GetFEM  5.4.3
getfem_fourth_order.h
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4  Copyright (C) 2006-2020 Yves Renard
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30 ===========================================================================*/
31 
32 /**@file getfem_fourth_order.h
33  @author Yves Renard <Yves.Renard@insa-lyon.fr>,
34  Julien Pommier <Julien.Pommier@insa-toulouse.fr>
35  @date January 6, 2006.
36  @brief assembly procedures and bricks for fourth order pdes.
37 */
38 #ifndef GETFEM_FOURTH_ORDER_H__
39 #define GETFEM_FOURTH_ORDER_H__
40 
41 #include "getfem_models.h"
42 #include "getfem_assembling.h"
43 
44 namespace getfem {
45 
46  /* ******************************************************************** */
47  /* Bilaplacian assembly routines. */
48  /* ******************************************************************** */
49 
50  /**
51  assembly of @f$\int_\Omega \Delta u \Delta v@f$.
52  @ingroup asm
53  */
54  template<typename MAT, typename VECT>
55  void asm_stiffness_matrix_for_bilaplacian
56  (const MAT &M, const mesh_im &mim, const mesh_fem &mf,
57  const mesh_fem &mf_data, const VECT &A,
58  const mesh_region &rg = mesh_region::all_convexes()) {
59  generic_assembly assem
60  ("a=data$1(#2);"
61  "M(#1,#1)+=sym(comp(Hess(#1).Hess(#1).Base(#2))(:,i,i,:,j,j,k).a(k))");
62  assem.push_mi(mim);
63  assem.push_mf(mf);
64  assem.push_mf(mf_data);
65  assem.push_data(A);
66  assem.push_mat(const_cast<MAT &>(M));
67  assem.assembly(rg);
68  }
69 
70  template<typename MAT, typename VECT>
71  void asm_stiffness_matrix_for_homogeneous_bilaplacian
72  (const MAT &M, const mesh_im &mim, const mesh_fem &mf,
73  const VECT &A, const mesh_region &rg = mesh_region::all_convexes()) {
74  generic_assembly assem
75  ("a=data$1(1);"
76  "M(#1,#1)+=sym(comp(Hess(#1).Hess(#1))(:,i,i,:,j,j).a(1))");
77  assem.push_mi(mim);
78  assem.push_mf(mf);
79  assem.push_data(A);
80  assem.push_mat(const_cast<MAT &>(M));
81  assem.assembly(rg);
82  }
83 
84 
85  template<typename MAT, typename VECT>
86  void asm_stiffness_matrix_for_bilaplacian_KL
87  (const MAT &M, const mesh_im &mim, const mesh_fem &mf,
88  const mesh_fem &mf_data, const VECT &D_, const VECT &nu_,
89  const mesh_region &rg = mesh_region::all_convexes()) {
90  generic_assembly assem
91  ("d=data$1(#2); n=data$2(#2);"
92  "t=comp(Hess(#1).Hess(#1).Base(#2).Base(#2));"
93  "M(#1,#1)+=sym(t(:,i,j,:,i,j,k,l).d(k)-t(:,i,j,:,i,j,k,l).d(k).n(l)"
94  "+t(:,i,i,:,j,j,k,l).d(k).n(l))");
95  assem.push_mi(mim);
96  assem.push_mf(mf);
97  assem.push_mf(mf_data);
98  assem.push_data(D_);
99  assem.push_data(nu_);
100  assem.push_mat(const_cast<MAT &>(M));
101  assem.assembly(rg);
102  }
103 
104  template<typename MAT, typename VECT>
105  void asm_stiffness_matrix_for_homogeneous_bilaplacian_KL
106  (const MAT &M, const mesh_im &mim, const mesh_fem &mf,
107  const VECT &D_, const VECT &nu_,
108  const mesh_region &rg = mesh_region::all_convexes()) {
109  generic_assembly assem
110  ("d=data$1(1); n=data$2(1);"
111  "t=comp(Hess(#1).Hess(#1));"
112  "M(#1,#1)+=sym(t(:,i,j,:,i,j).d(1)-t(:,i,j,:,i,j).d(1).n(1)"
113  "+t(:,i,i,:,j,j).d(1).n(1))");
114  assem.push_mi(mim);
115  assem.push_mf(mf);
116  assem.push_data(D_);
117  assem.push_data(nu_);
118  assem.push_mat(const_cast<MAT &>(M));
119  assem.assembly(rg);
120  }
121 
122  /* ******************************************************************** */
123  /* Bilaplacian bricks. */
124  /* ******************************************************************** */
125 
126 
127  /** Adds a bilaplacian brick on the variable
128  `varname` and on the mesh region `region`.
129  This represent a term :math:`\Delta(D \Delta u)`.
130  where :math:`D(x)` is a coefficient determined by `dataname` which
131  could be constant or described on a f.e.m. The corresponding weak form
132  is :math:`\int D(x)\Delta u(x) \Delta v(x) dx`.
133  */
134  size_type add_bilaplacian_brick
135  (model &md, const mesh_im &mim, const std::string &varname,
136  const std::string &dataname, size_type region = size_type(-1));
137 
138  /** Adds a bilaplacian brick on the variable
139  `varname` and on the mesh region `region`.
140  This represent a term :math:`\Delta(D \Delta u)` where :math:`D(x)`
141  is a the flexion modulus determined by `dataname1`. The term is
142  integrated by part following a Kirchhoff-Love plate model
143  with `dataname2` the poisson ratio.
144  */
145  size_type add_bilaplacian_brick_KL
146  (model &md, const mesh_im &mim, const std::string &varname,
147  const std::string &dataname1, const std::string &dataname2,
148  size_type region = size_type(-1));
149 
150 
151  /* ******************************************************************** */
152  /* Normale derivative source term assembly routines. */
153  /* ******************************************************************** */
154 
155  /**
156  assembly of @f$\int_\Gamma{\partial_n u f}@f$.
157  @ingroup asm
158  */
159  template<typename VECT1, typename VECT2>
160  void asm_normal_derivative_source_term
161  (VECT1 &B, const mesh_im &mim, const mesh_fem &mf, const mesh_fem &mf_data,
162  const VECT2 &F, const mesh_region &rg) {
163  GMM_ASSERT1(mf_data.get_qdim() == 1,
164  "invalid data mesh fem (Qdim=1 required)");
165 
166  size_type Q = gmm::vect_size(F) / mf_data.nb_dof();
167 
168  // const char *s;
169  // if (mf.get_qdim() == 1 && Q == 1)
170  // s = "F=data(#2);"
171  // "V(#1)+=comp(Grad(#1).Normal().Base(#2))(:,i,i,j).F(j);";
172  // else if (mf.get_qdim() == 1 && Q == gmm::sqr(mf.linked_mesh().dim()))
173  // s = "F=data(mdim(#1),mdim(#1),#2);"
174  // "V(#1)+=comp(Grad(#1).Normal().Normal().Normal().Base(#2))"
175  // "(:,i,i,k,l,j).F(k,l,j);";
176  // else if (mf.get_qdim() > size_type(1) && Q == mf.get_qdim())
177  // s = "F=data(qdim(#1),#2);"
178  // "V(#1)+=comp(vGrad(#1).Normal().Base(#2))(:,i,k,k,j).F(i,j);";
179  // else if (mf.get_qdim() > size_type(1) &&
180  // Q == size_type(mf.get_qdim()*gmm::sqr(mf.linked_mesh().dim())))
181  // s = "F=data(qdim(#1),mdim(#1),mdim(#1),#2);"
182  // "V(#1)+=comp(vGrad(#1).Normal().Normal().Normal().Base(#2))"
183  // "(:,i,k,k,l,m,j).F(i,l,m,j);";
184  // else
185  // GMM_ASSERT1(false, "invalid rhs vector");
186  // asm_real_or_complex_1_param(B, mim, mf, mf_data, F, rg, s);
187 
188  const char *s;
189  if (mf.get_qdim() == 1 && Q == 1)
190  s = "Grad_Test_u.(A*Normal)";
191  else if (mf.get_qdim() == 1 && Q == gmm::sqr(mf.linked_mesh().dim()))
192  s = "Grad_Test_u.(((Reshape(A,meshdim,meshdim)*Normal).Normal)*Normal)";
193  else if (mf.get_qdim() > size_type(1) && Q == mf.get_qdim())
194  s = "((Grad_Test_u')*A).Normal";
195  else if (mf.get_qdim() > size_type(1) &&
196  Q == size_type(mf.get_qdim()*gmm::sqr(mf.linked_mesh().dim())))
197  s = "((((Grad_Test_u').Reshape(A,qdim(u),meshdim,meshdim)).Normal).Normal).Normal";
198  else
199  GMM_ASSERT1(false, "invalid rhs vector");
200  asm_real_or_complex_1_param_vec(B, mim, mf, &mf_data, F, rg, s);
201  }
202 
203  template<typename VECT1, typename VECT2>
204  void asm_homogeneous_normal_derivative_source_term
205  (VECT1 &B, const mesh_im &mim, const mesh_fem &mf,
206  const VECT2 &F, const mesh_region &rg) {
207 
208  size_type Q = gmm::vect_size(F);
209 
210  // const char *s;
211  // if (mf.get_qdim() == 1 && Q == 1)
212  // s = "F=data(1);"
213  // "V(#1)+=comp(Grad(#1).Normal())(:,i,i).F(1);";
214  // else if (mf.get_qdim() == 1 && Q == gmm::sqr(mf.linked_mesh().dim()))
215  // s = "F=data(mdim(#1),mdim(#1));"
216  // "V(#1)+=comp(Grad(#1).Normal().Normal().Normal())"
217  // "(:,i,i,l,j).F(l,j);";
218  // else if (mf.get_qdim() > size_type(1) && Q == mf.get_qdim())
219  // s = "F=data(qdim(#1));"
220  // "V(#1)+=comp(vGrad(#1).Normal())(:,i,k,k).F(i);";
221  // else if (mf.get_qdim() > size_type(1) &&
222  // Q == size_type(mf.get_qdim()*gmm::sqr(mf.linked_mesh().dim())))
223  // s = "F=data(qdim(#1),mdim(#1),mdim(#1));"
224  // "V(#1)+=comp(vGrad(#1).Normal().Normal().Normal())"
225  // "(:,i,k,k,l,m).F(i,l,m);";
226  // else
227  // GMM_ASSERT1(false, "invalid rhs vector");
228  // asm_real_or_complex_1_param(B, mim, mf, mf, F, rg, s);
229 
230  const char *s;
231  if (mf.get_qdim() == 1 && Q == 1)
232  s = "Test_Grad_u.(A*Normal)";
233  else if (mf.get_qdim() == 1 && Q == gmm::sqr(mf.linked_mesh().dim()))
234  s = "Test_Grad_u.(((Reshape(A,meshdim,meshdim)*Normal).Normal)*Normal)";
235  else if (mf.get_qdim() > size_type(1) && Q == mf.get_qdim())
236  s = "((Test_Grad_u')*A).Normal";
237  else if (mf.get_qdim() > size_type(1) &&
238  Q == size_type(mf.get_qdim()*gmm::sqr(mf.linked_mesh().dim())))
239  s = "((((Test_Grad_u').Reshape(A,qdim(u),meshdim,meshdim)).Normal).Normal).Normal";
240  else
241  GMM_ASSERT1(false, "invalid rhs vector");
242  asm_real_or_complex_1_param_vec(B, mim, mf, 0, F, rg, s);
243  }
244 
245 
246  /* ******************************************************************** */
247  /* Normale derivative source term brick. */
248  /* ******************************************************************** */
249 
250 
251  /** Adds a normal derivative source term brick
252  :math:`F = \int b.\partial_n v` on the variable `varname` and the
253  mesh region `region`.
254 
255  Update the right hand side of the linear system.
256  `dataname` represents `b` and `varname` represents `v`.
257  */
258  size_type add_normal_derivative_source_term_brick
259  (model &md, const mesh_im &mim, const std::string &varname,
260  const std::string &dataname, size_type region);
261 
262 
263  /* ******************************************************************** */
264  /* Special boundary condition for Kirchhoff-Love model. */
265  /* ******************************************************************** */
266 
267  /*
268  assembly of the special boundary condition for Kirchhoff-Love model.
269  @ingroup asm
270  */
271  template<typename VECT1, typename VECT2>
272  void asm_neumann_KL_term
273  (VECT1 &B, const mesh_im &mim, const mesh_fem &mf, const mesh_fem &mf_data,
274  const VECT2 &M, const VECT2 &divM, const mesh_region &rg) {
275  GMM_ASSERT1(mf_data.get_qdim() == 1,
276  "invalid data mesh fem (Qdim=1 required)");
277 
278  generic_assembly assem
279  ("MM=data$1(mdim(#1),mdim(#1),#2);"
280  "divM=data$2(mdim(#1),#2);"
281  "V(#1)+=comp(Base(#1).Normal().Base(#2))(:,i,j).divM(i,j);"
282  "V(#1)+=comp(Grad(#1).Normal().Base(#2))(:,i,j,k).MM(i,j,k)*(-1);"
283  "V(#1)+=comp(Grad(#1).Normal().Normal().Normal().Base(#2))(:,i,i,j,k,l).MM(j,k,l);");
284 
285  assem.push_mi(mim);
286  assem.push_mf(mf);
287  assem.push_mf(mf_data);
288  assem.push_data(M);
289  assem.push_data(divM);
290  assem.push_vec(B);
291  assem.assembly(rg);
292  }
293 
294  template<typename VECT1, typename VECT2>
295  void asm_neumann_KL_homogeneous_term
296  (VECT1 &B, const mesh_im &mim, const mesh_fem &mf,
297  const VECT2 &M, const VECT2 &divM, const mesh_region &rg) {
298 
299  generic_assembly assem
300  ("MM=data$1(mdim(#1),mdim(#1));"
301  "divM=data$2(mdim(#1));"
302  "V(#1)+=comp(Base(#1).Normal())(:,i).divM(i);"
303  "V(#1)+=comp(Grad(#1).Normal())(:,i,j).MM(i,j)*(-1);"
304  "V(#1)+=comp(Grad(#1).Normal().Normal().Normal())(:,i,i,j,k).MM(j,k);");
305 
306  assem.push_mi(mim);
307  assem.push_mf(mf);
308  assem.push_data(M);
309  assem.push_data(divM);
310  assem.push_vec(B);
311  assem.assembly(rg);
312  }
313 
314  /* ******************************************************************** */
315  /* Kirchhoff Love Neumann term brick. */
316  /* ******************************************************************** */
317 
318 
319  /** Adds a Neumann term brick for Kirchhoff-Love model
320  on the variable `varname` and the mesh region `region`.
321  `dataname1` represents the bending moment tensor and `dataname2`
322  its divergence.
323  */
324  size_type add_Kirchhoff_Love_Neumann_term_brick
325  (model &md, const mesh_im &mim, const std::string &varname,
326  const std::string &dataname1, const std::string &dataname2,
327  size_type region);
328 
329 
330  /* ******************************************************************** */
331  /* Normal derivative Dirichlet assembly routines. */
332  /* ******************************************************************** */
333 
334  /**
335  Assembly of normal derivative Dirichlet constraints
336  @f$ \partial_n u(x) = r(x) @f$ in a weak form
337  @f[ \int_{\Gamma} \partial_n u(x)v(x)=\int_{\Gamma} r(x)v(x) \forall v@f],
338  where @f$ v @f$ is in
339  the space of multipliers corresponding to mf_mult.
340 
341  size(r_data) = Q * nb_dof(mf_rh);
342 
343  version = |ASMDIR_BUILDH : build H
344  |ASMDIR_BUILDR : build R
345  |ASMDIR_BUILDALL : do everything.
346 
347  @ingroup asm
348  */
349 
350  template<typename MAT, typename VECT1, typename VECT2>
351  void asm_normal_derivative_dirichlet_constraints
352  (MAT &H, VECT1 &R, const mesh_im &mim, const mesh_fem &mf_u,
353  const mesh_fem &mf_mult, const mesh_fem &mf_r,
354  const VECT2 &r_data, const mesh_region &rg, bool R_must_be_derivated,
355  int version) {
356  typedef typename gmm::linalg_traits<VECT1>::value_type value_type;
357  typedef typename gmm::number_traits<value_type>::magnitude_type magn_type;
358 
359  rg.from_mesh(mim.linked_mesh()).error_if_not_faces();
360 
361  if (version & ASMDIR_BUILDH) {
362  const char *s;
363  if (mf_u.get_qdim() == 1 && mf_mult.get_qdim() == 1)
364  s = "M(#1,#2)+=comp(Base(#1).Grad(#2).Normal())(:,:,i,i)";
365  else
366  s = "M(#1,#2)+=comp(vBase(#1).vGrad(#2).Normal())(:,i,:,i,j,j);";
367 
368  generic_assembly assem(s);
369  assem.push_mi(mim);
370  assem.push_mf(mf_mult);
371  assem.push_mf(mf_u);
372  assem.push_mat(H);
373  assem.assembly(rg);
374  gmm::clean(H, gmm::default_tol(magn_type())
375  * gmm::mat_maxnorm(H) * magn_type(1000));
376  }
377  if (version & ASMDIR_BUILDR) {
378  GMM_ASSERT1(mf_r.get_qdim() == 1,
379  "invalid data mesh fem (Qdim=1 required)");
380  if (!R_must_be_derivated) {
381  asm_normal_source_term(R, mim, mf_mult, mf_r, r_data, rg);
382  } else {
383  asm_real_or_complex_1_param_vec(R, mim, mf_mult, &mf_r, r_data, rg,
384  "(Grad_A.Normal)*Test_u");
385  // asm_real_or_complex_1_param
386  // (R, mim, mf_mult, mf_r, r_data, rg,
387  // "R=data(#2); V(#1)+=comp(Base(#1).Grad(#2).Normal())(:,i,j,j).R(i)");
388  }
389  }
390  }
391 
392  /* ******************************************************************** */
393  /* Normal derivative Dirichlet condition bricks. */
394  /* ******************************************************************** */
395 
396  /** Adds a Dirichlet condition on the normal derivative of the variable
397  `varname` and on the mesh region `region` (which should be a boundary).
398  The general form is
399  :math:`\int \partial_n u(x)v(x) = \int r(x)v(x) \forall v`
400  where :math:`r(x)` is
401  the right hand side for the Dirichlet condition (0 for
402  homogeneous conditions) and :math:`v` is in a space of multipliers
403  defined by the variable `multname` on the part of boundary determined
404  by `region`. `dataname` is an optional parameter which represents
405  the right hand side of the Dirichlet condition.
406  If `R_must_be_derivated` is set to `true` then the normal
407  derivative of `dataname` is considered.
408  */
409  size_type add_normal_derivative_Dirichlet_condition_with_multipliers
410  (model &md, const mesh_im &mim, const std::string &varname,
411  const std::string &multname, size_type region,
412  const std::string &dataname = std::string(),
413  bool R_must_be_derivated = false);
414 
415 
416  /** Adds a Dirichlet condition on the normal derivative of the variable
417  `varname` and on the mesh region `region` (which should be a boundary).
418  The general form is
419  :math:`\int \partial_n u(x)v(x) = \int r(x)v(x) \forall v`
420  where :math:`r(x)` is
421  the right hand side for the Dirichlet condition (0 for
422  homogeneous conditions) and :math:`v` is in a space of multipliers
423  defined by the trace of mf_mult on the part of boundary determined
424  by `region`. `dataname` is an optional parameter which represents
425  the right hand side of the Dirichlet condition.
426  If `R_must_be_derivated` is set to `true` then the normal
427  derivative of `dataname` is considered.
428  */
429  size_type add_normal_derivative_Dirichlet_condition_with_multipliers
430  (model &md, const mesh_im &mim, const std::string &varname,
431  const mesh_fem &mf_mult, size_type region,
432  const std::string &dataname = std::string(),
433  bool R_must_be_derivated = false);
434 
435  /** Adds a Dirichlet condition on the normal derivative of the variable
436  `varname` and on the mesh region `region` (which should be a boundary).
437  The general form is
438  :math:`\int \partial_n u(x)v(x) = \int r(x)v(x) \forall v`
439  where :math:`r(x)` is
440  the right hand side for the Dirichlet condition (0 for
441  homogeneous conditions) and :math:`v` is in a space of multipliers
442  defined by the trace of a Lagranfe finite element method of degree
443  `degree` and on the boundary determined
444  by `region`. `dataname` is an optional parameter which represents
445  the right hand side of the Dirichlet condition.
446  If `R_must_be_derivated` is set to `true` then the normal
447  derivative of `dataname` is considered.
448  */
449  size_type add_normal_derivative_Dirichlet_condition_with_multipliers
450  (model &md, const mesh_im &mim, const std::string &varname,
451  dim_type degree, size_type region,
452  const std::string &dataname = std::string(),
453  bool R_must_be_derivated = false);
454 
455  /** Adds a Dirichlet condition on the normal derivative of the variable
456  `varname` and on the mesh region `region` (which should be a boundary).
457  The general form is
458  :math:`\int \partial_n u(x)v(x) = \int r(x)v(x) \forall v`
459  where :math:`r(x)` is
460  the right hand side for the Dirichlet condition (0 for
461  homogeneous conditions). For this brick the condition is enforced with
462  a penalisation with a penanalization parameter `penalization_coeff` on
463  the boundary determined by `region`.
464  `dataname` is an optional parameter which represents
465  the right hand side of the Dirichlet condition.
466  If `R_must_be_derivated` is set to `true` then the normal
467  derivative of `dataname` is considered.
468  Note that is is possible to change the penalization coefficient
469  using the function `getfem::change_penalization_coeff` of the standard
470  Dirichlet condition.
471  */
472  size_type add_normal_derivative_Dirichlet_condition_with_penalization
473  (model &md, const mesh_im &mim, const std::string &varname,
474  scalar_type penalisation_coeff, size_type region,
475  const std::string &dataname = std::string(),
476  bool R_must_be_derivated = false);
477 
478 
479 
480 
481 
482 
483 } /* end of namespace getfem. */
484 
485 
486 #endif /* GETFEM_FOURTH_ORDER_H__ */
getfem::generic_assembly
Generic assembly of vectors, matrices.
Definition: getfem_assembling_tensors.h:607
getfem::generic_assembly::push_data
void push_data(const VEC &d)
Add a new data (dense array)
Definition: getfem_assembling_tensors.h:659
getfem::generic_assembly::push_mat
void push_mat(const MAT &m)
Add a new output matrix (fake const version..)
Definition: getfem_assembling_tensors.h:671
getfem::generic_assembly::assembly
void assembly(const mesh_region &region=mesh_region::all_convexes())
do the assembly on the specified region (boundary or set of convexes)
Definition: getfem_assembling_tensors.cc:1821
getfem::generic_assembly::push_mi
void push_mi(const mesh_im &im_)
Add a new mesh_im.
Definition: getfem_assembling_tensors.h:652
getfem::generic_assembly::push_mf
void push_mf(const mesh_fem &mf_)
Add a new mesh_fem.
Definition: getfem_assembling_tensors.h:650
getfem::mesh_fem
Describe a finite element method linked to a mesh.
Definition: getfem_mesh_fem.h:152
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_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
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.h
Miscelleanous assembly routines for common terms. Use the low-level generic assembly....
getfem_models.h
Model representation in Getfem.
getfem::asm_stiffness_matrix_for_bilaplacian
void asm_stiffness_matrix_for_bilaplacian(const 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 .
Definition: getfem_fourth_order.h:56
getfem::asm_normal_derivative_dirichlet_constraints
void asm_normal_derivative_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 &rg, bool R_must_be_derivated, int version)
Assembly of normal derivative Dirichlet constraints in a weak form.
Definition: getfem_fourth_order.h:352
getfem::asm_normal_derivative_source_term
void asm_normal_derivative_source_term(VECT1 &B, const mesh_im &mim, const mesh_fem &mf, const mesh_fem &mf_data, const VECT2 &F, const mesh_region &rg)
assembly of .
Definition: getfem_fourth_order.h:161
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
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::add_bilaplacian_brick
size_type add_bilaplacian_brick(model &md, const mesh_im &mim, const std::string &varname, const std::string &dataname, size_type region=size_type(-1))
Adds a bilaplacian brick on the variable varname and on the mesh region region.
Definition: getfem_fourth_order.cc:120
getfem::add_bilaplacian_brick_KL
size_type add_bilaplacian_brick_KL(model &md, const mesh_im &mim, const std::string &varname, const std::string &dataname1, const std::string &dataname2, size_type region=size_type(-1))
Adds a bilaplacian brick on the variable varname and on the mesh region region.
Definition: getfem_fourth_order.cc:132
getfem::add_normal_derivative_Dirichlet_condition_with_multipliers
size_type add_normal_derivative_Dirichlet_condition_with_multipliers(model &md, const mesh_im &mim, const std::string &varname, const std::string &multname, size_type region, const std::string &dataname=std::string(), bool R_must_be_derivated=false)
Adds a Dirichlet condition on the normal derivative of the variable varname and on the mesh region re...
Definition: getfem_fourth_order.cc:620
getfem::add_normal_derivative_source_term_brick
size_type add_normal_derivative_source_term_brick(model &md, const mesh_im &mim, const std::string &varname, const std::string &dataname, size_type region)
Adds a normal derivative source term brick :math:F = \int b.
Definition: getfem_fourth_order.cc:250
getfem::add_Kirchhoff_Love_Neumann_term_brick
size_type add_Kirchhoff_Love_Neumann_term_brick(model &md, const mesh_im &mim, const std::string &varname, const std::string &dataname1, const std::string &dataname2, size_type region)
Adds a Neumann term brick for Kirchhoff-Love model on the variable varname and the mesh region region...
Definition: getfem_fourth_order.cc:333
getfem::add_normal_derivative_Dirichlet_condition_with_penalization
size_type add_normal_derivative_Dirichlet_condition_with_penalization(model &md, const mesh_im &mim, const std::string &varname, scalar_type penalisation_coeff, size_type region, const std::string &dataname=std::string(), bool R_must_be_derivated=false)
Adds a Dirichlet condition on the normal derivative of the variable varname and on the mesh region re...
Definition: getfem_fourth_order.cc:656