GetFEM  5.4.4
getfem_assembling.h
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2 /*===========================================================================
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4  Copyright (C) 2000-2020 Yves Renard, Julien Pommier
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30 ===========================================================================*/
31 
32 /** @file getfem_assembling.h
33  @author Yves Renard <Yves.Renard@insa-lyon.fr>
34  @author Julien Pommier <Julien.Pommier@insa-toulouse.fr>
35  @date November 17, 2000.
36  @brief Miscelleanous assembly routines for common terms. Use the low-level
37  generic assembly. Prefer the high-level one.
38  */
39 
40 /** @defgroup asm Assembly routines */
41 
42 #ifndef GETFEM_ASSEMBLING_H__
43 #define GETFEM_ASSEMBLING_H__
44 
45 #include "getfem_assembling_tensors.h"
46 #include "getfem_generic_assembly.h"
47 
48 namespace getfem {
49 
50  /**
51  compute @f$ \|U\|_2 @f$, U might be real or complex
52  @ingroup asm
53  */
54  template<typename VEC>
55  inline scalar_type asm_L2_norm
56  (const mesh_im &mim, const mesh_fem &mf, const VEC &U,
57  const mesh_region &rg=mesh_region::all_convexes())
58  { return sqrt(asm_L2_norm_sqr(mim, mf, U, rg)); }
59 
60  template<typename VEC>
61  scalar_type asm_L2_norm_sqr
62  (const mesh_im &mim, const mesh_fem &mf, const VEC &U,
63  const mesh_region &rg=mesh_region::all_convexes()) {
64  return asm_L2_norm_sqr(mim, mf, U, rg,
65  typename gmm::linalg_traits<VEC>::value_type());
66  }
67 
68  template<typename VEC, typename T>
69  inline scalar_type asm_L2_norm_sqr(const mesh_im &mim, const mesh_fem &mf,
70  const VEC &U, const mesh_region &rg_, T) {
71  ga_workspace workspace;
72  model_real_plain_vector UU(mf.nb_dof());
73  gmm::copy(U, UU);
74  gmm::sub_interval Iu(0, mf.nb_dof());
75  workspace.add_fem_variable("u", mf, Iu, UU);
76  workspace.add_expression("u.u", mim, rg_);
77  workspace.assembly(0);
78  return workspace.assembled_potential();
79  }
80 
81  inline scalar_type asm_L2_norm_sqr(const mesh_im &mim, const mesh_fem &mf,
82  const model_real_plain_vector &U,
83  const mesh_region &rg_, scalar_type) {
84  ga_workspace workspace;
85  gmm::sub_interval Iu(0, mf.nb_dof());
86  workspace.add_fem_variable("u", mf, Iu, U);
87  workspace.add_expression("u.u", mim, rg_);
88  workspace.assembly(0);
89  return workspace.assembled_potential();
90  }
91 
92  template<typename VEC, typename T>
93  inline scalar_type asm_L2_norm_sqr(const mesh_im &mim, const mesh_fem &mf,
94  const VEC &U,
95  const mesh_region &rg, std::complex<T>) {
96  ga_workspace workspace;
97  model_real_plain_vector UUR(mf.nb_dof()), UUI(mf.nb_dof());
98  gmm::copy(gmm::real_part(U), UUR);
99  gmm::copy(gmm::imag_part(U), UUI);
100  gmm::sub_interval Iur(0, mf.nb_dof()), Iui(mf.nb_dof(), mf.nb_dof());
101  workspace.add_fem_variable("u", mf, Iur, UUR);
102  workspace.add_fem_variable("v", mf, Iui, UUI);
103  workspace.add_expression("u.u + v.v", mim, rg);
104  workspace.assembly(0);
105  return workspace.assembled_potential();
106  }
107 
108  /**
109  Compute the distance between U1 and U2, defined on two different
110  mesh_fems (but sharing the same mesh), without interpolating U1 on mf2.
111 
112  @ingroup asm
113  */
114  template<typename VEC1, typename VEC2>
115  inline scalar_type asm_L2_dist
116  (const mesh_im &mim, const mesh_fem &mf1, const VEC1 &U1,
117  const mesh_fem &mf2, const VEC2 &U2,
118  mesh_region rg = mesh_region::all_convexes()) {
119  return sqrt(asm_L2_dist_sqr(mim, mf1, U1, mf2, U2, rg,
120  typename gmm::linalg_traits<VEC1>::value_type()));
121  }
122 
123  template<typename VEC1, typename VEC2, typename T>
124  inline scalar_type asm_L2_dist_sqr
125  (const mesh_im &mim, const mesh_fem &mf1, const VEC1 &U1,
126  const mesh_fem &mf2, const VEC2 &U2, mesh_region rg, T) {
127  ga_workspace workspace;
128  model_real_plain_vector UU1(mf1.nb_dof()), UU2(mf2.nb_dof());
129  gmm::copy(U1, UU1); gmm::copy(U2, UU2);
130  gmm::sub_interval Iu1(0, mf1.nb_dof()), Iu2(mf1.nb_dof(), mf2.nb_dof());
131  workspace.add_fem_variable("u1", mf1, Iu1, UU1);
132  workspace.add_fem_variable("u2", mf2, Iu2, UU2);
133  workspace.add_expression("(u2-u1).(u2-u1)", mim, rg);
134  workspace.assembly(0);
135  return workspace.assembled_potential();
136  }
137 
138  inline scalar_type asm_L2_dist_sqr
139  (const mesh_im &mim, const mesh_fem &mf1, const model_real_plain_vector &U1,
140  const mesh_fem &mf2, const model_real_plain_vector &U2,
141  mesh_region rg, scalar_type) {
142  ga_workspace workspace;
143  gmm::sub_interval Iu1(0, mf1.nb_dof()), Iu2(mf1.nb_dof(), mf2.nb_dof());
144  workspace.add_fem_variable("u1", mf1, Iu1, U1);
145  workspace.add_fem_variable("u2", mf2, Iu2, U2);
146  workspace.add_expression("(u2-u1).(u2-u1)", mim, rg);
147  workspace.assembly(0);
148  return workspace.assembled_potential();
149  }
150 
151  template<typename VEC1, typename VEC2, typename T>
152  inline scalar_type asm_L2_dist_sqr
153  (const mesh_im &mim, const mesh_fem &mf1, const VEC1 &U1,
154  const mesh_fem &mf2, const VEC2 &U2, mesh_region rg, std::complex<T>) {
155  ga_workspace workspace;
156  model_real_plain_vector UU1R(mf1.nb_dof()), UU2R(mf2.nb_dof());
157  model_real_plain_vector UU1I(mf1.nb_dof()), UU2I(mf2.nb_dof());
158  gmm::copy(gmm::real_part(U1), UU1R); gmm::copy(gmm::imag_part(U1), UU1I);
159  gmm::copy(gmm::real_part(U2), UU2R); gmm::copy(gmm::imag_part(U2), UU2I);
160  gmm::sub_interval Iu1r(0, mf1.nb_dof()), Iu2r(mf1.nb_dof(), mf2.nb_dof());
161  gmm::sub_interval Iu1i(Iu2r.last(), mf1.nb_dof());
162  gmm::sub_interval Iu2i(Iu1i.last(), mf2.nb_dof());
163  workspace.add_fem_variable("u1", mf1, Iu1r, UU1R);
164  workspace.add_fem_variable("u2", mf2, Iu2r, UU2R);
165  workspace.add_fem_variable("v1", mf1, Iu1i, UU1I);
166  workspace.add_fem_variable("v2", mf2, Iu2i, UU2I);
167  workspace.add_expression("(u2-u1).(u2-u1) + (v2-v1).(v2-v1)", mim, rg);
168  workspace.assembly(0);
169  return workspace.assembled_potential();
170  }
171 
172 
173  /**
174  compute @f$\|\nabla U\|_2@f$, U might be real or complex
175  @ingroup asm
176  */
177  template<typename VEC>
178  scalar_type asm_H1_semi_norm
179  (const mesh_im &mim, const mesh_fem &mf, const VEC &U,
180  const mesh_region &rg = mesh_region::all_convexes()) {
181  typedef typename gmm::linalg_traits<VEC>::value_type T;
182  return sqrt(asm_H1_semi_norm_sqr(mim, mf, U, rg, T()));
183  }
184 
185  template<typename VEC, typename T>
186  inline scalar_type asm_H1_semi_norm_sqr
187  (const mesh_im &mim, const mesh_fem &mf, const VEC &U,
188  const mesh_region &rg_, T) {
189  ga_workspace workspace;
190  model_real_plain_vector UU(mf.nb_dof()); gmm::copy(U, UU);
191  gmm::sub_interval Iu(0, mf.nb_dof());
192  workspace.add_fem_variable("u", mf, Iu, UU);
193  workspace.add_expression("Grad_u:Grad_u", mim, rg_);
194  workspace.assembly(0);
195  return workspace.assembled_potential();
196  }
197 
198  inline scalar_type asm_H1_semi_norm_sqr
199  (const mesh_im &mim, const mesh_fem &mf, const model_real_plain_vector &U,
200  const mesh_region &rg_, scalar_type) {
201  ga_workspace workspace;
202  gmm::sub_interval Iu(0, mf.nb_dof());
203  workspace.add_fem_variable("u", mf, Iu, U);
204  workspace.add_expression("Grad_u:Grad_u", mim, rg_);
205  workspace.assembly(0);
206  return workspace.assembled_potential();
207  }
208 
209 
210  template<typename VEC, typename T>
211  inline scalar_type asm_H1_semi_norm_sqr
212  (const mesh_im &mim, const mesh_fem &mf, const VEC &U,
213  const mesh_region &rg, std::complex<T>) {
214  ga_workspace workspace;
215  model_real_plain_vector UUR(mf.nb_dof()), UUI(mf.nb_dof());
216  gmm::copy(gmm::real_part(U), UUR);
217  gmm::copy(gmm::imag_part(U), UUI);
218  gmm::sub_interval Iur(0, mf.nb_dof()), Iui(mf.nb_dof(), mf.nb_dof());
219  workspace.add_fem_variable("u", mf, Iur, UUR);
220  workspace.add_fem_variable("v", mf, Iui, UUI);
221  workspace.add_expression("Grad_u:Grad_u + Grad_v:Grad_v", mim, rg);
222  workspace.assembly(0);
223  return workspace.assembled_potential();
224  }
225 
226  /**
227  Compute the H1 semi-distance between U1 and U2, defined on two different
228  mesh_fems (but sharing the same mesh), without interpolating U1 on mf2.
229 
230  @ingroup asm
231  */
232  template<typename VEC1, typename VEC2>
233  inline scalar_type asm_H1_semi_dist
234  (const mesh_im &mim, const mesh_fem &mf1, const VEC1 &U1,
235  const mesh_fem &mf2, const VEC2 &U2,
236  mesh_region rg = mesh_region::all_convexes()) {
237  return sqrt(asm_H1_semi_dist_sqr(mim, mf1, U1, mf2, U2, rg,
238  typename gmm::linalg_traits<VEC1>::value_type()));
239  }
240 
241  template<typename VEC1, typename VEC2, typename T>
242  inline scalar_type asm_H1_semi_dist_sqr
243  (const mesh_im &mim, const mesh_fem &mf1, const VEC1 &U1,
244  const mesh_fem &mf2, const VEC2 &U2, mesh_region rg, T) {
245  ga_workspace workspace;
246  model_real_plain_vector UU1(mf1.nb_dof()), UU2(mf2.nb_dof());
247  gmm::copy(U1, UU1); gmm::copy(U2, UU2);
248  gmm::sub_interval Iu1(0, mf1.nb_dof()), Iu2(mf1.nb_dof(), mf2.nb_dof());
249  workspace.add_fem_variable("u1", mf1, Iu1, UU1);
250  workspace.add_fem_variable("u2", mf2, Iu2, UU2);
251  workspace.add_expression("(Grad_u2-Grad_u1):(Grad_u2-Grad_u1)", mim, rg);
252  workspace.assembly(0);
253  return workspace.assembled_potential();
254  }
255 
256  inline scalar_type asm_H1_semi_dist_sqr
257  (const mesh_im &mim, const mesh_fem &mf1, const model_real_plain_vector &U1,
258  const mesh_fem &mf2, const model_real_plain_vector &U2,
259  mesh_region rg, scalar_type) {
260  ga_workspace workspace;
261  gmm::sub_interval Iu1(0, mf1.nb_dof()), Iu2(mf1.nb_dof(), mf2.nb_dof());
262  workspace.add_fem_variable("u1", mf1, Iu1, U1);
263  workspace.add_fem_variable("u2", mf2, Iu2, U2);
264  workspace.add_expression("(Grad_u2-Grad_u1):(Grad_u2-Grad_u1)", mim, rg);
265  workspace.assembly(0);
266  return workspace.assembled_potential();
267  }
268 
269  template<typename VEC1, typename VEC2, typename T>
270  inline scalar_type asm_H1_semi_dist_sqr
271  (const mesh_im &mim, const mesh_fem &mf1, const VEC1 &U1,
272  const mesh_fem &mf2, const VEC2 &U2, mesh_region rg, std::complex<T>) {
273  ga_workspace workspace;
274  model_real_plain_vector UU1R(mf1.nb_dof()), UU2R(mf2.nb_dof());
275  model_real_plain_vector UU1I(mf1.nb_dof()), UU2I(mf2.nb_dof());
276  gmm::copy(gmm::real_part(U1), UU1R); gmm::copy(gmm::imag_part(U1), UU1I);
277  gmm::copy(gmm::real_part(U2), UU2R); gmm::copy(gmm::imag_part(U2), UU2I);
278  gmm::sub_interval Iu1r(0, mf1.nb_dof()), Iu2r(mf1.nb_dof(), mf2.nb_dof());
279  gmm::sub_interval Iu1i(Iu2r.last(), mf1.nb_dof());
280  gmm::sub_interval Iu2i(Iu1i.last(), mf2.nb_dof());
281  workspace.add_fem_variable("u1", mf1, Iu1r, UU1R);
282  workspace.add_fem_variable("u2", mf2, Iu2r, UU2R);
283  workspace.add_fem_variable("v1", mf1, Iu1i, UU1I);
284  workspace.add_fem_variable("v2", mf2, Iu2i, UU2I);
285  workspace.add_expression("(Grad_u2-Grad_u1):(Grad_u2-Grad_u1)"
286  "+ (Grad_v2-Grad_v1):(Grad_v2-Grad_v1)", mim, rg);
287  workspace.assembly(0);
288  return workspace.assembled_potential();
289  }
290 
291  /**
292  compute the H1 norm of U.
293  @ingroup asm
294  */
295 
296  /**
297  compute @f$\|\nabla U\|_2@f$, U might be real or complex
298  @ingroup asm
299  */
300  template<typename VEC>
301  scalar_type asm_H1_norm
302  (const mesh_im &mim, const mesh_fem &mf, const VEC &U,
303  const mesh_region &rg = mesh_region::all_convexes()) {
304  typedef typename gmm::linalg_traits<VEC>::value_type T;
305  return sqrt(asm_H1_norm_sqr(mim, mf, U, rg, T()));
306  }
307 
308  template<typename VEC, typename T>
309  inline scalar_type asm_H1_norm_sqr
310  (const mesh_im &mim, const mesh_fem &mf, const VEC &U,
311  const mesh_region &rg_, T) {
312  ga_workspace workspace;
313  model_real_plain_vector UU(mf.nb_dof()); gmm::copy(U, UU);
314  gmm::sub_interval Iu(0, mf.nb_dof());
315  workspace.add_fem_variable("u", mf, Iu, UU);
316  workspace.add_expression("u.u + Grad_u:Grad_u", mim, rg_);
317  workspace.assembly(0);
318  return workspace.assembled_potential();
319  }
320 
321  inline scalar_type asm_H1_norm_sqr
322  (const mesh_im &mim, const mesh_fem &mf, const model_real_plain_vector &U,
323  const mesh_region &rg_, scalar_type) {
324  ga_workspace workspace;
325  gmm::sub_interval Iu(0, mf.nb_dof());
326  workspace.add_fem_variable("u", mf, Iu, U);
327  workspace.add_expression("u.u + Grad_u:Grad_u", mim, rg_);
328  workspace.assembly(0);
329  return workspace.assembled_potential();
330  }
331 
332 
333  template<typename VEC, typename T>
334  inline scalar_type asm_H1_norm_sqr
335  (const mesh_im &mim, const mesh_fem &mf, const VEC &U,
336  const mesh_region &rg, std::complex<T>) {
337  ga_workspace workspace;
338  model_real_plain_vector UUR(mf.nb_dof()), UUI(mf.nb_dof());
339  gmm::copy(gmm::real_part(U), UUR);
340  gmm::copy(gmm::imag_part(U), UUI);
341  gmm::sub_interval Iur(0, mf.nb_dof()), Iui(mf.nb_dof(), mf.nb_dof());
342  workspace.add_fem_variable("u", mf, Iur, UUR);
343  workspace.add_fem_variable("v", mf, Iui, UUI);
344  workspace.add_expression("u.u+v.v + Grad_u:Grad_u+Grad_v:Grad_v", mim, rg);
345  workspace.assembly(0);
346  return workspace.assembled_potential();
347  }
348 
349  /**
350  Compute the H1 distance between U1 and U2
351  @ingroup asm
352  */
353  template<typename VEC1, typename VEC2>
354  inline scalar_type asm_H1_dist
355  (const mesh_im &mim, const mesh_fem &mf1, const VEC1 &U1,
356  const mesh_fem &mf2, const VEC2 &U2,
357  mesh_region rg = mesh_region::all_convexes()) {
358  return sqrt(asm_H1_dist_sqr(mim, mf1, U1, mf2, U2, rg,
359  typename gmm::linalg_traits<VEC1>::value_type()));
360  }
361 
362  template<typename VEC1, typename VEC2, typename T>
363  inline scalar_type asm_H1_dist_sqr
364  (const mesh_im &mim, const mesh_fem &mf1, const VEC1 &U1,
365  const mesh_fem &mf2, const VEC2 &U2, mesh_region rg, T) {
366  ga_workspace workspace;
367  model_real_plain_vector UU1(mf1.nb_dof()), UU2(mf2.nb_dof());
368  gmm::copy(U1, UU1); gmm::copy(U2, UU2);
369  gmm::sub_interval Iu1(0, mf1.nb_dof()), Iu2(mf1.nb_dof(), mf2.nb_dof());
370  workspace.add_fem_variable("u1", mf1, Iu1, UU1);
371  workspace.add_fem_variable("u2", mf2, Iu2, UU2);
372  workspace.add_expression("(u2-u1).(u2-u1)"
373  "+ (Grad_u2-Grad_u1):(Grad_u2-Grad_u1)", mim, rg);
374  workspace.assembly(0);
375  return workspace.assembled_potential();
376  }
377 
378  inline scalar_type asm_H1_dist_sqr
379  (const mesh_im &mim, const mesh_fem &mf1, const model_real_plain_vector &U1,
380  const mesh_fem &mf2, const model_real_plain_vector &U2,
381  mesh_region rg, scalar_type) {
382  ga_workspace workspace;
383  gmm::sub_interval Iu1(0, mf1.nb_dof()), Iu2(mf1.nb_dof(), mf2.nb_dof());
384  workspace.add_fem_variable("u1", mf1, Iu1, U1);
385  workspace.add_fem_variable("u2", mf2, Iu2, U2);
386  workspace.add_expression("(u2-u1).(u2-u1)"
387  "+ (Grad_u2-Grad_u1):(Grad_u2-Grad_u1)", mim, rg);
388  workspace.assembly(0);
389  return workspace.assembled_potential();
390  }
391 
392  template<typename VEC1, typename VEC2, typename T>
393  inline scalar_type asm_H1_dist_sqr
394  (const mesh_im &mim, const mesh_fem &mf1, const VEC1 &U1,
395  const mesh_fem &mf2, const VEC2 &U2, mesh_region rg, std::complex<T>) {
396  ga_workspace workspace;
397  model_real_plain_vector UU1R(mf1.nb_dof()), UU2R(mf2.nb_dof());
398  model_real_plain_vector UU1I(mf1.nb_dof()), UU2I(mf2.nb_dof());
399  gmm::copy(gmm::real_part(U1), UU1R); gmm::copy(gmm::imag_part(U1), UU1I);
400  gmm::copy(gmm::real_part(U2), UU2R); gmm::copy(gmm::imag_part(U2), UU2I);
401  gmm::sub_interval Iu1r(0, mf1.nb_dof()), Iu2r(mf1.nb_dof(), mf2.nb_dof());
402  gmm::sub_interval Iu1i(Iu2r.last(), mf1.nb_dof());
403  gmm::sub_interval Iu2i(Iu1i.last(), mf2.nb_dof());
404  workspace.add_fem_variable("u1", mf1, Iu1r, UU1R);
405  workspace.add_fem_variable("u2", mf2, Iu2r, UU2R);
406  workspace.add_fem_variable("v1", mf1, Iu1i, UU1I);
407  workspace.add_fem_variable("v2", mf2, Iu2i, UU2I);
408  workspace.add_expression("(u2-u1).(u2-u1) + (v2-v1).(v2-v1)"
409  "+ (Grad_u2-Grad_u1):(Grad_u2-Grad_u1)"
410  "+ (Grad_v2-Grad_v1):(Grad_v2-Grad_v1)", mim, rg);
411  workspace.assembly(0);
412  return workspace.assembled_potential();
413  }
414 
415  /**
416  compute @f$\|Hess U\|_2@f$, U might be real or complex. For C^1 elements
417  @ingroup asm
418  */
419 
420  template<typename VEC>
421  scalar_type asm_H2_semi_norm
422  (const mesh_im &mim, const mesh_fem &mf, const VEC &U,
423  const mesh_region &rg = mesh_region::all_convexes()) {
424  typedef typename gmm::linalg_traits<VEC>::value_type T;
425  return sqrt(asm_H2_semi_norm_sqr(mim, mf, U, rg, T()));
426  }
427 
428  template<typename VEC, typename T>
429  inline scalar_type asm_H2_semi_norm_sqr
430  (const mesh_im &mim, const mesh_fem &mf, const VEC &U,
431  const mesh_region &rg_, T) {
432  ga_workspace workspace;
433  model_real_plain_vector UU(mf.nb_dof()); gmm::copy(U, UU);
434  gmm::sub_interval Iu(0, mf.nb_dof());
435  workspace.add_fem_variable("u", mf, Iu, UU);
436  workspace.add_expression("Hess_u:Hess_u", mim, rg_);
437  workspace.assembly(0);
438  return workspace.assembled_potential();
439  }
440 
441  inline scalar_type asm_H2_semi_norm_sqr
442  (const mesh_im &mim, const mesh_fem &mf, const model_real_plain_vector &U,
443  const mesh_region &rg_, scalar_type) {
444  ga_workspace workspace;
445  gmm::sub_interval Iu(0, mf.nb_dof());
446  workspace.add_fem_variable("u", mf, Iu, U);
447  workspace.add_expression("Hess_u:Hess_u", mim, rg_);
448  workspace.assembly(0);
449  return workspace.assembled_potential();
450  }
451 
452 
453  template<typename VEC, typename T>
454  inline scalar_type asm_H2_semi_norm_sqr
455  (const mesh_im &mim, const mesh_fem &mf, const VEC &U,
456  const mesh_region &rg, std::complex<T>) {
457  ga_workspace workspace;
458  model_real_plain_vector UUR(mf.nb_dof()), UUI(mf.nb_dof());
459  gmm::copy(gmm::real_part(U), UUR);
460  gmm::copy(gmm::imag_part(U), UUI);
461  gmm::sub_interval Iur(0, mf.nb_dof()), Iui(mf.nb_dof(), mf.nb_dof());
462  workspace.add_fem_variable("u", mf, Iur, UUR);
463  workspace.add_fem_variable("v", mf, Iui, UUI);
464  workspace.add_expression("Hess_u:Hess_u + Hess_v:Hess_v", mim, rg);
465  workspace.assembly(0);
466  return workspace.assembled_potential();
467  }
468 
469 
470  template<typename VEC1, typename VEC2>
471  inline scalar_type asm_H2_semi_dist
472  (const mesh_im &mim, const mesh_fem &mf1, const VEC1 &U1,
473  const mesh_fem &mf2, const VEC2 &U2,
474  mesh_region rg = mesh_region::all_convexes()) {
475  return sqrt(asm_H2_semi_dist_sqr(mim, mf1, U1, mf2, U2, rg,
476  typename gmm::linalg_traits<VEC1>::value_type()));
477  }
478 
479  template<typename VEC1, typename VEC2, typename T>
480  inline scalar_type asm_H2_semi_dist_sqr
481  (const mesh_im &mim, const mesh_fem &mf1, const VEC1 &U1,
482  const mesh_fem &mf2, const VEC2 &U2, mesh_region rg, T) {
483  ga_workspace workspace;
484  model_real_plain_vector UU1(mf1.nb_dof()), UU2(mf2.nb_dof());
485  gmm::copy(U1, UU1); gmm::copy(U2, UU2);
486  gmm::sub_interval Iu1(0, mf1.nb_dof()), Iu2(mf1.nb_dof(), mf2.nb_dof());
487  workspace.add_fem_variable("u1", mf1, Iu1, UU1);
488  workspace.add_fem_variable("u2", mf2, Iu2, UU2);
489  workspace.add_expression("(Hess_u2-Hess_u1):(Hess_u2-Hess_u1)", mim, rg);
490  workspace.assembly(0);
491  return workspace.assembled_potential();
492  }
493 
494  inline scalar_type asm_H2_semi_dist_sqr
495  (const mesh_im &mim, const mesh_fem &mf1, const model_real_plain_vector &U1,
496  const mesh_fem &mf2, const model_real_plain_vector &U2,
497  mesh_region rg, scalar_type) {
498  ga_workspace workspace;
499  gmm::sub_interval Iu1(0, mf1.nb_dof()), Iu2(mf1.nb_dof(), mf2.nb_dof());
500  workspace.add_fem_variable("u1", mf1, Iu1, U1);
501  workspace.add_fem_variable("u2", mf2, Iu2, U2);
502  workspace.add_expression("(Hess_u2-Hess_u1):(Hess_u2-Hess_u1)", mim, rg);
503  workspace.assembly(0);
504  return workspace.assembled_potential();
505  }
506 
507  template<typename VEC1, typename VEC2, typename T>
508  inline scalar_type asm_H2_semi_dist_sqr
509  (const mesh_im &mim, const mesh_fem &mf1, const VEC1 &U1,
510  const mesh_fem &mf2, const VEC2 &U2, mesh_region rg, std::complex<T>) {
511  ga_workspace workspace;
512  model_real_plain_vector UU1R(mf1.nb_dof()), UU2R(mf2.nb_dof());
513  model_real_plain_vector UU1I(mf1.nb_dof()), UU2I(mf2.nb_dof());
514  gmm::copy(gmm::real_part(U1), UU1R); gmm::copy(gmm::imag_part(U1), UU1I);
515  gmm::copy(gmm::real_part(U2), UU2R); gmm::copy(gmm::imag_part(U2), UU2I);
516  gmm::sub_interval Iu1r(0, mf1.nb_dof()), Iu2r(mf1.nb_dof(), mf2.nb_dof());
517  gmm::sub_interval Iu1i(Iu2r.last(), mf1.nb_dof());
518  gmm::sub_interval Iu2i(Iu1i.last(), mf2.nb_dof());
519  workspace.add_fem_variable("u1", mf1, Iu1r, UU1R);
520  workspace.add_fem_variable("u2", mf2, Iu2r, UU2R);
521  workspace.add_fem_variable("v1", mf1, Iu1i, UU1I);
522  workspace.add_fem_variable("v2", mf2, Iu2i, UU2I);
523  workspace.add_expression("(Hess_u2-Hess_u1):(Hess_u2-Hess_u1)"
524  "+ (Hess_v2-Hess_v1):(Hess_v2-Hess_v1)", mim, rg);
525  workspace.assembly(0);
526  return workspace.assembled_potential();
527  }
528 
529  /**
530  compute the H2 norm of U (for C^1 elements).
531  @ingroup asm
532  */
533  template<typename VEC>
534  scalar_type asm_H2_norm(const mesh_im &mim, const mesh_fem &mf,
535  const VEC &U,
536  const mesh_region &rg
537  = mesh_region::all_convexes()) {
538  typedef typename gmm::linalg_traits<VEC>::value_type T;
539  return sqrt(asm_H1_norm_sqr(mim, mf, U, rg, T())
540  + asm_H2_semi_norm_sqr(mim, mf, U, rg, T()));
541  }
542 
543  /**
544  Compute the H2 distance between U1 and U2
545  @ingroup asm
546  */
547  template<typename VEC1, typename VEC2>
548  scalar_type asm_H2_dist(const mesh_im &mim,
549  const mesh_fem &mf1, const VEC1 &U1,
550  const mesh_fem &mf2, const VEC2 &U2,
551  const mesh_region &rg
552  = mesh_region::all_convexes()) {
553  typedef typename gmm::linalg_traits<VEC1>::value_type T;
554  return sqrt(asm_H1_dist_sqr(mim,mf1,U1,mf2,U2,rg,T()) +
555  asm_H2_semi_dist_sqr(mim,mf1,U1,mf2,U2,rg,T()));
556  }
557 
558  /*
559  assembly of a matrix with 1 parameter (real or complex)
560  (the most common here for the assembly routines below)
561  */
562  template <typename MAT, typename VECT>
563  inline void asm_real_or_complex_1_param_mat
564  (MAT &M, const mesh_im &mim, const mesh_fem &mf_u, const mesh_fem *mf_data,
565  const VECT &A, const mesh_region &rg, const char *assembly_description) {
566  asm_real_or_complex_1_param_mat_
567  (M, mim, mf_u, mf_data, A, rg, assembly_description,
568  typename gmm::linalg_traits<VECT>::value_type());
569  }
570 
571  /* real version */
572  template<typename MAT, typename VECT, typename T>
573  inline void asm_real_or_complex_1_param_mat_
574  (const MAT &M, const mesh_im &mim, const mesh_fem &mf_u,
575  const mesh_fem *mf_data, const VECT &A, const mesh_region &rg,
576  const char *assembly_description, T) {
577  ga_workspace workspace;
578  gmm::sub_interval Iu(0, mf_u.nb_dof());
579  base_vector u(mf_u.nb_dof()), AA(gmm::vect_size(A));
580  gmm::copy(A, AA);
581  workspace.add_fem_variable("u", mf_u, Iu, u);
582  if (mf_data)
583  workspace.add_fem_constant("A", *mf_data, AA);
584  else
585  workspace.add_fixed_size_constant("A", AA);
586  workspace.add_expression(assembly_description, mim, rg);
587  workspace.assembly(2);
588  if (gmm::mat_nrows(workspace.assembled_matrix()))
589  gmm::add(workspace.assembled_matrix(), const_cast<MAT &>(M));
590  }
591 
592  inline void asm_real_or_complex_1_param_mat_
593  (model_real_sparse_matrix &M, const mesh_im &mim, const mesh_fem &mf_u,
594  const mesh_fem *mf_data, const model_real_plain_vector &A,
595  const mesh_region &rg,
596  const char *assembly_description, scalar_type) {
597  ga_workspace workspace;
598  gmm::sub_interval Iu(0, mf_u.nb_dof());
599  base_vector u(mf_u.nb_dof());
600  workspace.add_fem_variable("u", mf_u, Iu, u);
601  if (mf_data)
602  workspace.add_fem_constant("A", *mf_data, A);
603  else
604  workspace.add_fixed_size_constant("A", A);
605  workspace.add_expression(assembly_description, mim, rg);
606  workspace.set_assembled_matrix(M);
607  workspace.assembly(2);
608  }
609 
610  /* complex version */
611  template<typename MAT, typename VECT, typename T>
612  inline void asm_real_or_complex_1_param_mat_
613  (MAT &M, const mesh_im &mim, const mesh_fem &mf_u, const mesh_fem *mf_data,
614  const VECT &A, const mesh_region &rg, const char *assembly_description,
615  std::complex<T>) {
616  asm_real_or_complex_1_param_mat_(gmm::real_part(M),mim,mf_u,mf_data,
617  gmm::real_part(A),rg,
618  assembly_description, T());
619  asm_real_or_complex_1_param_mat_(gmm::imag_part(M),mim,mf_u,mf_data,
620  gmm::imag_part(A),rg,
621  assembly_description, T());
622  }
623 
624  /*
625  assembly of a vector with 1 parameter (real or complex)
626  (the most common here for the assembly routines below)
627  */
628  template <typename MAT, typename VECT>
629  inline void asm_real_or_complex_1_param_vec
630  (MAT &M, const mesh_im &mim, const mesh_fem &mf_u, const mesh_fem *mf_data,
631  const VECT &A, const mesh_region &rg, const char *assembly_description) {
632  asm_real_or_complex_1_param_vec_
633  (M, mim, mf_u, mf_data, A, rg, assembly_description,
634  typename gmm::linalg_traits<VECT>::value_type());
635  }
636 
637  /* real version */
638  template<typename VECTA, typename VECT, typename T>
639  inline void asm_real_or_complex_1_param_vec_
640  (const VECTA &V, const mesh_im &mim, const mesh_fem &mf_u,
641  const mesh_fem *mf_data, const VECT &A, const mesh_region &rg,
642  const char *assembly_description, T) {
643  ga_workspace workspace;
644  gmm::sub_interval Iu(0, mf_u.nb_dof());
645  base_vector u(mf_u.nb_dof()), AA(gmm::vect_size(A));
646  gmm::copy(A, AA);
647  workspace.add_fem_variable("u", mf_u, Iu, u);
648  if (mf_data)
649  workspace.add_fem_constant("A", *mf_data, AA);
650  else
651  workspace.add_fixed_size_constant("A", AA);
652  workspace.add_expression(assembly_description, mim, rg);
653  workspace.assembly(1);
654  if (gmm::vect_size(workspace.assembled_vector()))
655  gmm::add(workspace.assembled_vector(), const_cast<VECTA &>(V));
656  }
657 
658  inline void asm_real_or_complex_1_param_vec_
659  (model_real_plain_vector &V, const mesh_im &mim, const mesh_fem &mf_u,
660  const mesh_fem *mf_data, const model_real_plain_vector &A,
661  const mesh_region &rg,
662  const char *assembly_description, scalar_type) {
663  ga_workspace workspace;
664  gmm::sub_interval Iu(0, mf_u.nb_dof());
665  base_vector u(mf_u.nb_dof());
666  workspace.add_fem_variable("u", mf_u, Iu, u);
667  if (mf_data)
668  workspace.add_fem_constant("A", *mf_data, A);
669  else
670  workspace.add_fixed_size_constant("A", A);
671  workspace.add_expression(assembly_description, mim, rg);
672  workspace.set_assembled_vector(V);
673  workspace.assembly(1);
674  }
675 
676  /* complex version */
677  template<typename MAT, typename VECT, typename T>
678  inline void asm_real_or_complex_1_param_vec_
679  (MAT &M, const mesh_im &mim, const mesh_fem &mf_u, const mesh_fem *mf_data,
680  const VECT &A, const mesh_region &rg,const char *assembly_description,
681  std::complex<T>) {
682  asm_real_or_complex_1_param_vec_(gmm::real_part(M),mim,mf_u,mf_data,
683  gmm::real_part(A),rg,
684  assembly_description, T());
685  asm_real_or_complex_1_param_vec_(gmm::imag_part(M),mim,mf_u,mf_data,
686  gmm::imag_part(A),rg,
687  assembly_description, T());
688  }
689 
690  /**
691  generic mass matrix assembly (on the whole mesh or on the specified
692  convex set or boundary)
693  @ingroup asm
694  */
695  template<typename MAT>
696  inline void asm_mass_matrix
697  (const MAT &M, const mesh_im &mim, const mesh_fem &mf1,
698  const mesh_region &rg = mesh_region::all_convexes()) {
699 
700  ga_workspace workspace;
701  gmm::sub_interval Iu1(0, mf1.nb_dof());
702  base_vector u1(mf1.nb_dof());
703  workspace.add_fem_variable("u1", mf1, Iu1, u1);
704  workspace.add_expression("Test_u1:Test2_u1", mim, rg);
705  workspace.assembly(2);
706  if (gmm::mat_nrows(workspace.assembled_matrix()))
707  gmm::add(workspace.assembled_matrix(), const_cast<MAT &>(M));
708  }
709 
710  inline void asm_mass_matrix
711  (model_real_sparse_matrix &M, const mesh_im &mim,
712  const mesh_fem &mf1,
713  const mesh_region &rg = mesh_region::all_convexes()) {
714  ga_workspace workspace;
715  gmm::sub_interval Iu1(0, mf1.nb_dof());
716  base_vector u1(mf1.nb_dof());
717  workspace.add_fem_variable("u1", mf1, Iu1, u1);
718  workspace.add_expression("Test_u1:Test2_u1", mim, rg);
719  workspace.set_assembled_matrix(M);
720  workspace.assembly(2);
721  }
722 
723  /**
724  * generic mass matrix assembly (on the whole mesh or on the specified
725  * boundary)
726  */
727 
728  template<typename MAT>
729  inline void asm_mass_matrix
730  (const MAT &M, const mesh_im &mim, const mesh_fem &mf1, const mesh_fem &mf2,
731  const mesh_region &rg = mesh_region::all_convexes()) {
732  ga_workspace workspace;
733  gmm::sub_interval Iu1(0, mf1.nb_dof()), Iu2(Iu1.last(), mf2.nb_dof());
734  base_vector u1(mf1.nb_dof()), u2(mf2.nb_dof());
735  workspace.add_fem_variable("u1", mf1, Iu1, u1);
736  workspace.add_fem_variable("u2", mf2, Iu2, u2);
737  workspace.add_expression("Test_u1:Test2_u2", mim, rg);
738  workspace.assembly(2);
739  if (gmm::mat_nrows(workspace.assembled_matrix()))
740  gmm::add(gmm::sub_matrix(workspace.assembled_matrix(), Iu1, Iu2),
741  const_cast<MAT &>(M));
742  }
743 
744  inline void asm_mass_matrix
745  (model_real_sparse_matrix &M, const mesh_im &mim,
746  const mesh_fem &mf1, const mesh_fem &mf2,
747  const mesh_region &rg = mesh_region::all_convexes()) {
748  ga_workspace workspace;
749  gmm::sub_interval Iu1(0, mf1.nb_dof()), Iu2(0, mf2.nb_dof());
750  base_vector u1(mf1.nb_dof()), u2(mf2.nb_dof());
751  workspace.add_fem_variable("u1", mf1, Iu1, u1);
752  workspace.add_fem_variable("u2", mf2, Iu2, u2);
753  workspace.add_expression("Test_u1:Test2_u2", mim, rg);
754  workspace.set_assembled_matrix(M);
755  workspace.assembly(2);
756  }
757 
758  /**
759  generic mass matrix assembly with an additional parameter
760  (on the whole mesh or on the specified boundary)
761  @ingroup asm
762  */
763  template<typename MAT, typename VECT>
764  inline void asm_mass_matrix_param
765  (const MAT &M, const mesh_im &mim, const mesh_fem &mf1, const mesh_fem &mf2,
766  const mesh_fem &mf_data, const VECT &A,
767  const mesh_region &rg = mesh_region::all_convexes()) {
768 
769  ga_workspace workspace;
770  gmm::sub_interval Iu1(0, mf1.nb_dof()), Iu2(Iu1.last(), mf2.nb_dof());
771  base_vector u1(mf1.nb_dof()), u2(mf2.nb_dof()), AA(mf_data.nb_dof());
772  gmm::copy(A, AA);
773  workspace.add_fem_variable("u1", mf1, Iu1, u1);
774  workspace.add_fem_variable("u2", mf2, Iu2, u2);
775  workspace.add_fem_constant("A", mf_data, AA);
776  workspace.add_expression("(A*Test_u1).Test2_u2", mim, rg);
777  workspace.assembly(2);
778  if (gmm::mat_nrows(workspace.assembled_matrix()))
779  gmm::add(gmm::sub_matrix(workspace.assembled_matrix(), Iu1, Iu2),
780  const_cast<MAT &>(M));
781  }
782 
783  inline void asm_mass_matrix_param
784  (model_real_sparse_matrix &M, const mesh_im &mim,
785  const mesh_fem &mf1, const mesh_fem &mf2,
786  const mesh_fem &mf_data, const model_real_plain_vector &A,
787  const mesh_region &rg = mesh_region::all_convexes()) {
788 
789  ga_workspace workspace;
790  gmm::sub_interval Iu1(0, mf1.nb_dof()), Iu2(0, mf2.nb_dof());
791  base_vector u1(mf1.nb_dof()), u2(mf2.nb_dof());
792  workspace.add_fem_variable("u1", mf1, Iu1, u1);
793  workspace.add_fem_variable("u2", mf2, Iu2, u2);
794  workspace.add_fem_constant("A", mf_data, A);
795  workspace.add_expression("(A*Test_u1).Test2_u2", mim, rg);
796  workspace.set_assembled_matrix(M);
797  workspace.assembly(2);
798  }
799 
800 
801 
802  /**
803  generic mass matrix assembly with an additional parameter
804  (on the whole mesh or on the specified boundary)
805  @ingroup asm
806  */
807  template<typename MAT, typename VECT>
808  void asm_mass_matrix_param
809  (MAT &M, const mesh_im &mim, const mesh_fem &mf_u, const mesh_fem &mf_data,
810  const VECT &F, const mesh_region &rg = mesh_region::all_convexes()) {
811  asm_real_or_complex_1_param_mat
812  (M, mim, mf_u, &mf_data, F, rg, "(A*Test_u):Test2_u");
813  }
814 
815  /**
816  generic mass matrix assembly with an additional constant parameter
817  (on the whole mesh or on the specified boundary)
818  @ingroup asm
819  */
820  template<typename MAT, typename VECT>
821  void asm_mass_matrix_homogeneous_param
822  (MAT &M, const mesh_im &mim, const mesh_fem &mf_u,
823  const VECT &F, const mesh_region &rg = mesh_region::all_convexes()) {
824  asm_real_or_complex_1_param_mat
825  (M, mim, mf_u, 0, F, rg, "(A*Test_u):Test2_u");
826  }
827 
828  /**
829  lumped mass matrix assembly from consistent mass matrix
830  */
831  template<typename MAT>
832  inline void asm_lumped_mass_matrix_for_first_order_from_consistent
833  (const MAT &M) {
834  size_type nbd = gmm::mat_ncols(M), nbr = gmm::mat_nrows(M);
835  GMM_ASSERT1(nbd == nbr, "mass matrix is not square");
836  typedef typename gmm::linalg_traits<MAT>::value_type T;
837  std::vector<T> V(nbd), W(nbr);
838  gmm::fill(V, T(1));
839  gmm::mult(M, V, W);
840  gmm::clear(const_cast<MAT &>(M));
841  for (size_type i =0; i < nbd; ++i) {
842  (const_cast<MAT &>(M))(i, i) = W[i];
843  }
844  }
845 
846  /**
847  lumped mass matrix assembly (on the whole mesh or on the specified
848  boundary)
849  @ingroup asm
850  */
851  template<typename MAT>
852  inline void asm_lumped_mass_matrix_for_first_order
853  (const MAT &M, const mesh_im &mim, const mesh_fem &mf1,
854  const mesh_region &rg = mesh_region::all_convexes()) {
855  asm_mass_matrix(M, mim, mf1, rg);
856  asm_lumped_mass_matrix_for_first_order_from_consistent(M);
857  }
858 
859  /**
860  lumped mass matrix assembly with an additional parameter
861  (on the whole mesh or on the specified boundary)
862  @ingroup asm
863  */
864  template<typename MAT, typename VECT>
865  inline void asm_lumped_mass_matrix_for_first_order_param
866  (MAT &M, const mesh_im &mim, const mesh_fem &mf_u, const mesh_fem &mf_data,
867  const VECT &F, const mesh_region &rg = mesh_region::all_convexes()) {
868  asm_mass_matrix_param(M, mim, mf_u, mf_data, F, rg);
869  asm_lumped_mass_matrix_for_first_order_from_consistent(M);
870  }
871 
872  /**
873  source term (for both volumic sources and boundary (Neumann) sources).
874  @ingroup asm
875  */
876  template<typename VECT1, typename VECT2>
877  void asm_source_term(const VECT1 &B, const mesh_im &mim, const mesh_fem &mf,
878  const mesh_fem &mf_data, const VECT2 &F,
879  const mesh_region &rg = mesh_region::all_convexes()) {
880  GMM_ASSERT1(mf_data.get_qdim() == 1 ||
881  mf_data.get_qdim() == mf.get_qdim(),
882  "invalid data mesh fem (same Qdim or Qdim=1 required)");
883  asm_real_or_complex_1_param_vec
884  (const_cast<VECT1 &>(B), mim, mf, &mf_data, F, rg, "A:Test_u");
885  }
886 
887  /**
888  source term (for both volumic sources and boundary (Neumann) sources).
889  For an homogeneous term.
890  @ingroup asm
891  */
892  template<typename VECT1, typename VECT2>
893  void asm_homogeneous_source_term(const VECT1 &B, const mesh_im &mim,
894  const mesh_fem &mf, const VECT2 &F,
895  const mesh_region &rg = mesh_region::all_convexes()) {
896  asm_real_or_complex_1_param_vec
897  (const_cast<VECT1 &>(B), mim, mf, 0, F, rg, "A:Test_u");
898  }
899 
900  /**
901  Normal source term (for boundary (Neumann) condition).
902  @ingroup asm
903  */
904  template<typename VECT1, typename VECT2>
905  void asm_normal_source_term(VECT1 &B, const mesh_im &mim,
906  const mesh_fem &mf,
907  const mesh_fem &mf_data, const VECT2 &F,
908  const mesh_region &rg) {
909  asm_real_or_complex_1_param_vec(B, mim, mf, &mf_data, F, rg,
910  "(Reshape(A, qdim(u), meshdim).Normal):Test_u");
911  }
912 
913  /**
914  Homogeneous normal source term (for boundary (Neumann) condition).
915  @ingroup asm
916  */
917  template<typename VECT1, typename VECT2>
918  void asm_homogeneous_normal_source_term
919  (VECT1 &B, const mesh_im &mim, const mesh_fem &mf, const VECT2 &F,
920  const mesh_region &rg)
921  { asm_real_or_complex_1_param_vec(B, mim, mf, 0,F,rg,
922  "(Reshape(A, qdim(u), meshdim).Normal):Test_u"); }
923 
924  /**
925  assembly of @f$\int{qu.v}@f$
926 
927  (if @f$u@f$ is a vector field of size @f$N@f$, @f$q@f$ is a square
928  matrix @f$N\times N@f$ used by assem_general_boundary_conditions
929 
930  convention: Q is of the form
931  Q1_11 Q2_11 ..... Qn_11
932  Q1_21 Q2_21 ..... Qn_21
933  Q1_12 Q2_12 ..... Qn_12
934  Q1_22 Q2_22 ..... Qn_22
935  if N = 2, and mf_d has n/N degree of freedom
936 
937  Q is a vector, so the matrix is assumed to be stored by columns
938  (fortran style)
939 
940  Works for both volumic assembly and boundary assembly
941  @ingroup asm
942  */
943  template<typename MAT, typename VECT>
944  void asm_qu_term(MAT &M, const mesh_im &mim, const mesh_fem &mf_u,
945  const mesh_fem &mf_d, const VECT &Q,
946  const mesh_region &rg) {
947  if (mf_d.get_qdim() == 1 && gmm::vect_size(Q) > mf_d.nb_dof())
948  asm_real_or_complex_1_param_mat
949  (M, mim,mf_u,&mf_d,Q,rg,"(Reshape(A,qdim(u),qdim(u)).Test_u):Test2_u");
950  else if (mf_d.get_qdim() == mf_u.get_qdim())
951  asm_real_or_complex_1_param_mat
952  (M, mim, mf_u, &mf_d, Q, rg, "(A*Test_u):Test2_u");
953  else GMM_ASSERT1(false, "invalid data mesh fem");
954  }
955 
956  template<typename MAT, typename VECT>
957  void asm_homogeneous_qu_term(MAT &M, const mesh_im &mim,
958  const mesh_fem &mf_u, const VECT &Q,
959  const mesh_region &rg) {
960  if (gmm::vect_size(Q) == 1)
961  asm_real_or_complex_1_param_mat
962  (M, mim,mf_u,0,Q,rg,"(A*Test_u):Test2_u");
963  else
964  asm_real_or_complex_1_param_mat
965  (M, mim,mf_u,0,Q,rg,"(Reshape(A,qdim(u),qdim(u)).Test_u):Test2_u");
966  }
967 
968  /**
969  Stiffness matrix for linear elasticity, with Lamé coefficients
970  @ingroup asm
971  */
972  template<class MAT, class VECT>
973  inline void asm_stiffness_matrix_for_linear_elasticity
974  (const MAT &M, const mesh_im &mim, const mesh_fem &mf,
975  const mesh_fem &mf_data, const VECT &LAMBDA, const VECT &MU,
976  const mesh_region &rg = mesh_region::all_convexes()) {
977  ga_workspace workspace;
978  gmm::sub_interval Iu(0, mf.nb_dof());
979  base_vector u(mf.nb_dof()), lambda(gmm::vect_size(LAMBDA));
980  base_vector mu(gmm::vect_size(MU));
981  gmm::copy(LAMBDA, lambda); gmm::copy(MU, mu);
982  workspace.add_fem_variable("u", mf, Iu, u);
983  workspace.add_fem_constant("lambda", mf_data, lambda);
984  workspace.add_fem_constant("mu", mf_data, mu);
985  workspace.add_expression("((lambda*Div_Test_u)*Id(meshdim)"
986  "+(2*mu)*Sym(Grad_Test_u)):Grad_Test2_u", mim, rg);
987  workspace.assembly(2);
988  if (gmm::mat_nrows(workspace.assembled_matrix()))
989  gmm::add(workspace.assembled_matrix(), const_cast<MAT &>(M));
990  }
991 
992  inline void asm_stiffness_matrix_for_linear_elasticity
993  (model_real_sparse_matrix &M, const mesh_im &mim, const mesh_fem &mf,
994  const mesh_fem &mf_data, const model_real_plain_vector &LAMBDA,
995  const model_real_plain_vector &MU,
996  const mesh_region &rg = mesh_region::all_convexes()) {
997  ga_workspace workspace;
998  gmm::sub_interval Iu(0, mf.nb_dof());
999  base_vector u(mf.nb_dof());
1000  workspace.add_fem_variable("u", mf, Iu, u);
1001  workspace.add_fem_constant("lambda", mf_data, LAMBDA);
1002  workspace.add_fem_constant("mu", mf_data, MU);
1003  workspace.add_expression("((lambda*Div_Test_u)*Id(meshdim)"
1004  "+(2*mu)*Sym(Grad_Test_u)):Grad_Test2_u", mim, rg);
1005  workspace.set_assembled_matrix(M);
1006  workspace.assembly(2);
1007  }
1008 
1009 
1010  /**
1011  Stiffness matrix for linear elasticity, with constant Lamé coefficients
1012  @ingroup asm
1013  */
1014  template<class MAT, class VECT>
1015  inline void asm_stiffness_matrix_for_homogeneous_linear_elasticity
1016  (const MAT &M, const mesh_im &mim, const mesh_fem &mf,
1017  const VECT &LAMBDA, const VECT &MU,
1018  const mesh_region &rg = mesh_region::all_convexes()) {
1019  ga_workspace workspace;
1020  gmm::sub_interval Iu(0, mf.nb_dof());
1021  base_vector u(mf.nb_dof()), lambda(gmm::vect_size(LAMBDA));
1022  base_vector mu(gmm::vect_size(MU));
1023  gmm::copy(LAMBDA, lambda); gmm::copy(MU, mu);
1024  workspace.add_fem_variable("u", mf, Iu, u);
1025  workspace.add_fixed_size_constant("lambda", lambda);
1026  workspace.add_fixed_size_constant("mu", mu);
1027  workspace.add_expression("((lambda*Div_Test_u)*Id(meshdim)"
1028  "+(2*mu)*Sym(Grad_Test_u)):Grad_Test2_u", mim, rg);
1029  workspace.assembly(2);
1030  if (gmm::mat_nrows(workspace.assembled_matrix()))
1031  gmm::add(workspace.assembled_matrix(), const_cast<MAT &>(M));
1032  }
1033 
1034 
1035  inline void asm_stiffness_matrix_for_homogeneous_linear_elasticity
1036  (model_real_sparse_matrix &M, const mesh_im &mim, const mesh_fem &mf,
1037  const model_real_plain_vector &LAMBDA, const model_real_plain_vector &MU,
1038  const mesh_region &rg = mesh_region::all_convexes()) {
1039  ga_workspace workspace;
1040  gmm::sub_interval Iu(0, mf.nb_dof());
1041  base_vector u(mf.nb_dof());
1042  workspace.add_fem_variable("u", mf, Iu, u);
1043  workspace.add_fixed_size_constant("lambda", LAMBDA);
1044  workspace.add_fixed_size_constant("mu", MU);
1045  workspace.add_expression("((lambda*Div_Test_u)*Id(meshdim)"
1046  "+(2*mu)*Sym(Grad_Test_u)):Grad_Test2_u", mim, rg);
1047  workspace.set_assembled_matrix(M);
1048  workspace.assembly(2);
1049  }
1050 
1051  /**
1052  Stiffness matrix for linear elasticity, with a general Hooke
1053  tensor. This is more a demonstration of generic assembly than
1054  something useful !
1055 
1056  Note that this function is just an alias for
1057  asm_stiffness_matrix_for_vector_elliptic.
1058 
1059  @ingroup asm
1060  */
1061  template<typename MAT, typename VECT> void
1062  asm_stiffness_matrix_for_linear_elasticity_Hooke
1063  (MAT &RM, const mesh_im &mim, const mesh_fem &mf, const mesh_fem &mf_data,
1064  const VECT &H, const mesh_region &rg = mesh_region::all_convexes()) {
1065  asm_stiffness_matrix_for_vector_elliptic(RM, mim, mf, mf_data, H, rg);
1066  }
1067 
1068  /**
1069  Build the mixed pressure term @f$ B = - \int p.div u @f$
1070 
1071  @ingroup asm
1072  */
1073  template<typename MAT>
1074  inline void asm_stokes_B(const MAT &B, const mesh_im &mim,
1075  const mesh_fem &mf_u, const mesh_fem &mf_p,
1076  const mesh_region &rg=mesh_region::all_convexes()) {
1077  ga_workspace workspace;
1078  gmm::sub_interval Iu(0, mf_u.nb_dof()), Ip(Iu.last(), mf_p.nb_dof());
1079  base_vector u(mf_u.nb_dof()), p(mf_p.nb_dof());
1080  workspace.add_fem_variable("u", mf_u, Iu, u);
1081  workspace.add_fem_variable("p", mf_p, Ip, p);
1082  workspace.add_expression("Test_p*Div_Test2_u", mim, rg);
1083  workspace.assembly(2);
1084  if (gmm::mat_nrows(workspace.assembled_matrix()))
1085  gmm::add(gmm::sub_matrix(workspace.assembled_matrix(), Ip, Iu),
1086  const_cast<MAT &>(B));
1087  }
1088 
1089  inline void asm_stokes_B(model_real_sparse_matrix &B, const mesh_im &mim,
1090  const mesh_fem &mf_u, const mesh_fem &mf_p,
1091  const mesh_region &rg=mesh_region::all_convexes()) {
1092  ga_workspace workspace;
1093  gmm::sub_interval Iu(0, mf_u.nb_dof()), Ip(0, mf_p.nb_dof());
1094  base_vector u(mf_u.nb_dof()), p(mf_p.nb_dof());
1095  workspace.add_fem_variable("u", mf_u, Iu, u);
1096  workspace.add_fem_variable("p", mf_p, Ip, p);
1097  workspace.add_expression("Test_p*Div_Test2_u", mim, rg);
1098  workspace.set_assembled_matrix(B);
1099  workspace.assembly(2);
1100  }
1101 
1102 
1103  /**
1104  assembly of @f$\int_\Omega \nabla u.\nabla v@f$.
1105 
1106  @ingroup asm
1107  */
1108  template<typename MAT>
1109  inline void asm_stiffness_matrix_for_homogeneous_laplacian
1110  (const MAT &M, const mesh_im &mim, const mesh_fem &mf,
1111  const mesh_region &rg = mesh_region::all_convexes()) {
1112  ga_workspace workspace;
1113  gmm::sub_interval Iu(0, mf.nb_dof());
1114  base_vector u(mf.nb_dof());
1115  workspace.add_fem_variable("u", mf, Iu, u);
1116  workspace.add_expression("Grad_Test_u:Grad_Test2_u", mim, rg);
1117  workspace.assembly(2);
1118  if (gmm::mat_nrows(workspace.assembled_matrix()))
1119  gmm::add(workspace.assembled_matrix(), const_cast<MAT &>(M));
1120  }
1121 
1122  inline void asm_stiffness_matrix_for_homogeneous_laplacian
1123  (model_real_sparse_matrix &M, const mesh_im &mim, const mesh_fem &mf,
1124  const mesh_region &rg = mesh_region::all_convexes()) {
1125  ga_workspace workspace;
1126  gmm::sub_interval Iu(0, mf.nb_dof());
1127  base_vector u(mf.nb_dof());
1128  workspace.add_fem_variable("u", mf, Iu, u);
1129  workspace.add_expression("Grad_Test_u:Grad_Test2_u", mim, rg);
1130  workspace.set_assembled_matrix(M);
1131  workspace.assembly(2);
1132  }
1133 
1134  /**
1135  assembly of @f$\int_\Omega \nabla u.\nabla v@f$.
1136  @ingroup asm
1137  */
1138  template<typename MAT>
1139  inline void asm_stiffness_matrix_for_homogeneous_laplacian_componentwise
1140  (const MAT &M, const mesh_im &mim, const mesh_fem &mf,
1141  const mesh_region &rg = mesh_region::all_convexes()) {
1142  return asm_stiffness_matrix_for_homogeneous_laplacian(M, mim, mf, rg);
1143  }
1144 
1145  /**
1146  assembly of @f$\int_\Omega a(x)\nabla u.\nabla v@f$ , where @f$a(x)@f$
1147  is scalar.
1148  @ingroup asm
1149  */
1150  template<typename MAT, typename VECT>
1151  inline void asm_stiffness_matrix_for_laplacian
1152  (MAT &M, const mesh_im &mim, const mesh_fem &mf, const mesh_fem &mf_data,
1153  const VECT &A, const mesh_region &rg = mesh_region::all_convexes()) {
1154  GMM_ASSERT1(mf_data.get_qdim() == 1
1155  && gmm::vect_size(A) == mf_data.nb_dof(), "invalid data");
1156  asm_real_or_complex_1_param_mat
1157  (M, mim, mf, &mf_data, A, rg, "(A*Grad_Test_u):Grad_Test2_u");
1158  }
1159 
1160  /** The same as getfem::asm_stiffness_matrix_for_laplacian , but on
1161  each component of mf when mf has a qdim > 1
1162  */
1163  template<typename MAT, typename VECT>
1164  inline void asm_stiffness_matrix_for_laplacian_componentwise
1165  (MAT &M, const mesh_im &mim, const mesh_fem &mf, const mesh_fem &mf_data,
1166  const VECT &A, const mesh_region &rg = mesh_region::all_convexes()) {
1167  asm_stiffness_matrix_for_laplacian(M, mim, mf, mf_data, A, rg);
1168  }
1169 
1170  /**
1171  assembly of @f$\int_\Omega A(x)\nabla u.\nabla v@f$, where @f$A(x)@f$
1172  is a (symmetric positive definite) NxN matrix.
1173  Arguments:
1174  @param M a sparse matrix of dimensions mf.nb_dof() x mf.nb_dof()
1175 
1176  @param mim the mesh_im.
1177 
1178  @param mf : the mesh_fem that describes the solution, with
1179  @c mf.get_qdim() == @c N.
1180 
1181  @param mf_data the mesh_fem that describes the coefficients of @c A
1182  (@c mf_data.get_qdim() == 1).
1183 
1184  @param A a (very large) vector, which is a flattened (n x n x
1185  mf_data.nb_dof()) 3D array. For each dof of mf_data, it contains
1186  the n x n coefficients of @f$A@f$. As usual, the order is the
1187  "fortran-order", i.e. @c A = [A_11(dof1) A_21(dof1) A_31(dof1)
1188  A_12(dof1) A_22(dof1) ... A_33(dof) A_11(dof2)
1189  .... A_33(lastdof)]
1190 
1191  @ingroup asm
1192  */
1193  template<typename MAT, typename VECT>
1194  void asm_stiffness_matrix_for_scalar_elliptic
1195  (MAT &M, const mesh_im &mim, const mesh_fem &mf, const mesh_fem &mf_data,
1196  const VECT &A, const mesh_region &rg = mesh_region::all_convexes()) {
1197  asm_real_or_complex_1_param_mat
1198  (M, mim, mf, &mf_data, A, rg,
1199  "(Reshape(A,meshdim,meshdim)*Grad_Test_u):Grad_Test2_u");
1200  }
1201 
1202  /** The same but with a constant matrix
1203  */
1204  template<typename MAT, typename VECT>
1205  void asm_stiffness_matrix_for_homogeneous_scalar_elliptic
1206  (MAT &M, const mesh_im &mim, const mesh_fem &mf,
1207  const VECT &A, const mesh_region &rg = mesh_region::all_convexes()) {
1208  asm_real_or_complex_1_param_mat
1209  (M, mim, mf, 0, A, rg,
1210  "(Reshape(A,meshdim,meshdim)*Grad_Test_u):Grad_Test2_u");
1211  }
1212 
1213  /** The same but on each component of mf when mf has a qdim > 1
1214  */
1215  template<typename MAT, typename VECT>
1216  void asm_stiffness_matrix_for_scalar_elliptic_componentwise
1217  (MAT &M, const mesh_im &mim, const mesh_fem &mf,
1218  const mesh_fem &mf_data, const VECT &A,
1219  const mesh_region &rg = mesh_region::all_convexes()) {
1220  asm_real_or_complex_1_param_mat
1221  (M, mim, mf, &mf_data, A, rg,
1222  "(Grad_Test_u*(Reshape(A,meshdim,meshdim)')):Grad_Test2_u");
1223  }
1224 
1225  /** The same but with a constant matrix
1226  */
1227  template<typename MAT, typename VECT>
1228  void asm_stiffness_matrix_for_homogeneous_scalar_elliptic_componentwise
1229  (MAT &M, const mesh_im &mim, const mesh_fem &mf, const VECT &A,
1230  const mesh_region &rg = mesh_region::all_convexes()) {
1231  asm_real_or_complex_1_param_mat
1232  (M, mim, mf, 0, A, rg,
1233  "(Grad_Test_u*(Reshape(A,meshdim,meshdim)')):Grad_Test2_u");
1234  }
1235 
1236 
1237  /**
1238  Assembly of @f$\int_\Omega A(x)\nabla u.\nabla v@f$, where @f$A(x)@f$
1239  is a NxNxQxQ (symmetric positive definite) tensor defined on mf_data.
1240  */
1241  template<typename MAT, typename VECT> void
1242  asm_stiffness_matrix_for_vector_elliptic
1243  (MAT &M, const mesh_im &mim, const mesh_fem &mf, const mesh_fem &mf_data,
1244  const VECT &A, const mesh_region &rg = mesh_region::all_convexes()) {
1245  /* M = a_{i,j,k,l}D_{i,j}(u)D_{k,l}(v) */
1246  asm_real_or_complex_1_param_mat
1247  (M, mim, mf, &mf_data, A, rg,
1248  "(Reshape(A,qdim(u),meshdim,qdim(u),meshdim):Grad_Test_u):Grad_Test2_u");
1249  }
1250 
1251  /**
1252  Assembly of @f$\int_\Omega A(x)\nabla u.\nabla v@f$, where @f$A(x)@f$
1253  is a NxNxQxQ (symmetric positive definite) constant tensor.
1254  */
1255  template<typename MAT, typename VECT> void
1256  asm_stiffness_matrix_for_homogeneous_vector_elliptic
1257  (MAT &M, const mesh_im &mim, const mesh_fem &mf,
1258  const VECT &A, const mesh_region &rg = mesh_region::all_convexes()) {
1259  /* M = a_{i,j,k,l}D_{i,j}(u)D_{k,l}(v) */
1260  asm_real_or_complex_1_param_mat
1261  (M, mim, mf, 0, A, rg,
1262  "(Reshape(A,qdim(u),meshdim,qdim(u),meshdim):Grad_Test_u):Grad_Test2_u");
1263  }
1264 
1265  /**
1266  assembly of the term @f$\int_\Omega Kuv - \nabla u.\nabla v@f$,
1267  for the helmholtz equation (@f$\Delta u + k^2u = 0@f$, with @f$K=k^2@f$).
1268 
1269  The argument K_squared may be a real or a complex-valued vector.
1270 
1271  @ingroup asm
1272  */
1273  template<typename MAT, typename VECT>
1274  void asm_Helmholtz(MAT &M, const mesh_im &mim, const mesh_fem &mf_u,
1275  const mesh_fem &mf_data, const VECT &K_squared,
1276  const mesh_region &rg = mesh_region::all_convexes()) {
1277  typedef typename gmm::linalg_traits<MAT>::value_type T;
1278  asm_Helmholtz_(M, mim, mf_u, &mf_data, K_squared, rg, T());
1279  }
1280 
1281  template<typename MAT, typename VECT, typename T>
1282  void asm_Helmholtz_(MAT &M, const mesh_im &mim, const mesh_fem &mf_u,
1283  const mesh_fem *mf_data, const VECT &K_squared,
1284  const mesh_region &rg, T) {
1285  asm_real_or_complex_1_param_mat
1286  (M, mim, mf_u, mf_data, K_squared, rg,
1287  "(A*Test_u).Test2_u - Grad_Test_u:Grad_Test2_u");
1288  }
1289 
1290  template<typename MAT, typename VECT, typename T>
1291  void asm_Helmholtz_(MAT &M, const mesh_im &mim, const mesh_fem &mf_u,
1292  const mesh_fem *mf_data, const VECT &K_squared,
1293  const mesh_region &rg, std::complex<T>) {
1294  // asm_real_or_complex_1_param_mat
1295  // (M, mim, mf_u, &mf_data, gmm::real_part(K_squared), rg,
1296  // "(A*Test_u).Test2_u - Grad_Test_u:Grad_Test2_u");
1297  // asm_real_or_complex_1_param_mat
1298  // (M, mim, mf_u, &mf_data, gmm::imag_part(K_squared), rg,
1299  // "(A*Test_u).Test2_u");
1300 
1301 
1302  ga_workspace workspace;
1303  gmm::sub_interval Iur(0, mf_u.nb_dof()), Iui(Iur.last(), mf_u.nb_dof());
1304  base_vector u(mf_u.nb_dof());
1305  base_vector AR(gmm::vect_size(K_squared)), AI(gmm::vect_size(K_squared));
1306  gmm::copy(gmm::real_part(K_squared), AR);
1307  gmm::copy(gmm::imag_part(K_squared), AI);
1308  workspace.add_fem_variable("u", mf_u, Iur, u);
1309  workspace.add_fem_variable("ui", mf_u, Iui, u);
1310 
1311  if (mf_data) {
1312  workspace.add_fem_constant("A", *mf_data, AR);
1313  workspace.add_fem_constant("AI", *mf_data, AI);
1314  } else {
1315  workspace.add_fixed_size_constant("A", AR);
1316  workspace.add_fixed_size_constant("AI", AI);
1317  }
1318  workspace.add_expression("(A*Test_u).Test2_u - Grad_Test_u:Grad_Test2_u",
1319  mim, rg);
1320  workspace.add_expression("(AI*Test_ui).Test2_ui", mim, rg);
1321  workspace.assembly(2);
1322 
1323  if (gmm::mat_nrows(workspace.assembled_matrix()))
1324  gmm::add(gmm::sub_matrix(workspace.assembled_matrix(),Iur,Iur),
1325  const_cast<MAT &>(M));
1326  if (gmm::mat_nrows(workspace.assembled_matrix()) > mf_u.nb_dof())
1327  gmm::add(gmm::sub_matrix(workspace.assembled_matrix(),Iui,Iui),
1328  gmm::imag_part(const_cast<MAT &>(M)));
1329 
1330 
1331 
1332  }
1333 
1334  /**
1335  assembly of the term @f$\int_\Omega Kuv - \nabla u.\nabla v@f$,
1336  for the helmholtz equation (@f$\Delta u + k^2u = 0@f$, with @f$K=k^2@f$).
1337 
1338  The argument K_squared may be a real or a complex-valued scalar.
1339 
1340  @ingroup asm
1341  */
1342  template<typename MAT, typename VECT>
1343  void asm_homogeneous_Helmholtz
1344  (MAT &M, const mesh_im &mim, const mesh_fem &mf_u, const VECT &K_squared,
1345  const mesh_region &rg = mesh_region::all_convexes()) {
1346  typedef typename gmm::linalg_traits<MAT>::value_type T;
1347  asm_Helmholtz_(M, mim, mf_u, 0, K_squared, rg, T());
1348  }
1349 
1350  enum { ASMDIR_BUILDH = 1, ASMDIR_BUILDR = 2, ASMDIR_SIMPLIFY = 4,
1351  ASMDIR_BUILDALL = 7 };
1352 
1353  /**
1354  Assembly of Dirichlet constraints @f$ u(x) = r(x) @f$ in a weak form
1355  @f[ \int_{\Gamma} u(x)v(x) = \int_{\Gamma} r(x)v(x) \forall v@f],
1356  where @f$ v @f$ is in
1357  the space of multipliers corresponding to mf_mult.
1358 
1359  size(r_data) = Q * nb_dof(mf_rh);
1360 
1361  A simplification can be done when the fem for u and r are the same and
1362  when the fem for the multipliers is of same dimension as the one for u.
1363  version = |ASMDIR_BUILDH : build H
1364  |ASMDIR_BUILDR : build R
1365  |ASMDIR_SIMPLIFY : simplify
1366  |ASMDIR_BUILDALL : do everything.
1367 
1368  @ingroup asm
1369  */
1370 
1371  template<typename MAT, typename VECT1, typename VECT2>
1372  void asm_dirichlet_constraints
1373  (MAT &H, VECT1 &R, const mesh_im &mim, const mesh_fem &mf_u,
1374  const mesh_fem &mf_mult, const mesh_fem &mf_r,
1375  const VECT2 &r_data, const mesh_region &region,
1376  int version = ASMDIR_BUILDALL) {
1377  typedef typename gmm::linalg_traits<VECT1>::value_type value_type;
1378  typedef typename gmm::number_traits<value_type>::magnitude_type magn_type;
1379 
1380  if ((version & ASMDIR_SIMPLIFY) &&
1381  (mf_u.is_reduced() || mf_mult.is_reduced() || mf_r.is_reduced())) {
1382  GMM_WARNING1("Sorry, no simplification for reduced fems");
1383  version = (version & (ASMDIR_BUILDR | ASMDIR_BUILDH));
1384  }
1385 
1386  region.from_mesh(mim.linked_mesh()).error_if_not_faces();
1387  GMM_ASSERT1(mf_r.get_qdim() == 1,
1388  "invalid data mesh fem (Qdim=1 required)");
1389  if (version & ASMDIR_BUILDH) {
1390  asm_mass_matrix(H, mim, mf_mult, mf_u, region);
1391  gmm::clean(H, gmm::default_tol(magn_type())
1392  * gmm::mat_maxnorm(H) * magn_type(1000));
1393  }
1394  if (version & ASMDIR_BUILDR)
1395  asm_source_term(R, mim, mf_mult, mf_r, r_data, region);
1396 
1397  // Verifications and simplifications
1398 
1399  pfem pf_u, pf_r, pf_m;
1400  bool warning_msg1 = false, warning_msg2 = false;
1401  dal::bit_vector simplifiable_dofs, nonsimplifiable_dofs;
1402  std::vector<size_type> simplifiable_indices(mf_mult.nb_basic_dof());
1403  std::vector<value_type> simplifiable_values(mf_mult.nb_basic_dof());
1404  std::vector<value_type> v1, v2, v3;
1405 
1406  for (mr_visitor v(region); !v.finished(); v.next()) {
1407  GMM_ASSERT1(v.is_face(), "attempt to impose a dirichlet "
1408  "on the interior of the domain!");
1409  size_type cv = v.cv(); short_type f = v.f();
1410 
1411  GMM_ASSERT1(mf_u.convex_index().is_in(cv) &&
1412  mf_r.convex_index().is_in(cv) &&
1413  mf_mult.convex_index().is_in(cv),
1414  "attempt to impose a dirichlet "
1415  "condition on a convex with no FEM!");
1416  pf_u = mf_u.fem_of_element(cv);
1417  pf_r = mf_r.fem_of_element(cv);
1418  pf_m = mf_mult.fem_of_element(cv);
1419 
1420  if (!pf_m->is_lagrange() && !warning_msg1) {
1421  GMM_WARNING3("Dirichlet condition with non-lagrange multiplier fem. "
1422  "see the documentation about Dirichlet conditions.");
1423  warning_msg1 = true;
1424  }
1425 
1426  if (!(version & ASMDIR_SIMPLIFY)) continue;
1427 
1428  mesh_fem::ind_dof_face_ct pf_u_ct
1429  = mf_u.ind_basic_dof_of_face_of_element(cv, f);
1430  mesh_fem::ind_dof_face_ct pf_r_ct
1431  = mf_r.ind_basic_dof_of_face_of_element(cv, f);
1432  mesh_fem::ind_dof_face_ct pf_m_ct
1433  = mf_mult.ind_basic_dof_of_face_of_element(cv, f);
1434 
1435  size_type pf_u_nbdf = pf_u_ct.size();
1436  size_type pf_m_nbdf = pf_m_ct.size();
1437  size_type pf_u_nbdf_loc = pf_u->structure(cv)->nb_points_of_face(f);
1438  size_type pf_m_nbdf_loc = pf_m->structure(cv)->nb_points_of_face(f);
1439  // size_type pf_r_nbdf_loc = pf_r->structure(cv)->nb_points_of_face(f);
1440 
1441  if (pf_u_nbdf < pf_m_nbdf && !warning_msg2) {
1442  GMM_WARNING2("Dirichlet condition with a too rich multiplier fem. "
1443  "see the documentation about Dirichlet conditions.");
1444  warning_msg2 = true;
1445  }
1446 
1447  if (pf_u != pf_r || pf_u_nbdf != pf_m_nbdf ||
1448  ((pf_u != pf_r) && (pf_u_nbdf_loc != pf_m_nbdf_loc))) {
1449  for (size_type i = 0; i < pf_m_nbdf; ++i)
1450  nonsimplifiable_dofs.add(pf_m_ct[i]);
1451  continue;
1452  }
1453 
1454  for (size_type i = 0; i < pf_m_nbdf; ++i) {
1455  simplifiable_dofs.add(pf_m_ct[i]);
1456  simplifiable_indices[pf_m_ct[i]] = pf_u_ct[i];
1457  }
1458 
1459  if (!(version & ASMDIR_BUILDR)) continue;
1460 
1461  if (pf_u == pf_r) { // simplest simplification.
1462  size_type Qratio = mf_u.get_qdim() / mf_r.get_qdim();
1463  for (size_type i = 0; i < pf_m_nbdf; ++i) {
1464  simplifiable_values[pf_m_ct[i]]
1465  = r_data[pf_r_ct[i/Qratio]*Qratio+(i%Qratio)];
1466  }
1467  }
1468  }
1469 
1470  if (version & ASMDIR_SIMPLIFY) {
1471  if (simplifiable_dofs.card() > 0)
1472  { GMM_TRACE3("Simplification of the Dirichlet condition"); }
1473  else
1474  GMM_TRACE3("Sorry, no simplification of the Dirichlet condition");
1475  if (nonsimplifiable_dofs.card() > 0 && simplifiable_dofs.card() > 0)
1476  GMM_WARNING3("Partial simplification of the Dirichlet condition");
1477 
1478  for (dal::bv_visitor i(simplifiable_dofs); !i.finished(); ++i)
1479  if (!(nonsimplifiable_dofs[i])) {
1480  if (version & ASMDIR_BUILDH) { /* "erase" the row i */
1481  const mesh::ind_cv_ct &cv_ct = mf_mult.convex_to_basic_dof(i);
1482  for (size_type j = 0; j < cv_ct.size(); ++j) {
1483  size_type cv = cv_ct[j];
1484  for (size_type k=0; k < mf_u.nb_basic_dof_of_element(cv); ++k)
1485  H(i, mf_u.ind_basic_dof_of_element(cv)[k]) = value_type(0);
1486  }
1487  H(i, simplifiable_indices[i]) = value_type(1);
1488  }
1489  if (version & ASMDIR_BUILDR) R[i] = simplifiable_values[i];
1490  }
1491  }
1492  }
1493 
1494  template<typename MATRM, typename VECT1, typename VECT2>
1495  void assembling_Dirichlet_condition
1496  (MATRM &RM, VECT1 &B, const getfem::mesh_fem &mf, size_type boundary,
1497  const VECT2 &F) {
1498  // Works only for Lagrange dofs.
1499  size_type Q=mf.get_qdim();
1500  GMM_ASSERT1(!(mf.is_reduced()), "This function is not adapted to "
1501  "reduced finite element methods");
1502  dal::bit_vector nndof = mf.basic_dof_on_region(boundary);
1503  getfem::pfem pf1;
1504  for (dal::bv_visitor cv(mf.convex_index()); !cv.finished(); ++cv) {
1505  pf1 = mf.fem_of_element(cv);
1506  getfem::pdof_description ldof = getfem::lagrange_dof(pf1->dim());
1507  size_type nbd = pf1->nb_dof(cv);
1508  for (size_type i = 0; i < nbd; i++) {
1509  size_type dof1 = mf.ind_basic_dof_of_element(cv)[i*Q];
1510  if (nndof.is_in(dof1) && pf1->dof_types()[i] == ldof) {
1511  // cout << "dof : " << i << endl;
1512  for (size_type j = 0; j < nbd; j++) {
1513  size_type dof2 = mf.ind_basic_dof_of_element(cv)[j*Q];
1514  for (size_type k = 0; k < Q; ++k)
1515  for (size_type l = 0; l < Q; ++l) {
1516  if (!(nndof.is_in(dof2)) &&
1517  getfem::dof_compatibility(pf1->dof_types()[j],
1518  getfem::lagrange_dof(pf1->dim())))
1519  B[dof2+k] -= RM(dof2+k, dof1+l) * F[dof1+l];
1520  RM(dof2+k, dof1+l) = RM(dof1+l, dof2+k) = 0;
1521  }
1522  }
1523  for (size_type k = 0; k < Q; ++k)
1524  { RM(dof1+k, dof1+k) = 1; B[dof1+k] = F[dof1+k]; }
1525  }
1526  }
1527  }
1528  }
1529 
1530  /**
1531  Assembly of generalized Dirichlet constraints h(x)u(x) = r(x),
1532  where h is a QxQ matrix field (Q == mf_u.get_qdim()), outputs a
1533  (under-determined) linear system HU=R.
1534 
1535  size(h_data) = Q^2 * nb_dof(mf_rh);
1536  size(r_data) = Q * nb_dof(mf_rh);
1537 
1538  This function tries hard to make H diagonal or mostly diagonal:
1539  this function is able to "simplify" the dirichlet constraints (see below)
1540  version = |ASMDIR_BUILDH : build H
1541  |ASMDIR_BUILDR : build R
1542  |ASMDIR_SIMPLIFY : simplify
1543  |ASMDIR_BUILDALL : do everything.
1544 
1545  @ingroup asm
1546  */
1547 
1548  template<typename MAT, typename VECT1, typename VECT2, typename VECT3>
1549  void asm_generalized_dirichlet_constraints
1550  (MAT &H, VECT1 &R, const mesh_im &mim, const mesh_fem &mf_u,
1551  const mesh_fem &mf_h, const mesh_fem &mf_r, const VECT2 &h_data,
1552  const VECT3 &r_data, const mesh_region &region,
1553  int version = ASMDIR_BUILDALL) {
1554  pfem pf_u, pf_rh;
1555 
1556  if ((version & ASMDIR_SIMPLIFY) &&
1557  (mf_u.is_reduced() || mf_h.is_reduced() || mf_r.is_reduced())) {
1558  GMM_WARNING1("Sorry, no simplification for reduced fems");
1559  version = (version & ASMDIR_BUILDR);
1560  }
1561 
1562  region.from_mesh(mim.linked_mesh()).error_if_not_faces();
1563  GMM_ASSERT1(mf_h.get_qdim() == 1 && mf_r.get_qdim() == 1,
1564  "invalid data mesh fem (Qdim=1 required)");
1565  if (version & ASMDIR_BUILDH) {
1566  asm_qu_term(H, mim, mf_u, mf_h, h_data, region);
1567  std::vector<size_type> ind(0);
1568  dal::bit_vector bdof = mf_u.basic_dof_on_region(region);
1569  // gmm::clean(H, 1E-15 * gmm::mat_maxnorm(H));
1570  for (size_type i = 0; i < mf_u.nb_dof(); ++i)
1571  if (!(bdof[i])) ind.push_back(i);
1572  gmm::clear(gmm::sub_matrix(H, gmm::sub_index(ind)));
1573  }
1574  if (version & ASMDIR_BUILDR)
1575  asm_source_term(R, mim, mf_u, mf_r, r_data, region);
1576  if (!(version & ASMDIR_SIMPLIFY)) return;
1577 
1578  /* step 2 : simplification of simple dirichlet conditions */
1579  if (&mf_r == &mf_h) {
1580  for (mr_visitor v(region); !v.finished(); v.next()) {
1581  size_type cv = v.cv();
1582  short_type f = v.f();
1583 
1584  GMM_ASSERT1(mf_u.convex_index().is_in(cv) &&
1585  mf_r.convex_index().is_in(cv),
1586  "attempt to impose a dirichlet "
1587  "condition on a convex with no FEM!");
1588 
1589  if (f >= mf_u.linked_mesh().structure_of_convex(cv)->nb_faces())
1590  continue;
1591  pf_u = mf_u.fem_of_element(cv);
1592  pf_rh = mf_r.fem_of_element(cv);
1593  /* don't try anything with vector elements */
1594  if (mf_u.fem_of_element(cv)->target_dim() != 1) continue;
1595  bgeot::pconvex_structure cvs_u = pf_u->structure(cv);
1596  bgeot::pconvex_structure cvs_rh = pf_rh->structure(cv);
1597  for (size_type i = 0; i < cvs_u->nb_points_of_face(f); ++i) {
1598 
1599  size_type Q = mf_u.get_qdim(); // pf_u->target_dim() (==1)
1600 
1601  size_type ind_u = cvs_u->ind_points_of_face(f)[i];
1602  pdof_description tdof_u = pf_u->dof_types()[ind_u];
1603 
1604  for (size_type j = 0; j < cvs_rh->nb_points_of_face(f); ++j) {
1605  size_type ind_rh = cvs_rh->ind_points_of_face(f)[j];
1606  pdof_description tdof_rh = pf_rh->dof_types()[ind_rh];
1607  /*
1608  same kind of dof and same location of dof ?
1609  => then the previous was not useful for this dofs (introducing
1610  a mass matrix which is not diagonal in the constraints matrix)
1611  -> the constraint is simplified:
1612  we replace \int{(H_j.psi_j)*phi_i}=\int{R_j.psi_j} (sum over j)
1613  with H_j*phi_i = R_j
1614  --> Le principe peut être faux : non identique à la projection
1615  L^2 et peut entrer en conccurence avec les autres ddl -> a revoir
1616  */
1617  if (tdof_u == tdof_rh &&
1618  gmm::vect_dist2_sqr((*(pf_u->node_tab(cv)))[ind_u],
1619  (*(pf_rh->node_tab(cv)))[ind_rh])
1620  < 1.0E-14) {
1621  /* the dof might be "duplicated" */
1622  for (size_type q = 0; q < Q; ++q) {
1623  size_type dof_u = mf_u.ind_basic_dof_of_element(cv)[ind_u*Q+q];
1624 
1625  /* "erase" the row */
1626  if (version & ASMDIR_BUILDH)
1627  for (size_type k=0; k < mf_u.nb_basic_dof_of_element(cv); ++k)
1628  H(dof_u, mf_u.ind_basic_dof_of_element(cv)[k]) = 0.0;
1629 
1630  size_type dof_rh = mf_r.ind_basic_dof_of_element(cv)[ind_rh];
1631  /* set the "simplified" row */
1632  if (version & ASMDIR_BUILDH)
1633  for (unsigned jj=0; jj < Q; jj++) {
1634  size_type dof_u2
1635  = mf_u.ind_basic_dof_of_element(cv)[ind_u*Q+jj];
1636  H(dof_u, dof_u2) = h_data[(jj*Q+q) + Q*Q*(dof_rh)];
1637  }
1638  if (version & ASMDIR_BUILDR) R[dof_u] = r_data[dof_rh*Q+q];
1639  }
1640  }
1641  }
1642  }
1643  }
1644  }
1645  }
1646 
1647  /**
1648  Build an orthogonal basis of the kernel of H in NS, gives the
1649  solution of minimal norm of H*U = R in U0 and return the
1650  dimension of the kernel. The function is based on a
1651  Gramm-Schmidt algorithm.
1652 
1653  @ingroup asm
1654  */
1655  template<typename MAT1, typename MAT2, typename VECT1, typename VECT2>
1656  size_type Dirichlet_nullspace(const MAT1 &H, MAT2 &NS,
1657  const VECT1 &R, VECT2 &U0) {
1658 
1659  typedef typename gmm::linalg_traits<MAT1>::value_type T;
1660  typedef typename gmm::number_traits<T>::magnitude_type MAGT;
1661  typedef typename gmm::temporary_vector<MAT1>::vector_type TEMP_VECT;
1662  MAGT tol = gmm::default_tol(MAGT());
1663  MAGT norminfH = gmm::mat_maxnorm(H);
1664  size_type nbd = gmm::mat_ncols(H), nbase = 0, nbr = gmm::mat_nrows(H);
1665  TEMP_VECT aux(nbr), e(nbd), f(nbd);
1666  dal::dynamic_array<TEMP_VECT> base_img;
1667  dal::dynamic_array<TEMP_VECT> base_img_inv;
1668  size_type nb_bimg = 0;
1669  gmm::clear(NS);
1670 
1671  if (!(gmm::is_col_matrix(H)))
1672  GMM_WARNING2("Dirichlet_nullspace inefficient for a row matrix H");
1673  // First, detection of null columns of H, and already orthogonals
1674  // vectors of the image of H.
1675  dal::bit_vector nn;
1676  for (size_type i = 0; i < nbd; ++i) {
1677  gmm::clear(e); e[i] = T(1);
1678  gmm::mult(H, e, aux);
1679  MAGT n = gmm::vect_norm2(aux);
1680 
1681  if (n < norminfH*tol*1000) {
1682  NS(i, nbase++) = T(1); nn[i] = true;
1683  }
1684  else {
1685  bool good = true;
1686  for (size_type j = 0; j < nb_bimg; ++j)
1687  if (gmm::abs(gmm::vect_sp(aux, base_img[j])) > MAGT(0))
1688  { good = false; break; }
1689  if (good) {
1690  gmm::copy(e, f);
1691  gmm::scale(f, T(MAGT(1)/n)); gmm::scale(aux, T(MAGT(1)/n));
1692  base_img_inv[nb_bimg] = TEMP_VECT(nbd);
1693  gmm::copy(f, base_img_inv[nb_bimg]);
1694  gmm::clean(aux, gmm::vect_norminf(aux)*tol);
1695  base_img[nb_bimg] = TEMP_VECT(nbr);
1696  gmm::copy(aux, base_img[nb_bimg++]);
1697  nn[i] = true;
1698  }
1699  }
1700  }
1701  size_type nb_triv_base = nbase;
1702 
1703  for (size_type i = 0; i < nbd; ++i) {
1704  if (!(nn[i])) {
1705  gmm::clear(e); e[i] = T(1); gmm::clear(f); f[i] = T(1);
1706  gmm::mult(H, e, aux);
1707  for (size_type j = 0; j < nb_bimg; ++j) {
1708  T c = gmm::vect_sp(aux, base_img[j]);
1709  // if (gmm::abs(c > 1.0E-6) { // à scaler sur l'ensemble de H ...
1710  if (c != T(0)) {
1711  gmm::add(gmm::scaled(base_img[j], -c), aux);
1712  gmm::add(gmm::scaled(base_img_inv[j], -c), f);
1713  }
1714  }
1715  if (gmm::vect_norm2(aux) < norminfH*tol*MAGT(10000)) {
1716  gmm::copy(f, gmm::mat_col(NS, nbase++));
1717  }
1718  else {
1719  MAGT n = gmm::vect_norm2(aux);
1720  gmm::scale(f, T(MAGT(1)/n)); gmm::scale(aux, T(MAGT(1)/n));
1721  gmm::clean(f, tol*gmm::vect_norminf(f));
1722  gmm::clean(aux, tol*gmm::vect_norminf(aux));
1723  base_img_inv[nb_bimg] = TEMP_VECT(nbd);
1724  gmm::copy(f, base_img_inv[nb_bimg]);
1725  base_img[nb_bimg] = TEMP_VECT(nbr);
1726  gmm::copy(aux, base_img[nb_bimg++]);
1727  }
1728  }
1729  }
1730  // Compute a solution in U0
1731  gmm::clear(U0);
1732  for (size_type i = 0; i < nb_bimg; ++i) {
1733  T c = gmm::vect_sp(base_img[i], R);
1734  gmm::add(gmm::scaled(base_img_inv[i], c), U0);
1735  }
1736  // Orthogonalisation of the basis of the kernel of H.
1737  for (size_type i = nb_triv_base; i < nbase; ++i) {
1738  for (size_type j = nb_triv_base; j < i; ++j) {
1739  T c = gmm::vect_sp(gmm::mat_col(NS,i), gmm::mat_col(NS,j));
1740  if (c != T(0))
1741  gmm::add(gmm::scaled(gmm::mat_col(NS,j), -c), gmm::mat_col(NS,i));
1742  }
1743  gmm::scale(gmm::mat_col(NS,i),
1744  T(1) / gmm::vect_norm2(gmm::mat_col(NS,i)));
1745  }
1746  // projection of U0 on the orthogonal to the kernel.
1747  for (size_type j = nb_triv_base; j < nbase; ++j) {
1748  T c = gmm::vect_sp(gmm::mat_col(NS,j), U0);
1749  if (c != T(0))
1750  gmm::add(gmm::scaled(gmm::mat_col(NS,j), -c), U0);
1751  }
1752  // Test ...
1753  gmm::mult(H, U0, gmm::scaled(R, T(-1)), aux);
1754  if (gmm::vect_norm2(aux) > gmm::vect_norm2(U0)*tol*MAGT(10000))
1755  GMM_WARNING2("Dirichlet condition not well inverted: residu="
1756  << gmm::vect_norm2(aux));
1757 
1758  return nbase;
1759  }
1760 
1761 } /* end of namespace getfem. */
1762 
1763 
1764 #endif /* GETFEM_ASSEMBLING_H__ */
bgeot::mesh_structure::structure_of_convex
pconvex_structure structure_of_convex(size_type ic) const
Return the pconvex_structure of the convex ic.
Definition: bgeot_mesh_structure.h:112
dal::dynamic_array
Dynamic Array.
Definition: dal_basic.h:196
getfem::mesh_fem
Describe a finite element method linked to a mesh.
Definition: getfem_mesh_fem.h:152
getfem::mesh_fem::ind_basic_dof_of_element
virtual ind_dof_ct ind_basic_dof_of_element(size_type cv) const
Give an array of the dof numbers a of convex.
Definition: getfem_mesh_fem.h:454
getfem::mesh_fem::get_qdim
virtual dim_type get_qdim() const
Return the Q dimension.
Definition: getfem_mesh_fem.h:316
getfem::mesh_fem::nb_dof
virtual size_type nb_dof() const
Return the total number of degrees of freedom.
Definition: getfem_mesh_fem.h:566
getfem::mesh_fem::linked_mesh
const mesh & linked_mesh() const
Return a reference to the underlying mesh.
Definition: getfem_mesh_fem.h:283
getfem::mesh_fem::nb_basic_dof
virtual size_type nb_basic_dof() const
Return the total number of basic degrees of freedom (before the optional reduction).
Definition: getfem_mesh_fem.h:560
getfem::mesh_fem::basic_dof_on_region
virtual dal::bit_vector basic_dof_on_region(const mesh_region &b) const
Get a list of basic dof lying on a given mesh_region.
Definition: getfem_mesh_fem.cc:77
getfem::mesh_fem::ind_basic_dof_of_face_of_element
virtual ind_dof_face_ct ind_basic_dof_of_face_of_element(size_type cv, short_type f) const
Give an array of the dof numbers lying of a convex face (all degrees of freedom whose associated base...
Definition: getfem_mesh_fem.h:472
getfem::mesh_fem::fem_of_element
virtual pfem fem_of_element(size_type cv) const
Return the basic fem associated with an element (if no fem is associated, the function will crash!...
Definition: getfem_mesh_fem.h:448
getfem::mesh_fem::convex_index
const dal::bit_vector & convex_index() const
Get the set of convexes where a finite element has been assigned.
Definition: getfem_mesh_fem.h:195
getfem::mesh_fem::nb_basic_dof_of_element
virtual size_type nb_basic_dof_of_element(size_type cv) const
Return the number of degrees of freedom attached to a given convex.
Definition: getfem_mesh_fem.h:498
getfem::mesh_fem::is_reduced
bool is_reduced() const
Return true if a reduction matrix is applied to the dofs.
Definition: getfem_mesh_fem.h:199
getfem::mesh_fem::convex_to_basic_dof
virtual const mesh::ind_cv_ct & convex_to_basic_dof(size_type d) const
Return the list of convexes attached to the specified dof.
Definition: getfem_mesh_fem.cc:267
getfem::mesh_im
Describe an integration method linked to a mesh.
Definition: getfem_mesh_im.h:47
getfem::mesh_im::linked_mesh
const mesh & linked_mesh() const
Give a reference to the linked mesh of type mesh.
Definition: getfem_mesh_im.h:79
getfem::mesh_region::visitor
"iterator" class for regions.
Definition: getfem_mesh_region.h:237
getfem::mesh_region
structure used to hold a set of convexes and/or convex faces.
Definition: getfem_mesh_region.h:55
getfem::mesh_region::from_mesh
const mesh_region & from_mesh(const mesh &m) const
For regions which have been built with just a number 'id', from_mesh(m) sets the current region to 'm...
Definition: getfem_mesh_region.cc:72
getfem::mesh_region::all_convexes
static mesh_region all_convexes()
provide a default value for the mesh_region parameters of assembly procedures etc.
Definition: getfem_mesh_region.h:142
getfem_assembling_tensors.h
Generic assembly implementation.
getfem_generic_assembly.h
A language for generic assembly of pde boundary value problems.
gmm::copy
void copy(const L1 &l1, L2 &l2)
*‍/
Definition: gmm_blas.h:977
gmm::add
void add(const L1 &l1, L2 &l2)
*‍/
Definition: gmm_blas.h:1276
getfem::asm_H2_dist
scalar_type asm_H2_dist(const mesh_im &mim, const mesh_fem &mf1, const VEC1 &U1, const mesh_fem &mf2, const VEC2 &U2, const mesh_region &rg=mesh_region::all_convexes())
Compute the H2 distance between U1 and U2.
Definition: getfem_assembling.h:548
getfem::asm_L2_dist
scalar_type asm_L2_dist(const mesh_im &mim, const mesh_fem &mf1, const VEC1 &U1, const mesh_fem &mf2, const VEC2 &U2, mesh_region rg=mesh_region::all_convexes())
Compute the distance between U1 and U2, defined on two different mesh_fems (but sharing the same mesh...
Definition: getfem_assembling.h:116
getfem::asm_stiffness_matrix_for_homogeneous_linear_elasticity
void asm_stiffness_matrix_for_homogeneous_linear_elasticity(const MAT &M, const mesh_im &mim, const mesh_fem &mf, const VECT &LAMBDA, const VECT &MU, const mesh_region &rg=mesh_region::all_convexes())
Stiffness matrix for linear elasticity, with constant Lamé coefficients.
Definition: getfem_assembling.h:1016
getfem::asm_mass_matrix
void asm_mass_matrix(const MAT &M, const mesh_im &mim, const mesh_fem &mf1, const mesh_region &rg=mesh_region::all_convexes())
generic mass matrix assembly (on the whole mesh or on the specified convex set or boundary)
Definition: getfem_assembling.h:697
getfem::asm_H2_norm
scalar_type asm_H2_norm(const mesh_im &mim, const mesh_fem &mf, const VEC &U, const mesh_region &rg=mesh_region::all_convexes())
compute the H2 norm of U (for C^1 elements).
Definition: getfem_assembling.h:534
getfem::asm_stiffness_matrix_for_homogeneous_laplacian
void asm_stiffness_matrix_for_homogeneous_laplacian(const MAT &M, const mesh_im &mim, const mesh_fem &mf, const mesh_region &rg=mesh_region::all_convexes())
assembly of .
Definition: getfem_assembling.h:1110
getfem::asm_stiffness_matrix_for_laplacian
void asm_stiffness_matrix_for_laplacian(MAT &M, const mesh_im &mim, const mesh_fem &mf, const mesh_fem &mf_data, const VECT &A, const mesh_region &rg=mesh_region::all_convexes())
assembly of , where is scalar.
Definition: getfem_assembling.h:1152
getfem::asm_stiffness_matrix_for_scalar_elliptic
void asm_stiffness_matrix_for_scalar_elliptic(MAT &M, const mesh_im &mim, const mesh_fem &mf, const mesh_fem &mf_data, const VECT &A, const mesh_region &rg=mesh_region::all_convexes())
assembly of , where is a (symmetric positive definite) NxN matrix.
Definition: getfem_assembling.h:1195
getfem::Dirichlet_nullspace
size_type Dirichlet_nullspace(const MAT1 &H, MAT2 &NS, const VECT1 &R, VECT2 &U0)
Build an orthogonal basis of the kernel of H in NS, gives the solution of minimal norm of H*U = R in ...
Definition: getfem_assembling.h:1656
getfem::asm_stiffness_matrix_for_linear_elasticity
void asm_stiffness_matrix_for_linear_elasticity(const MAT &M, const mesh_im &mim, const mesh_fem &mf, const mesh_fem &mf_data, const VECT &LAMBDA, const VECT &MU, const mesh_region &rg=mesh_region::all_convexes())
Stiffness matrix for linear elasticity, with Lamé coefficients.
Definition: getfem_assembling.h:974
getfem::asm_source_term
void asm_source_term(const VECT1 &B, const mesh_im &mim, const mesh_fem &mf, const mesh_fem &mf_data, const VECT2 &F, const mesh_region &rg=mesh_region::all_convexes())
source term (for both volumic sources and boundary (Neumann) sources).
Definition: getfem_assembling.h:877
getfem::asm_mass_matrix_homogeneous_param
void asm_mass_matrix_homogeneous_param(MAT &M, const mesh_im &mim, const mesh_fem &mf_u, const VECT &F, const mesh_region &rg=mesh_region::all_convexes())
generic mass matrix assembly with an additional constant parameter (on the whole mesh or on the speci...
Definition: getfem_assembling.h:822
getfem::asm_L2_norm
scalar_type asm_L2_norm(const mesh_im &mim, const mesh_fem &mf, const VEC &U, const mesh_region &rg=mesh_region::all_convexes())
compute , U might be real or complex
Definition: getfem_assembling.h:56
getfem::asm_homogeneous_normal_source_term
void asm_homogeneous_normal_source_term(VECT1 &B, const mesh_im &mim, const mesh_fem &mf, const VECT2 &F, const mesh_region &rg)
Homogeneous normal source term (for boundary (Neumann) condition).
Definition: getfem_assembling.h:919
getfem::asm_homogeneous_Helmholtz
void asm_homogeneous_Helmholtz(MAT &M, const mesh_im &mim, const mesh_fem &mf_u, const VECT &K_squared, const mesh_region &rg=mesh_region::all_convexes())
assembly of the term , for the helmholtz equation ( , with ).
Definition: getfem_assembling.h:1344
getfem::asm_lumped_mass_matrix_for_first_order_param
void asm_lumped_mass_matrix_for_first_order_param(MAT &M, const mesh_im &mim, const mesh_fem &mf_u, const mesh_fem &mf_data, const VECT &F, const mesh_region &rg=mesh_region::all_convexes())
lumped mass matrix assembly with an additional parameter (on the whole mesh or on the specified bound...
Definition: getfem_assembling.h:866
getfem::asm_H1_norm
scalar_type asm_H1_norm(const mesh_im &mim, const mesh_fem &mf, const VEC &U, const mesh_region &rg=mesh_region::all_convexes())
compute the H1 norm of U.
Definition: getfem_assembling.h:302
getfem::asm_Helmholtz
void asm_Helmholtz(MAT &M, const mesh_im &mim, const mesh_fem &mf_u, const mesh_fem &mf_data, const VECT &K_squared, const mesh_region &rg=mesh_region::all_convexes())
assembly of the term , for the helmholtz equation ( , with ).
Definition: getfem_assembling.h:1274
getfem::asm_H1_semi_dist
scalar_type asm_H1_semi_dist(const mesh_im &mim, const mesh_fem &mf1, const VEC1 &U1, const mesh_fem &mf2, const VEC2 &U2, mesh_region rg=mesh_region::all_convexes())
Compute the H1 semi-distance between U1 and U2, defined on two different mesh_fems (but sharing the s...
Definition: getfem_assembling.h:234
getfem::asm_H1_semi_norm
scalar_type asm_H1_semi_norm(const mesh_im &mim, const mesh_fem &mf, const VEC &U, const mesh_region &rg=mesh_region::all_convexes())
compute , U might be real or complex
Definition: getfem_assembling.h:179
getfem::asm_stiffness_matrix_for_homogeneous_laplacian_componentwise
void asm_stiffness_matrix_for_homogeneous_laplacian_componentwise(const MAT &M, const mesh_im &mim, const mesh_fem &mf, const mesh_region &rg=mesh_region::all_convexes())
assembly of .
Definition: getfem_assembling.h:1140
getfem::asm_stiffness_matrix_for_linear_elasticity_Hooke
void asm_stiffness_matrix_for_linear_elasticity_Hooke(MAT &RM, const mesh_im &mim, const mesh_fem &mf, const mesh_fem &mf_data, const VECT &H, const mesh_region &rg=mesh_region::all_convexes())
Stiffness matrix for linear elasticity, with a general Hooke tensor.
Definition: getfem_assembling.h:1063
getfem::asm_dirichlet_constraints
void asm_dirichlet_constraints(MAT &H, VECT1 &R, const mesh_im &mim, const mesh_fem &mf_u, const mesh_fem &mf_mult, const mesh_fem &mf_r, const VECT2 &r_data, const mesh_region &region, int version=ASMDIR_BUILDALL)
Assembly of Dirichlet constraints in a weak form.
Definition: getfem_assembling.h:1373
getfem::asm_H1_dist
scalar_type asm_H1_dist(const mesh_im &mim, const mesh_fem &mf1, const VEC1 &U1, const mesh_fem &mf2, const VEC2 &U2, mesh_region rg=mesh_region::all_convexes())
Compute the H1 distance between U1 and U2.
Definition: getfem_assembling.h:355
getfem::asm_H2_semi_norm
scalar_type asm_H2_semi_norm(const mesh_im &mim, const mesh_fem &mf, const VEC &U, const mesh_region &rg=mesh_region::all_convexes())
compute , U might be real or complex.
Definition: getfem_assembling.h:422
getfem::asm_normal_source_term
void asm_normal_source_term(VECT1 &B, const mesh_im &mim, const mesh_fem &mf, const mesh_fem &mf_data, const VECT2 &F, const mesh_region &rg)
Normal source term (for boundary (Neumann) condition).
Definition: getfem_assembling.h:905
getfem::asm_stokes_B
void asm_stokes_B(const MAT &B, const mesh_im &mim, const mesh_fem &mf_u, const mesh_fem &mf_p, const mesh_region &rg=mesh_region::all_convexes())
Build the mixed pressure term .
Definition: getfem_assembling.h:1074
getfem::asm_lumped_mass_matrix_for_first_order
void asm_lumped_mass_matrix_for_first_order(const MAT &M, const mesh_im &mim, const mesh_fem &mf1, const mesh_region &rg=mesh_region::all_convexes())
lumped mass matrix assembly (on the whole mesh or on the specified boundary)
Definition: getfem_assembling.h:853
getfem::asm_mass_matrix_param
void asm_mass_matrix_param(const MAT &M, const mesh_im &mim, const mesh_fem &mf1, const mesh_fem &mf2, const mesh_fem &mf_data, const VECT &A, const mesh_region &rg=mesh_region::all_convexes())
generic mass matrix assembly with an additional parameter (on the whole mesh or on the specified boun...
Definition: getfem_assembling.h:765
getfem::asm_generalized_dirichlet_constraints
void asm_generalized_dirichlet_constraints(MAT &H, VECT1 &R, const mesh_im &mim, const mesh_fem &mf_u, const mesh_fem &mf_h, const mesh_fem &mf_r, const VECT2 &h_data, const VECT3 &r_data, const mesh_region &region, int version=ASMDIR_BUILDALL)
Assembly of generalized Dirichlet constraints h(x)u(x) = r(x), where h is a QxQ matrix field (Q == mf...
Definition: getfem_assembling.h:1550
getfem::asm_homogeneous_source_term
void asm_homogeneous_source_term(const VECT1 &B, const mesh_im &mim, const mesh_fem &mf, const VECT2 &F, const mesh_region &rg=mesh_region::all_convexes())
source term (for both volumic sources and boundary (Neumann) sources).
Definition: getfem_assembling.h:893
getfem::asm_qu_term
void asm_qu_term(MAT &M, const mesh_im &mim, const mesh_fem &mf_u, const mesh_fem &mf_d, const VECT &Q, const mesh_region &rg)
assembly of
Definition: getfem_assembling.h:944
getfem::dof_compatibility
bool dof_compatibility(pdof_description, pdof_description)
Says if the two dofs can be identified.
Definition: getfem_fem.cc:619
getfem::lagrange_dof
pdof_description lagrange_dof(dim_type d)
Description of a unique dof of lagrange type (value at the node).
Definition: getfem_fem.cc:391
getfem::pdof_description
dof_description * pdof_description
Type representing a pointer on a dof_description.
Definition: getfem_fem.h:160
getfem::pfem
std::shared_ptr< const getfem::virtual_fem > pfem
type of pointer on a fem description
Definition: getfem_fem.h:244
bgeot::short_type
gmm::uint16_type short_type
used as the common short type integer in the library
Definition: bgeot_config.h:73
bgeot::pconvex_structure
std::shared_ptr< const convex_structure > pconvex_structure
Pointer on a convex structure description.
Definition: bgeot_convex_structure.h:54
bgeot::size_type
size_t size_type
used as the common size type in the library
Definition: bgeot_poly.h:49
getfem
GEneric Tool for Finite Element Methods.
Definition: getfem_accumulated_distro.h:47
getfem::asm_lumped_mass_matrix_for_first_order_from_consistent
void asm_lumped_mass_matrix_for_first_order_from_consistent(const MAT &M)
lumped mass matrix assembly from consistent mass matrix
Definition: getfem_assembling.h:833
getfem::asm_stiffness_matrix_for_homogeneous_scalar_elliptic_componentwise
void asm_stiffness_matrix_for_homogeneous_scalar_elliptic_componentwise(MAT &M, const mesh_im &mim, const mesh_fem &mf, const VECT &A, const mesh_region &rg=mesh_region::all_convexes())
The same but with a constant matrix.
Definition: getfem_assembling.h:1229
getfem::asm_stiffness_matrix_for_scalar_elliptic_componentwise
void asm_stiffness_matrix_for_scalar_elliptic_componentwise(MAT &M, const mesh_im &mim, const mesh_fem &mf, const mesh_fem &mf_data, const VECT &A, const mesh_region &rg=mesh_region::all_convexes())
The same but on each component of mf when mf has a qdim > 1.
Definition: getfem_assembling.h:1217
getfem::asm_stiffness_matrix_for_vector_elliptic
void asm_stiffness_matrix_for_vector_elliptic(MAT &M, const mesh_im &mim, const mesh_fem &mf, const mesh_fem &mf_data, const VECT &A, const mesh_region &rg=mesh_region::all_convexes())
Assembly of , where is a NxNxQxQ (symmetric positive definite) tensor defined on mf_data.
Definition: getfem_assembling.h:1243
getfem::asm_stiffness_matrix_for_laplacian_componentwise
void asm_stiffness_matrix_for_laplacian_componentwise(MAT &M, const mesh_im &mim, const mesh_fem &mf, const mesh_fem &mf_data, const VECT &A, const mesh_region &rg=mesh_region::all_convexes())
The same as getfem::asm_stiffness_matrix_for_laplacian , but on each component of mf when mf has a qd...
Definition: getfem_assembling.h:1165
getfem::asm_stiffness_matrix_for_homogeneous_scalar_elliptic
void asm_stiffness_matrix_for_homogeneous_scalar_elliptic(MAT &M, const mesh_im &mim, const mesh_fem &mf, const VECT &A, const mesh_region &rg=mesh_region::all_convexes())
The same but with a constant matrix.
Definition: getfem_assembling.h:1206
getfem::asm_stiffness_matrix_for_homogeneous_vector_elliptic
void asm_stiffness_matrix_for_homogeneous_vector_elliptic(MAT &M, const mesh_im &mim, const mesh_fem &mf, const VECT &A, const mesh_region &rg=mesh_region::all_convexes())
Assembly of , where is a NxNxQxQ (symmetric positive definite) constant tensor.
Definition: getfem_assembling.h:1257