MFEM  v4.5.2 Finite element discretization library
ex31p.cpp
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1 // MFEM Example 31 - Parallel Version
2 //
3 // Compile with: make ex31p
4 //
5 // Sample runs: mpirun -np 4 ex31p -m ../data/hexagon.mesh -o 2
6 // mpirun -np 4 ex31p -m ../data/star.mesh
7 // mpirun -np 4 ex31p -m ../data/square-disc.mesh -o 2
8 // mpirun -np 4 ex31p -m ../data/fichera.mesh -o 3 -rs 1 -rp 0
9 // mpirun -np 4 ex31p -m ../data/square-disc-nurbs.mesh -o 3
10 // mpirun -np 4 ex31p -m ../data/amr-quad.mesh -o 2 -rs 1
11 // mpirun -np 4 ex31p -m ../data/amr-hex.mesh -rs 1
12 //
13 // Description: This example code solves a simple electromagnetic diffusion
14 // problem corresponding to the second order definite Maxwell
15 // equation curl curl E + sigma E = f with boundary condition
16 // E x n = <given tangential field>. In this example sigma is an
17 // anisotropic 3x3 tensor. Here, we use a given exact solution E
18 // and compute the corresponding r.h.s. f. We discretize with
19 // Nedelec finite elements in 1D, 2D, or 3D.
20 //
21 // The example demonstrates the use of restricted H(curl) finite
22 // element spaces with the curl-curl and the (vector finite
23 // element) mass bilinear form, as well as the computation of
24 // discretization error when the exact solution is known. These
25 // restricted spaces allow the solution of 1D or 2D
26 // electromagnetic problems which involve 3D field vectors. Such
27 // problems arise in plasma physics and crystallography.
28 //
29 // We recommend viewing example 3 before viewing this example.
30
31 #include "mfem.hpp"
32 #include <fstream>
33 #include <iostream>
34
35 using namespace std;
36 using namespace mfem;
37
38 // Exact solution, E, and r.h.s., f. See below for implementation.
39 void E_exact(const Vector &, Vector &);
40 void CurlE_exact(const Vector &, Vector &);
41 void f_exact(const Vector &, Vector &);
42 double freq = 1.0, kappa;
43 int dim;
44
45 int main(int argc, char *argv[])
46 {
47  // 1. Initialize MPI.
48  Mpi::Init(argc, argv);
49  int num_procs = Mpi::WorldSize();
50  int myid = Mpi::WorldRank();
51  Hypre::Init();
52
53  // 2. Parse command-line options.
54  const char *mesh_file = "../data/inline-quad.mesh";
55  int ser_ref_levels = 2;
56  int par_ref_levels = 1;
57  int order = 1;
58  bool use_ams = true;
59  bool visualization = 1;
60
61  OptionsParser args(argc, argv);
63  "Mesh file to use.");
65  "Number of times to refine the mesh uniformly in serial.");
67  "Number of times to refine the mesh uniformly in parallel.");
69  "Finite element order (polynomial degree).");
70  args.AddOption(&freq, "-f", "--frequency", "Set the frequency for the exact"
71  " solution.");
73  "--superlu", "Use AMS or SuperLU solver.");
75  "--no-visualization",
76  "Enable or disable GLVis visualization.");
77  args.ParseCheck();
78
79  kappa = freq * M_PI;
80
81  // 3. Read the (serial) mesh from the given mesh file on all processors. We
82  // can handle triangular, quadrilateral, tetrahedral, hexahedral, surface
83  // and volume meshes with the same code.
84  Mesh *mesh = new Mesh(mesh_file, 1, 1);
85  dim = mesh->Dimension();
86
87  // 4. Refine the serial mesh on all processors to increase the resolution. In
88  // this example we do 'ref_levels' of uniform refinement (2 by default, or
89  // specified on the command line with -rs).
90  for (int lev = 0; lev < ser_ref_levels; lev++)
91  {
92  mesh->UniformRefinement();
93  }
94
95  // 5. Define a parallel mesh by a partitioning of the serial mesh. Refine
96  // this mesh further in parallel to increase the resolution (1 time by
97  // default, or specified on the command line with -rp). Once the parallel
98  // mesh is defined, the serial mesh can be deleted.
99  ParMesh pmesh(MPI_COMM_WORLD, *mesh);
100  delete mesh;
101  for (int lev = 0; lev < par_ref_levels; lev++)
102  {
103  pmesh.UniformRefinement();
104  }
105
106  // 6. Define a parallel finite element space on the parallel mesh. Here we
107  // use the Nedelec finite elements of the specified order.
108  FiniteElementCollection *fec = NULL;
109  if (dim == 1)
110  {
111  fec = new ND_R1D_FECollection(order, dim);
112  }
113  else if (dim == 2)
114  {
115  fec = new ND_R2D_FECollection(order, dim);
116  }
117  else
118  {
119  fec = new ND_FECollection(order, dim);
120  }
121  ParFiniteElementSpace fespace(&pmesh, fec);
122  HYPRE_Int size = fespace.GlobalTrueVSize();
123  if (Mpi::Root()) { cout << "Number of H(Curl) unknowns: " << size << endl; }
124
125  // 7. Determine the list of true (i.e. parallel conforming) essential
126  // boundary dofs. In this example, the boundary conditions are defined
127  // by marking all the boundary attributes from the mesh as essential
128  // (Dirichlet) and converting them to a list of true dofs.
129  Array<int> ess_tdof_list;
130  if (pmesh.bdr_attributes.Size())
131  {
132  Array<int> ess_bdr(pmesh.bdr_attributes.Max());
133  ess_bdr = 1;
134  fespace.GetEssentialTrueDofs(ess_bdr, ess_tdof_list);
135  }
136
137  // 8. Set up the parallel linear form b(.) which corresponds to the
138  // right-hand side of the FEM linear system, which in this case is
139  // (f,phi_i) where f is given by the function f_exact and phi_i are the
140  // basis functions in the finite element fespace.
142  ParLinearForm b(&fespace);
144  b.Assemble();
145
146  // 9. Define the solution vector x as a parallel finite element grid function
147  // corresponding to fespace. Initialize x by projecting the exact
148  // solution. Note that only values from the boundary edges will be used
149  // when eliminating the non-homogeneous boundary condition to modify the
150  // r.h.s. vector b.
151  ParGridFunction sol(&fespace);
154  sol.ProjectCoefficient(E);
155
156  // 10. Set up the parallel bilinear form corresponding to the EM diffusion
157  // operator curl muinv curl + sigma I, by adding the curl-curl and the
158  // mass domain integrators.
159  DenseMatrix sigmaMat(3);
160  sigmaMat(0,0) = 2.0; sigmaMat(1,1) = 2.0; sigmaMat(2,2) = 2.0;
161  sigmaMat(0,2) = 0.0; sigmaMat(2,0) = 0.0;
162  sigmaMat(0,1) = M_SQRT1_2; sigmaMat(1,0) = M_SQRT1_2; // 1/sqrt(2) in cmath
163  sigmaMat(1,2) = M_SQRT1_2; sigmaMat(2,1) = M_SQRT1_2;
164
165  ConstantCoefficient muinv(1.0);
167  ParBilinearForm a(&fespace);
170
171  // 11. Assemble the parallel bilinear form and the corresponding linear
172  // system, applying any necessary transformations such as: parallel
173  // assembly, eliminating boundary conditions, applying conforming
174  // constraints for non-conforming AMR, etc.
175  a.Assemble();
176
177  OperatorPtr A;
178  Vector B, X;
179
180  a.FormLinearSystem(ess_tdof_list, sol, b, A, X, B);
181
182  // 12. Solve the system AX=B using PCG with the AMS preconditioner from hypre
183  if (use_ams)
184  {
185  if (Mpi::Root())
186  {
187  cout << "Size of linear system: "
188  << A.As<HypreParMatrix>()->GetGlobalNumRows() << endl;
189  }
190
191  HypreAMS ams(*A.As<HypreParMatrix>(), &fespace);
192
193  HyprePCG pcg(*A.As<HypreParMatrix>());
194  pcg.SetTol(1e-12);
195  pcg.SetMaxIter(1000);
196  pcg.SetPrintLevel(2);
197  pcg.SetPreconditioner(ams);
198  pcg.Mult(B, X);
199  }
200  else
201 #ifdef MFEM_USE_SUPERLU
202  {
203  if (Mpi::Root())
204  {
205  cout << "Size of linear system: "
206  << A.As<HypreParMatrix>()->GetGlobalNumRows() << endl;
207  }
208
209  SuperLURowLocMatrix A_SuperLU(*A.As<HypreParMatrix>());
210  SuperLUSolver AInv(MPI_COMM_WORLD);
211  AInv.SetOperator(A_SuperLU);
212  AInv.Mult(B,X);
213  }
214 #else
215  {
216  if (Mpi::Root()) { cout << "No solvers available." << endl; }
217  return 1;
218  }
219 #endif
220
221  // 13. Recover the parallel grid function corresponding to X. This is the
222  // local finite element solution on each processor.
223  a.RecoverFEMSolution(X, b, sol);
224
225  // 14. Compute and print the H(Curl) norm of the error.
226  {
227  double error = sol.ComputeHCurlError(&E, &CurlE);
228  if (Mpi::Root())
229  {
230  cout << "\n|| E_h - E ||_{H(Curl)} = " << error << '\n' << endl;
231  }
232  }
233
234
235  // 15. Save the refined mesh and the solution in parallel. This output can
236  // be viewed later using GLVis: "glvis -np <np> -m mesh -g sol".
237  {
238  ostringstream mesh_name, sol_name;
239  mesh_name << "mesh." << setfill('0') << setw(6) << myid;
240  sol_name << "sol." << setfill('0') << setw(6) << myid;
241
242  ofstream mesh_ofs(mesh_name.str().c_str());
243  mesh_ofs.precision(8);
244  pmesh.Print(mesh_ofs);
245
246  ofstream sol_ofs(sol_name.str().c_str());
247  sol_ofs.precision(8);
248  sol.Save(sol_ofs);
249  }
250
251  // 16. Send the solution by socket to a GLVis server.
252  if (visualization)
253  {
254  char vishost[] = "localhost";
255  int visport = 19916;
256
257  VectorGridFunctionCoefficient solCoef(&sol);
258  CurlGridFunctionCoefficient dsolCoef(&sol);
259
260  if (dim ==1)
261  {
262  socketstream x_sock(vishost, visport);
263  socketstream y_sock(vishost, visport);
264  socketstream z_sock(vishost, visport);
265  socketstream dy_sock(vishost, visport);
266  socketstream dz_sock(vishost, visport);
267  x_sock.precision(8);
268  y_sock.precision(8);
269  z_sock.precision(8);
270  dy_sock.precision(8);
271  dz_sock.precision(8);
272
273  Vector xVec(3); xVec = 0.0; xVec(0) = 1;
274  Vector yVec(3); yVec = 0.0; yVec(1) = 1;
275  Vector zVec(3); zVec = 0.0; zVec(2) = 1;
276  VectorConstantCoefficient xVecCoef(xVec);
277  VectorConstantCoefficient yVecCoef(yVec);
278  VectorConstantCoefficient zVecCoef(zVec);
279
280  H1_FECollection fec_h1(order, dim);
281  L2_FECollection fec_l2(order-1, dim);
282
283  ParFiniteElementSpace fes_h1(&pmesh, &fec_h1);
284  ParFiniteElementSpace fes_l2(&pmesh, &fec_l2);
285
286  ParGridFunction xComp(&fes_l2);
287  ParGridFunction yComp(&fes_h1);
288  ParGridFunction zComp(&fes_h1);
289
290  ParGridFunction dyComp(&fes_l2);
291  ParGridFunction dzComp(&fes_l2);
292
293  InnerProductCoefficient xCoef(xVecCoef, solCoef);
294  InnerProductCoefficient yCoef(yVecCoef, solCoef);
295  InnerProductCoefficient zCoef(zVecCoef, solCoef);
296
297  xComp.ProjectCoefficient(xCoef);
298  yComp.ProjectCoefficient(yCoef);
299  zComp.ProjectCoefficient(zCoef);
300
301  x_sock << "parallel " << num_procs << " " << myid << "\n"
302  << "solution\n" << pmesh << xComp << flush
303  << "window_title 'X component'" << endl;
304  y_sock << "parallel " << num_procs << " " << myid << "\n"
305  << "solution\n" << pmesh << yComp << flush
306  << "window_geometry 403 0 400 350 "
307  << "window_title 'Y component'" << endl;
308  z_sock << "parallel " << num_procs << " " << myid << "\n"
309  << "solution\n" << pmesh << zComp << flush
310  << "window_geometry 806 0 400 350 "
311  << "window_title 'Z component'" << endl;
312
313  InnerProductCoefficient dyCoef(yVecCoef, dsolCoef);
314  InnerProductCoefficient dzCoef(zVecCoef, dsolCoef);
315
316  dyComp.ProjectCoefficient(dyCoef);
317  dzComp.ProjectCoefficient(dzCoef);
318
319  dy_sock << "parallel " << num_procs << " " << myid << "\n"
320  << "solution\n" << pmesh << dyComp << flush
321  << "window_geometry 403 375 400 350 "
322  << "window_title 'Y component of Curl'" << endl;
323  dz_sock << "parallel " << num_procs << " " << myid << "\n"
324  << "solution\n" << pmesh << dzComp << flush
325  << "window_geometry 806 375 400 350 "
326  << "window_title 'Z component of Curl'" << endl;
327  }
328  else if (dim == 2)
329  {
330  socketstream xy_sock(vishost, visport);
331  socketstream z_sock(vishost, visport);
332  socketstream dxy_sock(vishost, visport);
333  socketstream dz_sock(vishost, visport);
334
335  DenseMatrix xyMat(2,3); xyMat = 0.0;
336  xyMat(0,0) = 1.0; xyMat(1,1) = 1.0;
337  MatrixConstantCoefficient xyMatCoef(xyMat);
338  Vector zVec(3); zVec = 0.0; zVec(2) = 1;
339  VectorConstantCoefficient zVecCoef(zVec);
340
341  MatrixVectorProductCoefficient xyCoef(xyMatCoef, solCoef);
342  InnerProductCoefficient zCoef(zVecCoef, solCoef);
343
344  H1_FECollection fec_h1(order, dim);
345  ND_FECollection fec_nd(order, dim);
346  RT_FECollection fec_rt(order-1, dim);
347  L2_FECollection fec_l2(order-1, dim);
348
349  ParFiniteElementSpace fes_h1(&pmesh, &fec_h1);
350  ParFiniteElementSpace fes_nd(&pmesh, &fec_nd);
351  ParFiniteElementSpace fes_rt(&pmesh, &fec_rt);
352  ParFiniteElementSpace fes_l2(&pmesh, &fec_l2);
353
354  ParGridFunction xyComp(&fes_nd);
355  ParGridFunction zComp(&fes_h1);
356
357  ParGridFunction dxyComp(&fes_rt);
358  ParGridFunction dzComp(&fes_l2);
359
360  xyComp.ProjectCoefficient(xyCoef);
361  zComp.ProjectCoefficient(zCoef);
362
363  xy_sock << "parallel " << num_procs << " " << myid << "\n";
364  xy_sock.precision(8);
365  xy_sock << "solution\n" << pmesh << xyComp
366  << "window_title 'XY components'\n" << flush;
367  z_sock << "parallel " << num_procs << " " << myid << "\n"
368  << "solution\n" << pmesh << zComp << flush
369  << "window_geometry 403 0 400 350 "
370  << "window_title 'Z component'" << endl;
371
372  MatrixVectorProductCoefficient dxyCoef(xyMatCoef, dsolCoef);
373  InnerProductCoefficient dzCoef(zVecCoef, dsolCoef);
374
375  dxyComp.ProjectCoefficient(dxyCoef);
376  dzComp.ProjectCoefficient(dzCoef);
377
378  dxy_sock << "parallel " << num_procs << " " << myid << "\n"
379  << "solution\n" << pmesh << dxyComp << flush
380  << "window_geometry 0 375 400 350 "
381  << "window_title 'XY components of Curl'" << endl;
382  dz_sock << "parallel " << num_procs << " " << myid << "\n"
383  << "solution\n" << pmesh << dzComp << flush
384  << "window_geometry 403 375 400 350 "
385  << "window_title 'Z component of Curl'" << endl;
386  }
387  else
388  {
389  socketstream sol_sock(vishost, visport);
390  socketstream dsol_sock(vishost, visport);
391
392  RT_FECollection fec_rt(order-1, dim);
393
394  ParFiniteElementSpace fes_rt(&pmesh, &fec_rt);
395
396  ParGridFunction dsol(&fes_rt);
397
398  dsol.ProjectCoefficient(dsolCoef);
399
400  sol_sock << "parallel " << num_procs << " " << myid << "\n";
401  sol_sock.precision(8);
402  sol_sock << "solution\n" << pmesh << sol
403  << "window_title 'Solution'" << flush << endl;
404  dsol_sock << "parallel " << num_procs << " " << myid << "\n"
405  << "solution\n" << pmesh << dsol << flush
406  << "window_geometry 0 375 400 350 "
407  << "window_title 'Curl of solution'" << endl;
408  }
409  }
410
411  // 17. Free the used memory.
412  delete fec;
413
414  return 0;
415 }
416
417
418 void E_exact(const Vector &x, Vector &E)
419 {
420  if (dim == 1)
421  {
422  E(0) = 1.1 * sin(kappa * x(0) + 0.0 * M_PI);
423  E(1) = 1.2 * sin(kappa * x(0) + 0.4 * M_PI);
424  E(2) = 1.3 * sin(kappa * x(0) + 0.9 * M_PI);
425  }
426  else if (dim == 2)
427  {
428  E(0) = 1.1 * sin(kappa * M_SQRT1_2 * (x(0) + x(1)) + 0.0 * M_PI);
429  E(1) = 1.2 * sin(kappa * M_SQRT1_2 * (x(0) + x(1)) + 0.4 * M_PI);
430  E(2) = 1.3 * sin(kappa * M_SQRT1_2 * (x(0) + x(1)) + 0.9 * M_PI);
431  }
432  else
433  {
434  E(0) = 1.1 * sin(kappa * M_SQRT1_2 * (x(0) + x(1)) + 0.0 * M_PI);
435  E(1) = 1.2 * sin(kappa * M_SQRT1_2 * (x(0) + x(1)) + 0.4 * M_PI);
436  E(2) = 1.3 * sin(kappa * M_SQRT1_2 * (x(0) + x(1)) + 0.9 * M_PI);
437  E *= cos(kappa * x(2));
438  }
439 }
440
441 void CurlE_exact(const Vector &x, Vector &dE)
442 {
443  if (dim == 1)
444  {
445  double c4 = cos(kappa * x(0) + 0.4 * M_PI);
446  double c9 = cos(kappa * x(0) + 0.9 * M_PI);
447
448  dE(0) = 0.0;
449  dE(1) = -1.3 * c9;
450  dE(2) = 1.2 * c4;
451  dE *= kappa;
452  }
453  else if (dim == 2)
454  {
455  double c0 = cos(kappa * M_SQRT1_2 * (x(0) + x(1)) + 0.0 * M_PI);
456  double c4 = cos(kappa * M_SQRT1_2 * (x(0) + x(1)) + 0.4 * M_PI);
457  double c9 = cos(kappa * M_SQRT1_2 * (x(0) + x(1)) + 0.9 * M_PI);
458
459  dE(0) = 1.3 * c9;
460  dE(1) = -1.3 * c9;
461  dE(2) = 1.2 * c4 - 1.1 * c0;
462  dE *= kappa * M_SQRT1_2;
463  }
464  else
465  {
466  double s0 = sin(kappa * M_SQRT1_2 * (x(0) + x(1)) + 0.0 * M_PI);
467  double c0 = cos(kappa * M_SQRT1_2 * (x(0) + x(1)) + 0.0 * M_PI);
468  double s4 = sin(kappa * M_SQRT1_2 * (x(0) + x(1)) + 0.4 * M_PI);
469  double c4 = cos(kappa * M_SQRT1_2 * (x(0) + x(1)) + 0.4 * M_PI);
470  double c9 = cos(kappa * M_SQRT1_2 * (x(0) + x(1)) + 0.9 * M_PI);
471  double sk = sin(kappa * x(2));
472  double ck = cos(kappa * x(2));
473
474  dE(0) = 1.2 * s4 * sk + 1.3 * M_SQRT1_2 * c9 * ck;
475  dE(1) = -1.1 * s0 * sk - 1.3 * M_SQRT1_2 * c9 * ck;
476  dE(2) = -M_SQRT1_2 * (1.1 * c0 - 1.2 * c4) * ck;
477  dE *= kappa;
478  }
479 }
480
481 void f_exact(const Vector &x, Vector &f)
482 {
483  if (dim == 1)
484  {
485  double s0 = sin(kappa * x(0) + 0.0 * M_PI);
486  double s4 = sin(kappa * x(0) + 0.4 * M_PI);
487  double s9 = sin(kappa * x(0) + 0.9 * M_PI);
488
489  f(0) = 2.2 * s0 + 1.2 * M_SQRT1_2 * s4;
490  f(1) = 1.2 * (2.0 + kappa * kappa) * s4 +
491  M_SQRT1_2 * (1.1 * s0 + 1.3 * s9);
492  f(2) = 1.3 * (2.0 + kappa * kappa) * s9 + 1.2 * M_SQRT1_2 * s4;
493  }
494  else if (dim == 2)
495  {
496  double s0 = sin(kappa * M_SQRT1_2 * (x(0) + x(1)) + 0.0 * M_PI);
497  double s4 = sin(kappa * M_SQRT1_2 * (x(0) + x(1)) + 0.4 * M_PI);
498  double s9 = sin(kappa * M_SQRT1_2 * (x(0) + x(1)) + 0.9 * M_PI);
499
500  f(0) = 0.55 * (4.0 + kappa * kappa) * s0 +
501  0.6 * (M_SQRT2 - kappa * kappa) * s4;
502  f(1) = 0.55 * (M_SQRT2 - kappa * kappa) * s0 +
503  0.6 * (4.0 + kappa * kappa) * s4 +
504  0.65 * M_SQRT2 * s9;
505  f(2) = 0.6 * M_SQRT2 * s4 + 1.3 * (2.0 + kappa * kappa) * s9;
506  }
507  else
508  {
509  double s0 = sin(kappa * M_SQRT1_2 * (x(0) + x(1)) + 0.0 * M_PI);
510  double c0 = cos(kappa * M_SQRT1_2 * (x(0) + x(1)) + 0.0 * M_PI);
511  double s4 = sin(kappa * M_SQRT1_2 * (x(0) + x(1)) + 0.4 * M_PI);
512  double c4 = cos(kappa * M_SQRT1_2 * (x(0) + x(1)) + 0.4 * M_PI);
513  double s9 = sin(kappa * M_SQRT1_2 * (x(0) + x(1)) + 0.9 * M_PI);
514  double c9 = cos(kappa * M_SQRT1_2 * (x(0) + x(1)) + 0.9 * M_PI);
515  double sk = sin(kappa * x(2));
516  double ck = cos(kappa * x(2));
517
518  f(0) = 0.55 * (4.0 + 3.0 * kappa * kappa) * s0 * ck +
519  0.6 * (M_SQRT2 - kappa * kappa) * s4 * ck -
520  0.65 * M_SQRT2 * kappa * kappa * c9 * sk;
521
522  f(1) = 0.55 * (M_SQRT2 - kappa * kappa) * s0 * ck +
523  0.6 * (4.0 + 3.0 * kappa * kappa) * s4 * ck +
524  0.65 * M_SQRT2 * s9 * ck -
525  0.65 * M_SQRT2 * kappa * kappa * c9 * sk;
526
527  f(2) = 0.6 * M_SQRT2 * s4 * ck -
528  M_SQRT2 * kappa * kappa * (0.55 * c0 + 0.6 * c4) * sk
529  + 1.3 * (2.0 + kappa * kappa) * s9 * ck;
530  }
531 }
A matrix coefficient that is constant in space and time.
void SetTol(double tol)
Definition: hypre.cpp:3996
virtual void GetEssentialTrueDofs(const Array< int > &bdr_attr_is_ess, Array< int > &ess_tdof_list, int component=-1)
Definition: pfespace.cpp:1032
The Auxiliary-space Maxwell Solver in hypre.
Definition: hypre.hpp:1743
A coefficient that is constant across space and time.
Definition: coefficient.hpp:84
int Dimension() const
Definition: mesh.hpp:1047
Scalar coefficient defined as the inner product of two vector coefficients.
Arbitrary order 3D H(curl)-conforming Nedelec finite elements in 1D.
Definition: fe_coll.hpp:496
virtual void Mult(const HypreParVector &b, HypreParVector &x) const
Solve Ax=b with hypre&#39;s PCG.
Definition: hypre.cpp:4044
Integrator for (curl u, curl v) for Nedelec elements.
Vector coefficient that is constant in space and time.
Pointer to an Operator of a specified type.
Definition: handle.hpp:33
T Max() const
Find the maximal element in the array, using the comparison operator < for class T.
Definition: array.cpp:68
Data type dense matrix using column-major storage.
Definition: densemat.hpp:23
Arbitrary order 3D H(curl)-conforming Nedelec finite elements in 2D.
Definition: fe_coll.hpp:550
Abstract parallel finite element space.
Definition: pfespace.hpp:28
virtual void ProjectCoefficient(Coefficient &coeff)
Project coeff Coefficient to this GridFunction. The projection computation depends on the choice of t...
Definition: pgridfunc.cpp:525
STL namespace.
void SetPrintLevel(int print_lvl)
Definition: hypre.cpp:4016
void Mult(const Vector &x, Vector &y) const
Operator application: y=A(x).
Definition: superlu.cpp:485
void SetOperator(const Operator &op)
Set/update the solver for the given operator.
Definition: superlu.cpp:591
Class for parallel linear form.
Definition: plinearform.hpp:26
constexpr char vishost[]
double freq
Definition: ex31p.cpp:42
double b
Definition: lissajous.cpp:42
void f_exact(const Vector &, Vector &)
Definition: ex31p.cpp:481
void UniformRefinement(int i, const DSTable &, int *, int *, int *)
Definition: mesh.cpp:9878
constexpr int visport
Vector coefficient defined as the Curl of a vector GridFunction.
virtual double ComputeHCurlError(VectorCoefficient *exsol, VectorCoefficient *excurl, const IntegrationRule *irs[]=NULL) const
Returns the error measured H(curl)-norm for ND elements.
Definition: pgridfunc.hpp:368
HYPRE_BigInt GlobalTrueVSize() const
Definition: pfespace.hpp:285
void SetMaxIter(int max_iter)
Definition: hypre.cpp:4006
Arbitrary order H(div)-conforming Raviart-Thomas finite elements.
Definition: fe_coll.hpp:373
A general vector function coefficient.
Array< int > bdr_attributes
A list of all unique boundary attributes used by the Mesh.
Definition: mesh.hpp:275
PCG solver in hypre.
Definition: hypre.hpp:1215
Collection of finite elements from the same family in multiple dimensions. This class is used to matc...
Definition: fe_coll.hpp:26
int dim
Definition: ex31p.cpp:43
void AddOption(bool *var, const char *enable_short_name, const char *enable_long_name, const char *disable_short_name, const char *disable_long_name, const char *description, bool required=false)
Add a boolean option and set &#39;var&#39; to receive the value. Enable/disable tags are used to set the bool...
Definition: optparser.hpp:82
double kappa
Definition: ex31p.cpp:42
Vector coefficient defined as a product of a matrix coefficient and a vector coefficient.
virtual void Save(std::ostream &out) const
Definition: pgridfunc.cpp:873
double a
Definition: lissajous.cpp:41
void E_exact(const Vector &, Vector &)
Definition: ex31p.cpp:418
OpType * As() const
Return the Operator pointer statically cast to a specified OpType. Similar to the method Get()...
Definition: handle.hpp:104
void SetPreconditioner(HypreSolver &precond)
Set the hypre solver to be used as a preconditioner.
Definition: hypre.cpp:4021
int main(int argc, char *argv[])
Definition: ex31p.cpp:45
Class for parallel bilinear form.
int Size() const
Return the logical size of the array.
Definition: array.hpp:141
for VectorFiniteElements (Nedelec, Raviart-Thomas)
Definition: lininteg.hpp:346
Arbitrary order H(curl)-conforming Nedelec finite elements.
Definition: fe_coll.hpp:447
Vector data type.
Definition: vector.hpp:60
Vector coefficient defined by a vector GridFunction.
Arbitrary order H1-conforming (continuous) finite elements.
Definition: fe_coll.hpp:252
void Print(std::ostream &out=mfem::out) const override
Definition: pmesh.cpp:4839
void CurlE_exact(const Vector &, Vector &)
Definition: ex31p.cpp:441
Class for parallel grid function.
Definition: pgridfunc.hpp:32
Wrapper for hypre&#39;s ParCSR matrix class.
Definition: hypre.hpp:343
Class for parallel meshes.
Definition: pmesh.hpp:32
void ParseCheck(std::ostream &out=mfem::out)
Definition: optparser.cpp:252
Arbitrary order "L2-conforming" discontinuous finite elements.
Definition: fe_coll.hpp:320
double f(const Vector &p)
double sigma(const Vector &x)
Definition: maxwell.cpp:102