN,
274 const double *elem_coords,
275 const double *glob_coords,
276 double *loc_coords, const double eps);
277
278// complex part
279void ShapeDiffMBTETinvJ_complex(double *diffN, __CLPK_doublecomplex *invJac,
280 __CLPK_doublecomplex *diffNinvJac,
281 enum CBLAS_TRANSPOSE Trans);
282PetscErrorCode ShapeFaceNormalMBTRI_complex(double *diffN,
283 __CLPK_doublecomplex *xcoords,
284 __CLPK_doublecomplex *xnormal);
285PetscErrorCode MakeComplexTensor(double *reA, double *imA,
286 __CLPK_doublecomplex *xA);
287PetscErrorCode InvertComplexGradient(__CLPK_doublecomplex *xF);
288PetscErrorCode DeterminantComplexGradient(__CLPK_doublecomplex *xF,
289 __CLPK_doublecomplex *det_xF);
290
291// integration
292/// Compute weights and integration points for edge using Grundmann_Moeller rule
293PetscErrorCode Grundmann_Moeller_integration_points_1D_EDGE(int rule,
294 double *G_TRI_X,
295 double *G_TRI_W);
296/// Compute weights and integration points for 2D Triangle using
297/// Grundmann_Moeller rule
298PetscErrorCode Grundmann_Moeller_integration_points_2D_TRI(int rule,
299 double *G_TRI_X,
300 double *G_TRI_Y,
301 double *G_TRI_W);
302/// Compute weights and integration points for 3D Tet using Grundmann_Moeller
303/// rule
304PetscErrorCode Grundmann_Moeller_integration_points_3D_TET(int rule,
305 double *G_TET_X,
306 double *G_TET_Y,
307 double *G_TET_Z,
308 double *G_TET_W);
309
310// http://people.sc.fsu.edu/~jburkardt/datasets/quadrature_rules_tet/quadrature_rules_tet.html
311// TRI
312static const double G_TRI_X1[] = {3.3333333333333331e-01};
313static const double G_TRI_Y1[] = {3.3333333333333331e-01};
314static const double G_TRI_W1[] = {1.};
315static const double G_TRI_X3[] = {0.5, 0., 0.5};
316static const double G_TRI_Y3[] = {0., 0.5, 0.5};
317static const double G_TRI_W3[] = {
318 3.3333333333333331e-01, 3.3333333333333331e-01, 3.3333333333333331e-01};
319static const double G_TRI_X4[] = {
320 7.503111022260811058e-02, 1.785587282636164064e-01,
321 2.800199154990741235e-01, 6.663902460147014262e-01};
322static const double G_TRI_Y4[] = {
323 2.800199154990741235e-01, 6.663902460147014262e-01,
324 7.503111022260811058e-02, 1.785587282636164064e-01};
325static const double G_TRI_W4[] = {
326 1.8195861825602258066e-01, 3.1804138174397683647e-01,
327 1.8195861825602258066e-01, 3.1804138174397683647e-01};
328static const double G_TRI_X7[] = {
329 0.333333333333333, 0.736712498968435, 0.736712498968435, 0.237932366472434,
330 0.237932366472434, 0.025355134551932, 0.025355134551932};
331static const double G_TRI_Y7[] = {
332 0.333333333333333, 0.237932366472434, 0.025355134551932, 0.736712498968435,
333 0.025355134551932, 0.736712498968435, 0.237932366472434};
334static const double G_TRI_W7[] = {
335 0.375000000000000, 0.104166666666667, 0.104166666666667, 0.104166666666667,
336 0.104166666666667, 0.104166666666667, 0.104166666666667};
337static const double G_TRI_X13[] = {
338 0.333333333333333, 0.479308067841923, 0.260345966079038, 0.260345966079038,
339 0.869739794195568, 0.065130102902216, 0.065130102902216, 0.638444188569809,
340 0.638444188569809, 0.312865496004875, 0.312865496004875, 0.048690315425316,
341 0.048690315425316};
342static const double G_TRI_Y13[] = {
343 0.333333333333333, 0.260345966079038, 0.479308067841923, 0.260345966079038,
344 0.065130102902216, 0.869739794195568, 0.065130102902216, 0.312865496004875,
345 0.048690315425316, 0.638444188569809, 0.048690315425316, 0.638444188569809,
346 0.312865496004875};
347static const double G_TRI_W13[] = {
348 -0.149570044467670, 0.175615257433204, 0.175615257433204, 0.175615257433204,
349 0.053347235608839, 0.053347235608839, 0.053347235608839, 0.077113760890257,
350 0.077113760890257, 0.077113760890257, 0.077113760890257, 0.077113760890257,
351 0.077113760890257};
352
353static const double G_TRI_X19[] = {
354 0.333333333333333, 0.797426985353087, 0.101286507323456, 0.101286507323456,
355 0.059715871789770, 0.470142064105115, 0.470142064105115, 0.535795346449899,
356 0.232102326775050, 0.232102326775050, 0.941038278231121, 0.029480860884440,
357 0.029480860884440, 0.738416812340510, 0.738416812340510, 0.232102326775050,
358 0.232102326775050, 0.029480860884440, 0.029480860884440};
359static const double G_TRI_Y19[] = {
360 0.333333333333333, 0.101286507323456, 0.797426985353087, 0.101286507323456,
361 0.470142064105115, 0.059715871789770, 0.470142064105115, 0.232102326775050,
362 0.535795346449899, 0.232102326775050, 0.029480860884440, 0.941038278231121,
363 0.029480860884440, 0.232102326775050, 0.029480860884440, 0.738416812340510,
364 0.029480860884440, 0.738416812340510, 0.232102326775050};
365static const double G_TRI_W19[] = {
366 9.71357962827961025E-002, 3.13347002271398278E-002,
367 3.13347002271398278E-002, 3.13347002271398278E-002,
368 7.78275410047754301E-002, 7.78275410047754301E-002,
369 7.78275410047754301E-002, 7.96477389272090969E-002,
370 7.96477389272090969E-002, 7.96477389272090969E-002,
371 2.55776756586981006E-002, 2.55776756586981006E-002,
372 2.55776756586981006E-002, 4.32835393772893970E-002,
373 4.32835393772893970E-002, 4.32835393772893970E-002,
374 4.32835393772893970E-002, 4.32835393772893970E-002,
375 4.32835393772893970E-002};
376
377static const double G_TRI_X28[] = {
378 0.333333333333333, 0.948021718143423, 0.025989140928288,
379 0.025989140928288, 0.811424994704155, 0.094287502647923,
380 0.094287502647923, 0.010726449965571, 0.494636775017215,
381 0.494636775017215, 0.585313234770972, 0.207343382614514,
382 0.207343382614514, 0.122184388599019, 0.438907805700491,
383 0.438907805700491, 0.677937654882590, 0.677937654882590,
384 0.044841677589131, 0.044841677589131, 0.277220667528279,
385 0.277220667528279, 0.858870281282636, 0.858870281282636,
386 0.0000000000000000, 0.0000000000000000, 0.141129718717364,
387 0.141129718717364};
388static const double G_TRI_Y28[] = {
389 0.333333333333333, 0.025989140928288, 0.948021718143423, 0.025989140928288,
390 0.094287502647923, 0.811424994704155, 0.094287502647923, 0.494636775017215,
391 0.010726449965571, 0.494636775017215, 0.207343382614514, 0.585313234770972,
392 0.207343382614514, 0.438907805700491, 0.122184388599019, 0.438907805700491,
393 0.044841677589131, 0.277220667528279, 0.677937654882590, 0.277220667528279,
394 0.677937654882590, 0.044841677589131, 0.000000000000000, 0.141129718717364,
395 0.858870281282636, 0.141129718717364, 0.858870281282636, 0.000000000000000};
396static const double G_TRI_W28[] = {
397 0.08797730116222190, 0.008744311553736190, 0.008744311553736190,
398 0.008744311553736190, 0.03808157199393533, 0.03808157199393533,
399 0.03808157199393533, 0.01885544805613125, 0.01885544805613125,
400 0.01885544805613125, 0.07215969754474100, 0.07215969754474100,
401 0.07215969754474100, 0.06932913870553720, 0.06932913870553720,
402 0.06932913870553720, 0.04105631542928860, 0.04105631542928860,
403 0.04105631542928860, 0.04105631542928860, 0.04105631542928860,
404 0.04105631542928860, 0.007362383783300573, 0.007362383783300573,
405 0.007362383783300573, 0.007362383783300573, 0.007362383783300573,
406 0.007362383783300573};
407
408static const double G_TRI_X37[] = {
409 0.333333333333333, 0.950275662924106, 0.024862168537947, 0.024862168537947,
410 0.171614914923835, 0.414192542538082, 0.414192542538082, 0.539412243677190,
411 0.230293878161405, 0.230293878161405, 0.772160036676533, 0.113919981661734,
412 0.113919981661734, 0.009085399949835, 0.495457300025082, 0.495457300025082,
413 0.062277290305887, 0.468861354847056, 0.468861354847056, 0.022076289653624,
414 0.022076289653624, 0.851306504174348, 0.851306504174348, 0.126617206172027,
415 0.126617206172027, 0.018620522802521, 0.018620522802521, 0.689441970728591,
416 0.689441970728591, 0.291937506468888, 0.291937506468888, 0.096506481292159,
417 0.096506481292159, 0.635867859433873, 0.635867859433873, 0.267625659273968,
418 0.267625659273968};
419static const double G_TRI_Y37[] = {
420 0.333333333333333, 0.024862168537947, 0.950275662924106, 0.024862168537947,
421 0.414192542538082, 0.171614914923835, 0.414192542538082, 0.230293878161405,
422 0.539412243677190, 0.230293878161405, 0.113919981661734, 0.772160036676533,
423 0.113919981661734, 0.495457300025082, 0.009085399949835, 0.495457300025082,
424 0.468861354847056, 0.062277290305887, 0.468861354847056, 0.851306504174348,
425 0.126617206172027, 0.022076289653624, 0.126617206172027, 0.022076289653624,
426 0.851306504174348, 0.689441970728591, 0.291937506468888, 0.018620522802521,
427 0.291937506468888, 0.018620522802521, 0.689441970728591, 0.635867859433873,
428 0.267625659273968, 0.096506481292159, 0.267625659273968, 0.096506481292159,
429 0.635867859433873};
430static const double G_TRI_W37[] = {
431 0.051739766065744, 0.008007799555565, 0.008007799555565, 0.008007799555565,
432 0.046868898981822, 0.046868898981822, 0.046868898981822, 0.046590940183976,
433 0.046590940183976, 0.046590940183976, 0.031016943313796, 0.031016943313796,
434 0.031016943313796, 0.010791612736631, 0.010791612736631, 0.010791612736631,
435 0.032195534242432, 0.032195534242432, 0.032195534242432, 0.015445834210702,
436 0.015445834210702, 0.015445834210702, 0.015445834210702, 0.015445834210702,
437 0.015445834210702, 0.017822989923179, 0.017822989923179, 0.017822989923179,
438 0.017822989923179, 0.017822989923179, 0.017822989923179, 0.037038683681385,
439 0.037038683681385, 0.037038683681385, 0.037038683681385, 0.037038683681385,
440 0.037038683681385};
441static const double G_TRI_X286[] = {0.04347826086956522,
442 0.1304347826086956,
443 0.2173913043478261,
444 0.3043478260869565,
445 0.391304347826087,
446 0.4782608695652174,
447 0.5652173913043478,
448 0.6521739130434783,
449 0.7391304347826086,
450 0.8260869565217391,
451 0.9130434782608695,
452 0.04347826086956522,
453 0.1304347826086956,
454 0.2173913043478261,
455 0.3043478260869565,
456 0.391304347826087,
457 0.4782608695652174,
458 0.5652173913043478,
459 0.6521739130434783,
460 0.7391304347826086,
461 0.8260869565217391,
462 0.04347826086956522,
463 0.1304347826086956,
464 0.2173913043478261,
465 0.3043478260869565,
466 0.391304347826087,
467 0.4782608695652174,
468 0.5652173913043478,
469 0.6521739130434783,
470 0.7391304347826086,
471 0.04347826086956522,
472 0.1304347826086956,
473 0.2173913043478261,
474 0.3043478260869565,
475 0.391304347826087,
476 0.4782608695652174,
477 0.5652173913043478,
478 0.6521739130434783,
479 0.04347826086956522,
480 0.1304347826086956,
481 0.2173913043478261,
482 0.3043478260869565,
483 0.391304347826087,
484 0.4782608695652174,
485 0.5652173913043478,
486 0.04347826086956522,
487 0.1304347826086956,
488 0.2173913043478261,
489 0.3043478260869565,
490 0.391304347826087,
491 0.4782608695652174,
492 0.04347826086956522,
493 0.1304347826086956,
494 0.2173913043478261,
495 0.3043478260869565,
496 0.391304347826087,
497 0.04347826086956522,
498 0.1304347826086956,
499 0.2173913043478261,
500 0.3043478260869565,
501 0.04347826086956522,
502 0.1304347826086956,
503 0.2173913043478261,
504 0.04347826086956522,
505 0.1304347826086956,
506 0.04347826086956522,
507 0.04761904761904762,
508 0.1428571428571428,
509 0.2380952380952381,
510 0.3333333333333333,
511 0.4285714285714285,
512 0.5238095238095238,
513 0.6190476190476191,
514 0.7142857142857143,
515 0.8095238095238095,
516 0.9047619047619048,
517 0.04761904761904762,
518 0.1428571428571428,
519 0.2380952380952381,
520 0.3333333333333333,
521 0.4285714285714285,
522 0.5238095238095238,
523 0.6190476190476191,
524 0.7142857142857143,
525 0.8095238095238095,
526 0.04761904761904762,
527 0.1428571428571428,
528 0.2380952380952381,
529 0.3333333333333333,
530 0.4285714285714285,
531 0.5238095238095238,
532 0.6190476190476191,
533 0.7142857142857143,
534 0.04761904761904762,
535 0.1428571428571428,
536 0.2380952380952381,
537 0.3333333333333333,
538 0.4285714285714285,
539 0.5238095238095238,
540 0.6190476190476191,
541 0.04761904761904762,
542 0.1428571428571428,
543 0.2380952380952381,
544 0.3333333333333333,
545 0.4285714285714285,
546 0.5238095238095238,
547 0.04761904761904762,
548 0.1428571428571428,
549 0.2380952380952381,
550 0.3333333333333333,
551 0.4285714285714285,
552 0.04761904761904762,
553 0.1428571428571428,
554 0.2380952380952381,
555 0.3333333333333333,
556 0.04761904761904762,
557 0.1428571428571428,
558 0.2380952380952381,
559 0.04761904761904762,
560 0.1428571428571428,
561 0.04761904761904762,
562 0.05263157894736842,
563 0.1578947368421053,
564 0.2631578947368421,
565 0.3684210526315789,
566 0.4736842105263158,
567 0.5789473684210527,
568 0.6842105263157895,
569 0.7894736842105263,
570 0.8947368421052632,
571 0.05263157894736842,
572 0.1578947368421053,
573 0.2631578947368421,
574 0.3684210526315789,
575 0.4736842105263158,
576 0.5789473684210527,
577 0.6842105263157895,
578 0.7894736842105263,
579 0.05263157894736842,
580 0.1578947368421053,
581 0.2631578947368421,
582 0.3684210526315789,
583 0.4736842105263158,
584 0.5789473684210527,
585 0.6842105263157895,
586 0.05263157894736842,
587 0.1578947368421053,
588 0.2631578947368421,
589 0.3684210526315789,
590 0.4736842105263158,
591 0.5789473684210527,
592 0.05263157894736842,
593 0.1578947368421053,
594 0.2631578947368421,
595 0.3684210526315789,
596 0.4736842105263158,
597 0.05263157894736842,
598 0.1578947368421053,
599 0.2631578947368421,
600 0.3684210526315789,
601 0.05263157894736842,
602 0.1578947368421053,
603 0.2631578947368421,
604 0.05263157894736842,
605 0.1578947368421053,
606 0.05263157894736842,
607 0.05882352941176471,
608 0.1764705882352941,
609 0.2941176470588235,
610 0.4117647058823529,
611 0.5294117647058824,
612 0.6470588235294118,
613 0.7647058823529411,
614 0.8823529411764706,
615 0.05882352941176471,
616 0.1764705882352941,
617 0.2941176470588235,
618 0.4117647058823529,
619 0.5294117647058824,
620 0.6470588235294118,
621 0.7647058823529411,
622 0.05882352941176471,
623 0.1764705882352941,
624 0.2941176470588235,
625 0.4117647058823529,
626 0.5294117647058824,
627 0.6470588235294118,
628 0.05882352941176471,
629 0.1764705882352941,
630 0.2941176470588235,
631 0.4117647058823529,
632 0.5294117647058824,
633 0.05882352941176471,
634 0.1764705882352941,
635 0.2941176470588235,
636 0.4117647058823529,
637 0.05882352941176471,
638 0.1764705882352941,
639 0.2941176470588235,
640 0.05882352941176471,
641 0.1764705882352941,
642 0.05882352941176471,
643 0.06666666666666667,
644 0.2,
645 0.3333333333333333,
646 0.4666666666666667,
647 0.6,
648 0.7333333333333333,
649 0.8666666666666667,
650 0.06666666666666667,
651 0.2,
652 0.3333333333333333,
653 0.4666666666666667,
654 0.6,
655 0.7333333333333333,
656 0.06666666666666667,
657 0.2,
658 0.3333333333333333,
659 0.4666666666666667,
660 0.6,
661 0.06666666666666667,
662 0.2,
663 0.3333333333333333,
664 0.4666666666666667,
665 0.06666666666666667,
666 0.2,
667 0.3333333333333333,
668 0.06666666666666667,
669 0.2,
670 0.06666666666666667,
671 0.07692307692307693,
672 0.2307692307692308,
673 0.3846153846153846,
674 0.5384615384615384,
675 0.6923076923076923,
676 0.8461538461538461,
677 0.07692307692307693,
678 0.2307692307692308,
679 0.3846153846153846,
680 0.5384615384615384,
681 0.6923076923076923,
682 0.07692307692307693,
683 0.2307692307692308,
684 0.3846153846153846,
685 0.5384615384615384,
686 0.07692307692307693,
687 0.2307692307692308,
688 0.3846153846153846,
689 0.07692307692307693,
690 0.2307692307692308,
691 0.07692307692307693,
692 0.09090909090909091,
693 0.2727272727272727,
694 0.4545454545454545,
695 0.6363636363636364,
696 0.8181818181818182,
697 0.09090909090909091,
698 0.2727272727272727,
699 0.4545454545454545,
700 0.6363636363636364,
701 0.09090909090909091,
702 0.2727272727272727,
703 0.4545454545454545,
704 0.09090909090909091,
705 0.2727272727272727,
706 0.09090909090909091,
707 0.1111111111111111,
708 0.3333333333333333,
709 0.5555555555555556,
710 0.7777777777777778,
711 0.1111111111111111,
712 0.3333333333333333,
713 0.5555555555555556,
714 0.1111111111111111,
715 0.3333333333333333,
716 0.1111111111111111,
717 0.1428571428571428,
718 0.4285714285714285,
719 0.7142857142857143,
720 0.1428571428571428,
721 0.4285714285714285,
722 0.1428571428571428,
723 0.2,
724 0.6,
725 0.2,
726 0.3333333333333333};
727static const double G_TRI_Y286[] = {0.04347826086956522,
728 0.04347826086956522,
729 0.04347826086956522,
730 0.04347826086956522,
731 0.04347826086956522,
732 0.04347826086956522,
733 0.04347826086956522,
734 0.04347826086956522,
735 0.04347826086956522,
736 0.04347826086956522,
737 0.04347826086956522,
738 0.1304347826086956,
739 0.1304347826086956,
740 0.1304347826086956,
741 0.1304347826086956,
742 0.1304347826086956,
743 0.1304347826086956,
744 0.1304347826086956,
745 0.1304347826086956,
746 0.1304347826086956,
747 0.1304347826086956,
748 0.2173913043478261,
749 0.2173913043478261,
750 0.2173913043478261,
751 0.2173913043478261,
752 0.2173913043478261,
753 0.2173913043478261,
754 0.2173913043478261,
755 0.2173913043478261,
756 0.2173913043478261,
757 0.3043478260869565,
758 0.3043478260869565,
759 0.3043478260869565,
760 0.3043478260869565,
761 0.3043478260869565,
762 0.3043478260869565,
763 0.3043478260869565,
764 0.3043478260869565,
765 0.391304347826087,
766 0.391304347826087,
767 0.391304347826087,
768 0.391304347826087,
769 0.391304347826087,
770 0.391304347826087,
771 0.391304347826087,
772 0.4782608695652174,
773 0.4782608695652174,
774 0.4782608695652174,
775 0.4782608695652174,
776 0.4782608695652174,
777 0.4782608695652174,
778 0.5652173913043478,
779 0.5652173913043478,
780 0.5652173913043478,
781 0.5652173913043478,
782 0.5652173913043478,
783 0.6521739130434783,
784 0.6521739130434783,
785 0.6521739130434783,
786 0.6521739130434783,
787 0.7391304347826086,
788 0.7391304347826086,
789 0.7391304347826086,
790 0.8260869565217391,
791 0.8260869565217391,
792 0.9130434782608695,
793 0.04761904761904762,
794 0.04761904761904762,
795 0.04761904761904762,
796 0.04761904761904762,
797 0.04761904761904762,
798 0.04761904761904762,
799 0.04761904761904762,
800 0.04761904761904762,
801 0.04761904761904762,
802 0.04761904761904762,
803 0.1428571428571428,
804 0.1428571428571428,
805 0.1428571428571428,
806 0.1428571428571428,
807 0.1428571428571428,
808 0.1428571428571428,
809 0.1428571428571428,
810 0.1428571428571428,
811 0.1428571428571428,
812 0.2380952380952381,
813 0.2380952380952381,
814 0.2380952380952381,
815 0.2380952380952381,
816 0.2380952380952381,
817 0.2380952380952381,
818 0.2380952380952381,
819 0.2380952380952381,
820 0.3333333333333333,
821 0.3333333333333333,
822 0.3333333333333333,
823 0.3333333333333333,
824 0.3333333333333333,
825 0.3333333333333333,
826 0.3333333333333333,
827 0.4285714285714285,
828 0.4285714285714285,
829 0.4285714285714285,
830 0.4285714285714285,
831 0.4285714285714285,
832 0.4285714285714285,
833 0.5238095238095238,
834 0.5238095238095238,
835 0.5238095238095238,
836 0.5238095238095238,
837 0.5238095238095238,
838 0.6190476190476191,
839 0.6190476190476191,
840 0.6190476190476191,
841 0.6190476190476191,
842 0.7142857142857143,
843 0.7142857142857143,
844 0.7142857142857143,
845 0.8095238095238095,
846 0.8095238095238095,
847 0.9047619047619048,
848 0.05263157894736842,
849 0.05263157894736842,
850 0.05263157894736842,
851 0.05263157894736842,
852 0.05263157894736842,
853 0.05263157894736842,
854 0.05263157894736842,
855 0.05263157894736842,
856 0.05263157894736842,
857 0.1578947368421053,
858 0.1578947368421053,
859 0.1578947368421053,
860 0.1578947368421053,
861 0.1578947368421053,
862 0.1578947368421053,
863 0.1578947368421053,
864 0.1578947368421053,
865 0.2631578947368421,
866 0.2631578947368421,
867 0.2631578947368421,
868 0.2631578947368421,
869 0.2631578947368421,
870 0.2631578947368421,
871 0.2631578947368421,
872 0.3684210526315789,
873 0.3684210526315789,
874 0.3684210526315789,
875 0.3684210526315789,
876 0.3684210526315789,
877 0.3684210526315789,
878 0.4736842105263158,
879 0.4736842105263158,
880 0.4736842105263158,
881 0.4736842105263158,
882 0.4736842105263158,
883 0.5789473684210527,
884 0.5789473684210527,
885 0.5789473684210527,
886 0.5789473684210527,
887 0.6842105263157895,
888 0.6842105263157895,
889 0.6842105263157895,
890 0.7894736842105263,
891 0.7894736842105263,
892 0.8947368421052632,
893 0.05882352941176471,
894 0.05882352941176471,
895 0.05882352941176471,
896 0.05882352941176471,
897 0.05882352941176471,
898 0.05882352941176471,
899 0.05882352941176471,
900 0.05882352941176471,
901 0.1764705882352941,
902 0.1764705882352941,
903 0.1764705882352941,
904 0.1764705882352941,
905 0.1764705882352941,
906 0.1764705882352941,
907 0.1764705882352941,
908 0.2941176470588235,
909 0.2941176470588235,
910 0.2941176470588235,
911 0.2941176470588235,
912 0.2941176470588235,
913 0.2941176470588235,
914 0.4117647058823529,
915 0.4117647058823529,
916 0.4117647058823529,
917 0.4117647058823529,
918 0.4117647058823529,
919 0.5294117647058824,
920 0.5294117647058824,
921 0.5294117647058824,
922 0.5294117647058824,
923 0.6470588235294118,
924 0.6470588235294118,
925 0.6470588235294118,
926 0.7647058823529411,
927 0.7647058823529411,
928 0.8823529411764706,
929 0.06666666666666667,
930 0.06666666666666667,
931 0.06666666666666667,
932 0.06666666666666667,
933 0.06666666666666667,
934 0.06666666666666667,
935 0.06666666666666667,
936 0.2,
937 0.2,
938 0.2,
939 0.2,
940 0.2,
941 0.2,
942 0.3333333333333333,
943 0.3333333333333333,
944 0.3333333333333333,
945 0.3333333333333333,
946 0.3333333333333333,
947 0.4666666666666667,
948 0.4666666666666667,
949 0.4666666666666667,
950 0.4666666666666667,
951 0.6,
952 0.6,
953 0.6,
954 0.7333333333333333,
955 0.7333333333333333,
956 0.8666666666666667,
957 0.07692307692307693,
958 0.07692307692307693,
959 0.07692307692307693,
960 0.07692307692307693,
961 0.07692307692307693,
962 0.07692307692307693,
963 0.2307692307692308,
964 0.2307692307692308,
965 0.2307692307692308,
966 0.2307692307692308,
967 0.2307692307692308,
968 0.3846153846153846,
969 0.3846153846153846,
970 0.3846153846153846,
971 0.3846153846153846,
972 0.5384615384615384,
973 0.5384615384615384,
974 0.5384615384615384,
975 0.6923076923076923,
976 0.6923076923076923,
977 0.8461538461538461,
978 0.09090909090909091,
979 0.09090909090909091,
980 0.09090909090909091,
981 0.09090909090909091,
982 0.09090909090909091,
983 0.2727272727272727,
984 0.2727272727272727,
985 0.2727272727272727,
986 0.2727272727272727,
987 0.4545454545454545,
988 0.4545454545454545,
989 0.4545454545454545,
990 0.6363636363636364,
991 0.6363636363636364,
992 0.8181818181818182,
993 0.1111111111111111,
994 0.1111111111111111,
995 0.1111111111111111,
996 0.1111111111111111,
997 0.3333333333333333,
998 0.3333333333333333,
999 0.3333333333333333,
1000 0.5555555555555556,
1001 0.5555555555555556,
1002 0.7777777777777778,
1003 0.1428571428571428,
1004 0.1428571428571428,
1005 0.1428571428571428,
1006 0.4285714285714285,
1007 0.4285714285714285,
1008 0.7142857142857143,
1009 0.2,
1010 0.2,
1011 0.6,
1012 0.3333333333333333};
1013static const double G_TRI_W286[] = {
1014 2.912193380035668, 2.912193380035668, 2.912193380035668,
1015 2.912193380035668, 2.912193380035668, 2.912193380035668,
1016 2.912193380035668, 2.912193380035668, 2.912193380035668,
1017 2.912193380035668, 2.912193380035668, 2.912193380035668,
1018 2.912193380035668, 2.912193380035668, 2.912193380035668,
1019 2.912193380035668, 2.912193380035668, 2.912193380035668,
1020 2.912193380035668, 2.912193380035668, 2.912193380035668,
1021 2.912193380035668, 2.912193380035668, 2.912193380035668,
1022 2.912193380035668, 2.912193380035668, 2.912193380035668,
1023 2.912193380035668, 2.912193380035668, 2.912193380035668,
1024 2.912193380035668, 2.912193380035668, 2.912193380035668,
1025 2.912193380035668, 2.912193380035668, 2.912193380035668,
1026 2.912193380035668, 2.912193380035668, 2.912193380035668,
1027 2.912193380035668, 2.912193380035668, 2.912193380035668,
1028 2.912193380035668, 2.912193380035668, 2.912193380035668,
1029 2.912193380035668, 2.912193380035668, 2.912193380035668,
1030 2.912193380035668, 2.912193380035668, 2.912193380035668,
1031 2.912193380035668, 2.912193380035668, 2.912193380035668,
1032 2.912193380035668, 2.912193380035668, 2.912193380035668,
1033 2.912193380035668, 2.912193380035668, 2.912193380035668,
1034 2.912193380035668, 2.912193380035668, 2.912193380035668,
1035 2.912193380035668, 2.912193380035668, 2.912193380035668,
1036 -9.914451197589852, -9.914451197589852, -9.914451197589852,
1037 -9.914451197589852, -9.914451197589852, -9.914451197589852,
1038 -9.914451197589852, -9.914451197589852, -9.914451197589852,
1039 -9.914451197589852, -9.914451197589852, -9.914451197589852,
1040 -9.914451197589852, -9.914451197589852, -9.914451197589852,
1041 -9.914451197589852, -9.914451197589852, -9.914451197589852,
1042 -9.914451197589852, -9.914451197589852, -9.914451197589852,
1043 -9.914451197589852, -9.914451197589852, -9.914451197589852,
1044 -9.914451197589852, -9.914451197589852, -9.914451197589852,
1045 -9.914451197589852, -9.914451197589852, -9.914451197589852,
1046 -9.914451197589852, -9.914451197589852, -9.914451197589852,
1047 -9.914451197589852, -9.914451197589852, -9.914451197589852,
1048 -9.914451197589852, -9.914451197589852, -9.914451197589852,
1049 -9.914451197589852, -9.914451197589852, -9.914451197589852,
1050 -9.914451197589852, -9.914451197589852, -9.914451197589852,
1051 -9.914451197589852, -9.914451197589852, -9.914451197589852,
1052 -9.914451197589852, -9.914451197589852, -9.914451197589852,
1053 -9.914451197589852, -9.914451197589852, -9.914451197589852,
1054 -9.914451197589852, 13.33158527957992, 13.33158527957992,
1055 13.33158527957992, 13.33158527957992, 13.33158527957992,
1056 13.33158527957992, 13.33158527957992, 13.33158527957992,
1057 13.33158527957992, 13.33158527957992, 13.33158527957992,
1058 13.33158527957992, 13.33158527957992, 13.33158527957992,
1059 13.33158527957992, 13.33158527957992, 13.33158527957992,
1060 13.33158527957992, 13.33158527957992, 13.33158527957992,
1061 13.33158527957992, 13.33158527957992, 13.33158527957992,
1062 13.33158527957992, 13.33158527957992, 13.33158527957992,
1063 13.33158527957992, 13.33158527957992, 13.33158527957992,
1064 13.33158527957992, 13.33158527957992, 13.33158527957992,
1065 13.33158527957992, 13.33158527957992, 13.33158527957992,
1066 13.33158527957992, 13.33158527957992, 13.33158527957992,
1067 13.33158527957992, 13.33158527957992, 13.33158527957992,
1068 13.33158527957992, 13.33158527957992, 13.33158527957992,
1069 13.33158527957992, -9.027792408986382, -9.027792408986382,
1070 -9.027792408986382, -9.027792408986382, -9.027792408986382,
1071 -9.027792408986382, -9.027792408986382, -9.027792408986382,
1072 -9.027792408986382, -9.027792408986382, -9.027792408986382,
1073 -9.027792408986382, -9.027792408986382, -9.027792408986382,
1074 -9.027792408986382, -9.027792408986382, -9.027792408986382,
1075 -9.027792408986382, -9.027792408986382, -9.027792408986382,
1076 -9.027792408986382, -9.027792408986382, -9.027792408986382,
1077 -9.027792408986382, -9.027792408986382, -9.027792408986382,
1078 -9.027792408986382, -9.027792408986382, -9.027792408986382,
1079 -9.027792408986382, -9.027792408986382, -9.027792408986382,
1080 -9.027792408986382, -9.027792408986382, -9.027792408986382,
1081 -9.027792408986382, 3.258672079964582, 3.258672079964582,
1082 3.258672079964582, 3.258672079964582, 3.258672079964582,
1083 3.258672079964582, 3.258672079964582, 3.258672079964582,
1084 3.258672079964582, 3.258672079964582, 3.258672079964582,
1085 3.258672079964582, 3.258672079964582, 3.258672079964582,
1086 3.258672079964582, 3.258672079964582, 3.258672079964582,
1087 3.258672079964582, 3.258672079964582, 3.258672079964582,
1088 3.258672079964582, 3.258672079964582, 3.258672079964582,
1089 3.258672079964582, 3.258672079964582, 3.258672079964582,
1090 3.258672079964582, 3.258672079964582, -0.6133639040302452,
1091 -0.6133639040302452, -0.6133639040302452, -0.6133639040302452,
1092 -0.6133639040302452, -0.6133639040302452, -0.6133639040302452,
1093 -0.6133639040302452, -0.6133639040302452, -0.6133639040302452,
1094 -0.6133639040302452, -0.6133639040302452, -0.6133639040302452,
1095 -0.6133639040302452, -0.6133639040302452, -0.6133639040302452,
1096 -0.6133639040302452, -0.6133639040302452, -0.6133639040302452,
1097 -0.6133639040302452, -0.6133639040302452, 0.05511571669513555,
1098 0.05511571669513555, 0.05511571669513555, 0.05511571669513555,
1099 0.05511571669513555, 0.05511571669513555, 0.05511571669513555,
1100 0.05511571669513555, 0.05511571669513555, 0.05511571669513555,
1101 0.05511571669513555, 0.05511571669513555, 0.05511571669513555,
1102 0.05511571669513555, 0.05511571669513555, -0.001979122382447095,
1103 -0.001979122382447095, -0.001979122382447095, -0.001979122382447095,
1104 -0.001979122382447095, -0.001979122382447095, -0.001979122382447095,
1105 -0.001979122382447095, -0.001979122382447095, -0.001979122382447095,
1106 2.02054621415273e-05, 2.02054621415273e-05, 2.02054621415273e-05,
1107 2.02054621415273e-05, 2.02054621415273e-05, 2.02054621415273e-05,
1108 -2.874940020535803e-08, -2.874940020535803e-08, -2.874940020535803e-08,
1109 8.829438425435718e-13};
1110
1111// TET
1112static const double G_TET_X1[] = {0.25};
1113static const double G_TET_Y1[] = {0.25};
1114static const double G_TET_Z1[] = {0.25};
1115static const double G_TET_W1[] = {1.};
1116static const double G_TET_X4[] = {0.1757281246520584, 0.2445310270213291,
1117 0.5556470949048655, 0.0240937534217468};
1118static const double G_TET_Y4[] = {0.5656137776620919, 0.0501800797762026,
1119 0.1487681308666864, 0.2354380116950194};
1120static const double G_TET_Z4[] = {0.2180665126782654, 0.5635595064952189,
1121 0.0350112499848832, 0.1833627308416330};
1122static const double G_TET_W4[] = {0.25, 0.25, 0.25, 0.25};
1123static const double G_TET_X5[] = {0.25000000000000000, 0.50000000000000000,
1124 0.16666666666666667, 0.16666666666666667,
1125 0.16666666666666667};
1126static const double G_TET_Y5[] = {0.25000000000000000, 0.16666666666666667,
1127 0.50000000000000000, 0.16666666666666667,
1128 0.16666666666666667};
1129static const double G_TET_Z5[] = {0.25000000000000000, 0.16666666666666667,
1130 0.16666666666666667, 0.50000000000000000,
1131 0.16666666666666667};
1132static const double G_TET_W5[] = {-0.80000000000000000, 0.45000000000000000,
1133 0.45000000000000000, 0.45000000000000000,
1134 0.45000000000000000};
1135static const double G_TET_X10[] = {0.5684305841968444, 0.1438564719343852,
1136 0.1438564719343852, 0.1438564719343852,
1137 0.0000000000000000, 0.5000000000000000,
1138 0.5000000000000000, 0.5000000000000000,
1139 0.0000000000000000, 0.0000000000000000};
1140static const double G_TET_Y10[] = {0.1438564719343852, 0.1438564719343852,
1141 0.1438564719343852, 0.5684305841968444,
1142 0.5000000000000000, 0.0000000000000000,
1143 0.5000000000000000, 0.0000000000000000,
1144 0.5000000000000000, 0.0000000000000000};
1145static const double G_TET_Z10[] = {0.1438564719343852, 0.1438564719343852,
1146 0.5684305841968444, 0.1438564719343852,
1147 0.5000000000000000, 0.5000000000000000,
1148 0.0000000000000000, 0.0000000000000000,
1149 0.0000000000000000, 0.5000000000000000};
1150static const double G_TET_W10[] = {0.2177650698804054, 0.2177650698804054,
1151 0.2177650698804054, 0.2177650698804054,
1152 0.0214899534130631, 0.0214899534130631,
1153 0.0214899534130631, 0.0214899534130631,
1154 0.0214899534130631, 0.0214899534130631};
1155
1156static const double G_TET_X45[] = {
1157 0.2500000000000000, 0.6175871903000830, 0.1274709365666390,
1158 0.1274709365666390, 0.1274709365666390, 0.9037635088221031,
1159 0.0320788303926323, 0.0320788303926323, 0.0320788303926323,
1160 0.4502229043567190, 0.0497770956432810, 0.0497770956432810,
1161 0.0497770956432810, 0.4502229043567190, 0.4502229043567190,
1162 0.3162695526014501, 0.1837304473985499, 0.1837304473985499,
1163 0.1837304473985499, 0.3162695526014501, 0.3162695526014501,
1164 0.0229177878448171, 0.2319010893971509, 0.2319010893971509,
1165 0.5132800333608811, 0.2319010893971509, 0.2319010893971509,
1166 0.2319010893971509, 0.0229177878448171, 0.5132800333608811,
1167 0.2319010893971509, 0.0229177878448171, 0.5132800333608811,
1168 0.7303134278075384, 0.0379700484718286, 0.0379700484718286,
1169 0.1937464752488044, 0.0379700484718286, 0.0379700484718286,
1170 0.0379700484718286, 0.7303134278075384, 0.1937464752488044,
1171 0.0379700484718286, 0.7303134278075384, 0.1937464752488044};
1172static const double G_TET_Y45[] = {
1173 0.2500000000000000, 0.1274709365666390, 0.1274709365666390,
1174 0.1274709365666390, 0.6175871903000830, 0.0320788303926323,
1175 0.0320788303926323, 0.0320788303926323, 0.9037635088221031,
1176 0.0497770956432810, 0.4502229043567190, 0.0497770956432810,
1177 0.4502229043567190, 0.0497770956432810, 0.4502229043567190,
1178 0.1837304473985499, 0.3162695526014501, 0.1837304473985499,
1179 0.3162695526014501, 0.1837304473985499, 0.3162695526014501,
1180 0.2319010893971509, 0.0229177878448171, 0.2319010893971509,
1181 0.2319010893971509, 0.5132800333608811, 0.2319010893971509,
1182 0.0229177878448171, 0.5132800333608811, 0.2319010893971509,
1183 0.5132800333608811, 0.2319010893971509, 0.0229177878448171,
1184 0.0379700484718286, 0.7303134278075384, 0.0379700484718286,
1185 0.0379700484718286, 0.1937464752488044, 0.0379700484718286,
1186 0.7303134278075384, 0.1937464752488044, 0.0379700484718286,
1187 0.1937464752488044, 0.0379700484718286, 0.7303134278075384};
1188static const double G_TET_Z45[] = {
1189 0.2500000000000000, 0.1274709365666390, 0.1274709365666390,
1190 0.6175871903000830, 0.1274709365666390, 0.0320788303926323,
1191 0.0320788303926323, 0.9037635088221031, 0.0320788303926323,
1192 0.0497770956432810, 0.0497770956432810, 0.4502229043567190,
1193 0.4502229043567190, 0.4502229043567190, 0.0497770956432810,
1194 0.1837304473985499, 0.1837304473985499, 0.3162695526014501,
1195 0.3162695526014501, 0.3162695526014501, 0.1837304473985499,
1196 0.2319010893971509, 0.2319010893971509, 0.0229177878448171,
1197 0.2319010893971509, 0.2319010893971509, 0.5132800333608811,
1198 0.5132800333608811, 0.2319010893971509, 0.0229177878448171,
1199 0.0229177878448171, 0.5132800333608811, 0.2319010893971509,
1200 0.0379700484718286, 0.0379700484718286, 0.7303134278075384,
1201 0.0379700484718286, 0.0379700484718286, 0.1937464752488044,
1202 0.1937464752488044, 0.0379700484718286, 0.7303134278075384,
1203 0.7303134278075384, 0.1937464752488044, 0.0379700484718286};
1204static const double G_TET_W45[] = {
1205 -0.2359620398477557, 0.0244878963560562, 0.0244878963560562,
1206 0.0244878963560562, 0.0244878963560562, 0.0039485206398261,
1207 0.0039485206398261, 0.0039485206398261, 0.0039485206398261,
1208 0.0263055529507371, 0.0263055529507371, 0.0263055529507371,
1209 0.0263055529507371, 0.0263055529507371, 0.0263055529507371,
1210 0.0829803830550589, 0.0829803830550589, 0.0829803830550589,
1211 0.0829803830550589, 0.0829803830550589, 0.0829803830550589,
1212 0.0254426245481023, 0.0254426245481023, 0.0254426245481023,
1213 0.0254426245481023, 0.0254426245481023, 0.0254426245481023,
1214 0.0254426245481023, 0.0254426245481023, 0.0254426245481023,
1215 0.0254426245481023, 0.0254426245481023, 0.0254426245481023,
1216 0.0134324384376852, 0.0134324384376852, 0.0134324384376852,
1217 0.0134324384376852, 0.0134324384376852, 0.0134324384376852,
1218 0.0134324384376852, 0.0134324384376852, 0.0134324384376852,
1219 0.0134324384376852, 0.0134324384376852, 0.0134324384376852};
1220static const double NC_TET_X84[] = {
1221 0.1000000000000000, 0.1000000000000000, 0.1000000000000000,
1222 0.7000000000000000, 0.1000000000000000, 0.1000000000000000,
1223 0.1000000000000000, 0.1000000000000000, 0.1000000000000000,
1224 0.1000000000000000, 0.6000000000000000, 0.6000000000000000,
1225 0.6000000000000000, 0.2000000000000000, 0.2000000000000000,
1226 0.2000000000000000, 0.1000000000000000, 0.1000000000000000,
1227 0.1000000000000000, 0.1000000000000000, 0.1000000000000000,
1228 0.1000000000000000, 0.5000000000000000, 0.5000000000000000,
1229 0.5000000000000000, 0.3000000000000000, 0.3000000000000000,
1230 0.3000000000000000, 0.2000000000000000, 0.2000000000000000,
1231 0.2000000000000000, 0.2000000000000000, 0.2000000000000000,
1232 0.2000000000000000, 0.1000000000000000, 0.1000000000000000,
1233 0.1000000000000000, 0.5000000000000000, 0.5000000000000000,
1234 0.5000000000000000, 0.4000000000000000, 0.4000000000000000,
1235 0.4000000000000000, 0.1000000000000000, 0.1000000000000000,
1236 0.1000000000000000, 0.4000000000000000, 0.4000000000000000,
1237 0.4000000000000000, 0.4000000000000000, 0.4000000000000000,
1238 0.4000000000000000, 0.3000000000000000, 0.3000000000000000,
1239 0.3000000000000000, 0.3000000000000000, 0.3000000000000000,
1240 0.3000000000000000, 0.2000000000000000, 0.2000000000000000,
1241 0.2000000000000000, 0.2000000000000000, 0.2000000000000000,
1242 0.2000000000000000, 0.1000000000000000, 0.1000000000000000,
1243 0.1000000000000000, 0.1000000000000000, 0.1000000000000000,
1244 0.1000000000000000, 0.2000000000000000, 0.2000000000000000,
1245 0.2000000000000000, 0.4000000000000000, 0.3000000000000000,
1246 0.3000000000000000, 0.3000000000000000, 0.1000000000000000,
1247 0.3000000000000000, 0.3000000000000000, 0.3000000000000000,
1248 0.2000000000000000, 0.2000000000000000, 0.2000000000000000};
1249static const double NC_TET_Y84[] = {
1250 0.1000000000000000, 0.1000000000000000, 0.7000000000000000,
1251 0.1000000000000000, 0.1000000000000000, 0.1000000000000000,
1252 0.6000000000000000, 0.6000000000000000, 0.2000000000000000,
1253 0.2000000000000000, 0.1000000000000000, 0.1000000000000000,
1254 0.2000000000000000, 0.1000000000000000, 0.1000000000000000,
1255 0.6000000000000000, 0.1000000000000000, 0.1000000000000000,
1256 0.5000000000000000, 0.5000000000000000, 0.3000000000000000,
1257 0.3000000000000000, 0.1000000000000000, 0.1000000000000000,
1258 0.3000000000000000, 0.1000000000000000, 0.1000000000000000,
1259 0.5000000000000000, 0.2000000000000000, 0.2000000000000000,
1260 0.1000000000000000, 0.1000000000000000, 0.5000000000000000,
1261 0.5000000000000000, 0.2000000000000000, 0.2000000000000000,
1262 0.5000000000000000, 0.2000000000000000, 0.2000000000000000,
1263 0.1000000000000000, 0.4000000000000000, 0.1000000000000000,
1264 0.1000000000000000, 0.4000000000000000, 0.4000000000000000,
1265 0.1000000000000000, 0.3000000000000000, 0.3000000000000000,
1266 0.2000000000000000, 0.2000000000000000, 0.1000000000000000,
1267 0.1000000000000000, 0.4000000000000000, 0.4000000000000000,
1268 0.2000000000000000, 0.2000000000000000, 0.1000000000000000,
1269 0.1000000000000000, 0.4000000000000000, 0.4000000000000000,
1270 0.3000000000000000, 0.3000000000000000, 0.1000000000000000,
1271 0.1000000000000000, 0.4000000000000000, 0.4000000000000000,
1272 0.3000000000000000, 0.3000000000000000, 0.2000000000000000,
1273 0.2000000000000000, 0.2000000000000000, 0.2000000000000000,
1274 0.4000000000000000, 0.2000000000000000, 0.3000000000000000,
1275 0.3000000000000000, 0.1000000000000000, 0.3000000000000000,
1276 0.3000000000000000, 0.2000000000000000, 0.2000000000000000,
1277 0.3000000000000000, 0.3000000000000000, 0.2000000000000000};
1278static const double NC_TET_Z84[] = {
1279 0.1000000000000000, 0.7000000000000000, 0.1000000000000000,
1280 0.1000000000000000, 0.6000000000000000, 0.2000000000000000,
1281 0.1000000000000000, 0.2000000000000000, 0.1000000000000000,
1282 0.6000000000000000, 0.1000000000000000, 0.2000000000000000,
1283 0.1000000000000000, 0.1000000000000000, 0.6000000000000000,
1284 0.1000000000000000, 0.5000000000000000, 0.3000000000000000,
1285 0.1000000000000000, 0.3000000000000000, 0.1000000000000000,
1286 0.5000000000000000, 0.1000000000000000, 0.3000000000000000,
1287 0.1000000000000000, 0.1000000000000000, 0.5000000000000000,
1288 0.1000000000000000, 0.1000000000000000, 0.5000000000000000,
1289 0.2000000000000000, 0.5000000000000000, 0.2000000000000000,
1290 0.1000000000000000, 0.2000000000000000, 0.5000000000000000,
1291 0.2000000000000000, 0.2000000000000000, 0.1000000000000000,
1292 0.2000000000000000, 0.1000000000000000, 0.4000000000000000,
1293 0.1000000000000000, 0.4000000000000000, 0.1000000000000000,
1294 0.4000000000000000, 0.2000000000000000, 0.1000000000000000,
1295 0.3000000000000000, 0.1000000000000000, 0.3000000000000000,
1296 0.2000000000000000, 0.2000000000000000, 0.1000000000000000,
1297 0.4000000000000000, 0.1000000000000000, 0.4000000000000000,
1298 0.2000000000000000, 0.3000000000000000, 0.1000000000000000,
1299 0.4000000000000000, 0.1000000000000000, 0.4000000000000000,
1300 0.3000000000000000, 0.3000000000000000, 0.2000000000000000,
1301 0.4000000000000000, 0.2000000000000000, 0.4000000000000000,
1302 0.3000000000000000, 0.2000000000000000, 0.4000000000000000,
1303 0.2000000000000000, 0.2000000000000000, 0.3000000000000000,
1304 0.1000000000000000, 0.3000000000000000, 0.3000000000000000,
1305 0.2000000000000000, 0.3000000000000000, 0.2000000000000000,
1306 0.3000000000000000, 0.2000000000000000, 0.3000000000000000};
1307static const double NC_TET_W84[] = {
1308 0.2843915343915344, 0.2843915343915344, 0.2843915343915344,
1309 0.2843915343915344, -0.3882275132275133, -0.3882275132275133,
1310 -0.3882275132275133, -0.3882275132275133, -0.3882275132275133,
1311 -0.3882275132275133, -0.3882275132275133, -0.3882275132275133,
1312 -0.3882275132275133, -0.3882275132275133, -0.3882275132275133,
1313 -0.3882275132275133, 0.8776455026455027, 0.8776455026455027,
1314 0.8776455026455027, 0.8776455026455027, 0.8776455026455027,
1315 0.8776455026455027, 0.8776455026455027, 0.8776455026455027,
1316 0.8776455026455027, 0.8776455026455027, 0.8776455026455027,
1317 0.8776455026455027, 0.1236772486772487, 0.1236772486772487,
1318 0.1236772486772487, 0.1236772486772487, 0.1236772486772487,
1319 0.1236772486772487, 0.1236772486772487, 0.1236772486772487,
1320 0.1236772486772487, 0.1236772486772487, 0.1236772486772487,
1321 0.1236772486772487, -0.8584656084656085, -0.8584656084656085,
1322 -0.8584656084656085, -0.8584656084656085, -0.8584656084656085,
1323 -0.8584656084656085, -0.2632275132275133, -0.2632275132275133,
1324 -0.2632275132275133, -0.2632275132275133, -0.2632275132275133,
1325 -0.2632275132275133, -0.2632275132275133, -0.2632275132275133,
1326 -0.2632275132275133, -0.2632275132275133, -0.2632275132275133,
1327 -0.2632275132275133, -0.2632275132275133, -0.2632275132275133,
1328 -0.2632275132275133, -0.2632275132275133, -0.2632275132275133,
1329 -0.2632275132275133, -0.2632275132275133, -0.2632275132275133,
1330 -0.2632275132275133, -0.2632275132275133, -0.2632275132275133,
1331 -0.2632275132275133, 0.0145502645502645, 0.0145502645502645,
1332 0.0145502645502645, 0.0145502645502645, 1.0165343915343916,
1333 1.0165343915343916, 1.0165343915343916, 1.0165343915343916,
1334 -0.0251322751322751, -0.0251322751322751, -0.0251322751322751,
1335 -0.0251322751322751, -0.0251322751322751, -0.0251322751322751};
1336
1337#ifdef __cplusplus
1338}
1339#endif
1340
1341#endif
invJac
MatrixDouble invJac
Definition HookeElement.hpp:683
eps
static const double eps
Definition check_base_functions_derivatives_on_tet.cpp:11
order
constexpr int order
Definition dg_projection.cpp:18
ShapeVolumeMBTETQ
double ShapeVolumeMBTETQ(const double *diffN, const double *coords, int G_DIM, double *G_TET_W)
Definition fem_tools.c:993
MakeComplexTensor
PetscErrorCode MakeComplexTensor(double *reA, double *imA, __CLPK_doublecomplex *xA)
Definition fem_tools.c:487
G_TRI_Y28
static const double G_TRI_Y28[]
Definition fem_tools.h:388
ShapeDiffMBTRIinvJ
void ShapeDiffMBTRIinvJ(double *diffN, double *invJac, double *diffNinvJac)
calculate derivatives of shape functions in space
G_TRI_W3
static const double G_TRI_W3[]
Definition fem_tools.h:317
ShapeDiffMBTET
PetscErrorCode ShapeDiffMBTET(double *diffN)
calculate derivatives of shape functions
Definition fem_tools.c:319
G_TRI_W13
static const double G_TRI_W13[]
Definition fem_tools.h:347
G_TET_X10
static const double G_TET_X10[]
Definition fem_tools.h:1135
ShapeJacMBTET
PetscErrorCode ShapeJacMBTET(double *diffN, const double *coords, double *jac)
calculate jacobian
Definition fem_tools.c:288
G_TRI_W19
static const double G_TRI_W19[]
Definition fem_tools.h:365
G_TRI_Y3
static const double G_TRI_Y3[]
Definition fem_tools.h:316
GradientOfDeformation
PetscErrorCode GradientOfDeformation(double *diffN, double *dofs, double *F)
calculate gradient of deformation
Definition fem_tools.c:425
G_TRI_W37
static const double G_TRI_W37[]
Definition fem_tools.h:430
print_mat_sym_upper
void print_mat_sym_upper(double *M, int m, int n)
print upper part of the symmetric matrix
Grundmann_Moeller_integration_points_2D_TRI
PetscErrorCode Grundmann_Moeller_integration_points_2D_TRI(int rule, double *G_TRI_X, double *G_TRI_Y, double *G_TRI_W)
Definition fem_tools.c:98
G_TRI_Y1
static const double G_TRI_Y1[]
Definition fem_tools.h:313
G_TET_X1
static const double G_TET_X1[]
Definition fem_tools.h:1112
G_TRI_X28
static const double G_TRI_X28[]
Definition fem_tools.h:377
NC_TET_Y84
static const double NC_TET_Y84[]
Definition fem_tools.h:1249
G_TRI_W4
static const double G_TRI_W4[]
Definition fem_tools.h:325
ShapeMBTET_inverse
PetscErrorCode ShapeMBTET_inverse(double *N, double *diffN, const double *elem_coords, const double *glob_coords, double *loc_coords)
calculate local coordinates for given global coordinates
Definition fem_tools.c:335
G_TRI_Y19
static const double G_TRI_Y19[]
Definition fem_tools.h:359
ShapeDiffMBTRIQ
PetscErrorCode ShapeDiffMBTRIQ(double *diffN, const double *X, const double *Y, const int G_DIM)
Definition fem_tools.c:795
G_TET_W4
static const double G_TET_W4[]
Definition fem_tools.h:1122
ShapeFaceDiffNormalMBTRI
PetscErrorCode ShapeFaceDiffNormalMBTRI(double *diffN, const double *coords, double *diff_normal)
calculate derivative of normal in respect to nodal positions
Definition fem_tools.c:237
ShapeFaceBaseMBTRI
PetscErrorCode ShapeFaceBaseMBTRI(double *diffN, const double *coords, double *normal, double *s1, double *s2)
Definition fem_tools.c:204
G_TET_W45
static const double G_TET_W45[]
Definition fem_tools.h:1204
ShapeFaceNormalMBTRI_complex
PetscErrorCode ShapeFaceNormalMBTRI_complex(double *diffN, __CLPK_doublecomplex *xcoords, __CLPK_doublecomplex *xnormal)
Definition fem_tools.c:452
ShapeJacMBTRI
void ShapeJacMBTRI(double *diffN, const double *coords, double *Jac)
calculate jacobioan
ShapeFaceNormalMBTRI
PetscErrorCode ShapeFaceNormalMBTRI(double *diffN, const double *coords, double *normal)
Definition fem_tools.c:229
NC_TET_X84
static const double NC_TET_X84[]
Definition fem_tools.h:1220
G_TRI_Y37
static const double G_TRI_Y37[]
Definition fem_tools.h:419
ShapeDiffMBTETQ
PetscErrorCode ShapeDiffMBTETQ(double *diffN, const double x, const double y, const double z)
Definition fem_tools.c:873
G_TET_W1
static const double G_TET_W1[]
Definition fem_tools.h:1115
Grundmann_Moeller_integration_points_3D_TET
PetscErrorCode Grundmann_Moeller_integration_points_3D_TET(int rule, double *G_TET_X, double *G_TET_Y, double *G_TET_Z, double *G_TET_W)
Definition fem_tools.c:143
ShapeInvJacVolume
PetscErrorCode ShapeInvJacVolume(double *jac)
Definition fem_tools.c:39
G_TRI_Y286
static const double G_TRI_Y286[]
Definition fem_tools.h:727
G_TET_Y1
static const double G_TET_Y1[]
Definition fem_tools.h:1113
ShapeDiffMBTETinvJ
PetscErrorCode ShapeDiffMBTETinvJ(double *diffN, double *invJac, double *diffNinvJac)
calculate shape functions derivatives in space
Definition fem_tools.c:415
G_TRI_W28
static const double G_TRI_W28[]
Definition fem_tools.h:396
G_TET_W10
static const double G_TET_W10[]
Definition fem_tools.h:1150
G_TET_Z45
static const double G_TET_Z45[]
Definition fem_tools.h:1188
ShapeDiffMBTRI
PetscErrorCode ShapeDiffMBTRI(double *diffN)
calculate derivatives of shape functions
Definition fem_tools.c:194
G_TRI_X19
static const double G_TRI_X19[]
Definition fem_tools.h:353
G_TET_Z4
static const double G_TET_Z4[]
Definition fem_tools.h:1120
G_TRI_X4
static const double G_TRI_X4[]
Definition fem_tools.h:319
ShapeMBTET
PetscErrorCode ShapeMBTET(double *N, const double *G_X, const double *G_Y, const double *G_Z, int DIM)
calculate shape functions
Definition fem_tools.c:306
print_mat
void print_mat(double *M, int m, int n)
print matric M
ShapeDiffMBEDGE
PetscErrorCode ShapeDiffMBEDGE(double *diffN)
Definition fem_tools.c:771
G_TRI_W1
static const double G_TRI_W1[]
Definition fem_tools.h:314
G_TRI_Y4
static const double G_TRI_Y4[]
Definition fem_tools.h:322
ShapeMBTETQ_GAUSS
PetscErrorCode ShapeMBTETQ_GAUSS(double *N, const double *X, const double *Y, const double *Z, const int G_DIM)
Definition fem_tools.c:908
G_TET_X45
static const double G_TET_X45[]
Definition fem_tools.h:1156
DeterminantComplexGradient
PetscErrorCode DeterminantComplexGradient(__CLPK_doublecomplex *xF, __CLPK_doublecomplex *det_xF)
Definition fem_tools.c:526
Spin
PetscErrorCode Spin(double *spinOmega, double *vecOmega)
calculate spin matrix from vector
Definition fem_tools.c:546
ShapeDiffMBTETinvJ_complex
void ShapeDiffMBTETinvJ_complex(double *diffN, __CLPK_doublecomplex *invJac, __CLPK_doublecomplex *diffNinvJac, enum CBLAS_TRANSPOSE Trans)
Definition fem_tools.c:437
Grundmann_Moeller_integration_points_1D_EDGE
PetscErrorCode Grundmann_Moeller_integration_points_1D_EDGE(int rule, double *G_TRI_X, double *G_TRI_W)
Compute weights and integration points for edge using Grundmann_Moeller rule.
Definition fem_tools.c:55
G_TET_Z1
static const double G_TET_Z1[]
Definition fem_tools.h:1114
G_TET_Y4
static const double G_TET_Y4[]
Definition fem_tools.h:1118
G_TET_X4
static const double G_TET_X4[]
Definition fem_tools.h:1116
InvertComplexGradient
PetscErrorCode InvertComplexGradient(__CLPK_doublecomplex *xF)
Definition fem_tools.c:499
NC_TET_Z84
static const double NC_TET_Z84[]
Definition fem_tools.h:1278
ShapeMBTRIQ
PetscErrorCode ShapeMBTRIQ(double *N, const double *X, const double *Y, const int G_DIM)
Definition fem_tools.c:780
ShapeMBTETQ
PetscErrorCode ShapeMBTETQ(double *N, const double x, const double y, const double z)
Definition fem_tools.c:858
G_TET_Y45
static const double G_TET_Y45[]
Definition fem_tools.h:1172
NC_TET_W84
static const double NC_TET_W84[]
Definition fem_tools.h:1307
G_TET_Z10
static const double G_TET_Z10[]
Definition fem_tools.h:1145
ShapeMBEDGE
PetscErrorCode ShapeMBEDGE(double *N, const double *G_X, int DIM)
Definition fem_tools.c:761
ShapeVolumeMBTET
double ShapeVolumeMBTET(double *diffN, const double *coords)
calculate TET volume
Definition fem_tools.c:298
ShapeMBTETQ_inverse
PetscErrorCode ShapeMBTETQ_inverse(double *N, double *diffN, const double *elem_coords, const double *glob_coords, double *loc_coords, const double eps)
Definition fem_tools.c:1007
make_complex_matrix
PetscErrorCode make_complex_matrix(double *reA, double *imA, __CLPK_doublecomplex *xA)
Compose complex matrix (3x3) from two real matrices.
Definition fem_tools.c:557
G_TET_Z5
static const double G_TET_Z5[]
Definition fem_tools.h:1129
ShapeDiffMBTETQ_GAUSS
PetscErrorCode ShapeDiffMBTETQ_GAUSS(double *diffN, const double *X, const double *Y, const double *Z, const int G_DIM)
Definition fem_tools.c:927
ShapeMBTETQ_detJac_at_Gauss_Points
PetscErrorCode ShapeMBTETQ_detJac_at_Gauss_Points(double *detJac_at_Gauss_Points, const double *diffN, const double *coords, int G_DIM)
Definition fem_tools.c:979
G_TRI_X13
static const double G_TRI_X13[]
Definition fem_tools.h:337
ShapeDetJacVolume
double ShapeDetJacVolume(double *jac)
determined of jacobian
Definition fem_tools.c:22
G_TET_X5
static const double G_TET_X5[]
Definition fem_tools.h:1123
G_TET_W5
static const double G_TET_W5[]
Definition fem_tools.h:1132
G_TRI_X37
static const double G_TRI_X37[]
Definition fem_tools.h:408
Base_scale
PetscErrorCode Base_scale(__CLPK_doublecomplex *xnormal, __CLPK_doublecomplex *xs1, __CLPK_doublecomplex *xs2)
Definition fem_tools.c:741
G_TRI_X286
static const double G_TRI_X286[]
Definition fem_tools.h:441
ShapeJacMBTETQ
PetscErrorCode ShapeJacMBTETQ(const double *diffN, const double *coords, double *Jac)
Definition fem_tools.c:967
ShapeMBTRI_inverse
PetscErrorCode ShapeMBTRI_inverse(double *N, double *diffN, const double *elem_coords, const double *glob_coords, double *loc_coords)
calculate local coordinates of triangle element for given global coordinates in 2D (Assume e....
Definition fem_tools.c:380
G_TET_Y5
static const double G_TET_Y5[]
Definition fem_tools.h:1126
G_TRI_W286
static const double G_TRI_W286[]
Definition fem_tools.h:1013
G_TRI_X7
static const double G_TRI_X7[]
Definition fem_tools.h:328
print_mat_complex
void print_mat_complex(__CLPK_doublecomplex *M, int m, int n)
priint complex matrix
ShapeMBTRI
PetscErrorCode ShapeMBTRI(double *N, const double *X, const double *Y, const int G_DIM)
calculate shape functions on triangle
Definition fem_tools.c:182
Normal_hierarchical
PetscErrorCode Normal_hierarchical(int order_approx, int *order_edge_approx, int order, int *order_edge, double *diffN, double *diffN_face, double *diffN_edge[], double *dofs, double *dofs_edge[], double *dofs_face, double *idofs, double *idofs_edge[], double *idofs_face, __CLPK_doublecomplex *xnormal, __CLPK_doublecomplex *s1, __CLPK_doublecomplex *s2, int gg)
Complex normal.
Definition fem_tools.c:569
G_TRI_Y7
static const double G_TRI_Y7[]
Definition fem_tools.h:331
G_TRI_X3
static const double G_TRI_X3[]
Definition fem_tools.h:315
G_TRI_Y13
static const double G_TRI_Y13[]
Definition fem_tools.h:342
G_TRI_X1
static const double G_TRI_X1[]
Definition fem_tools.h:312
G_TRI_W7
static const double G_TRI_W7[]
Definition fem_tools.h:334
G_TET_Y10
static const double G_TET_Y10[]
Definition fem_tools.h:1140
F
@ F
Definition free_surface.cpp:394
n
const double n
refractive index of diffusive medium
Definition initial_diffusion.cpp:38
lapack_wrap.h
m
FTensor::Index< 'm', 3 > m
Definition shallow_wave.cpp:80
N
const int N
Definition speed_test.cpp:3
__CLPK_doublecomplex
Definition lapack_wrap.h:34
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