MFEM  v4.5.1 Finite element discretization library
ex5p.cpp
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1 // MFEM Example 5 - Parallel Version
2 //
3 // Compile with: make ex5p
4 //
5 // Sample runs: mpirun -np 4 ex5p -m ../data/square-disc.mesh
6 // mpirun -np 4 ex5p -m ../data/star.mesh
7 // mpirun -np 4 ex5p -m ../data/star.mesh -r 2 -pa
8 // mpirun -np 4 ex5p -m ../data/beam-tet.mesh
9 // mpirun -np 4 ex5p -m ../data/beam-hex.mesh
10 // mpirun -np 4 ex5p -m ../data/beam-hex.mesh -pa
11 // mpirun -np 4 ex5p -m ../data/escher.mesh
12 // mpirun -np 4 ex5p -m ../data/fichera.mesh
13 //
14 // Device sample runs:
15 // mpirun -np 4 ex5p -m ../data/star.mesh -r 2 -pa -d cuda
16 // mpirun -np 4 ex5p -m ../data/star.mesh -r 2 -pa -d raja-cuda
17 // mpirun -np 4 ex5p -m ../data/star.mesh -r 2 -pa -d raja-omp
18 // mpirun -np 4 ex5p -m ../data/beam-hex.mesh -pa -d cuda
19 //
20 // Description: This example code solves a simple 2D/3D mixed Darcy problem
21 // corresponding to the saddle point system
22 //
23 // k*u + grad p = f
24 // - div u = g
25 //
26 // with natural boundary condition -p = <given pressure>.
27 // Here, we use a given exact solution (u,p) and compute the
28 // corresponding r.h.s. (f,g). We discretize with Raviart-Thomas
29 // finite elements (velocity u) and piecewise discontinuous
30 // polynomials (pressure p).
31 //
32 // The example demonstrates the use of the BlockOperator class, as
33 // well as the collective saving of several grid functions in
34 // VisIt (visit.llnl.gov) and ParaView (paraview.org) formats.
36 // also illustrated.
37 //
38 // We recommend viewing examples 1-4 before viewing this example.
39
40 #include "mfem.hpp"
41 #include <fstream>
42 #include <iostream>
43
44 using namespace std;
45 using namespace mfem;
46
47 // Define the analytical solution and forcing terms / boundary conditions
48 void uFun_ex(const Vector & x, Vector & u);
49 double pFun_ex(const Vector & x);
50 void fFun(const Vector & x, Vector & f);
51 double gFun(const Vector & x);
52 double f_natural(const Vector & x);
53
54 int main(int argc, char *argv[])
55 {
56  StopWatch chrono;
57
58  // 1. Initialize MPI and HYPRE.
59  Mpi::Init(argc, argv);
60  int num_procs = Mpi::WorldSize();
61  int myid = Mpi::WorldRank();
62  Hypre::Init();
63  bool verbose = (myid == 0);
64
65  // 2. Parse command-line options.
66  const char *mesh_file = "../data/star.mesh";
67  int ref_levels = -1;
68  int order = 1;
69  bool par_format = false;
70  bool pa = false;
71  const char *device_config = "cpu";
72  bool visualization = 1;
74
75  OptionsParser args(argc, argv);
77  "Mesh file to use.");
79  "Number of times to refine the mesh uniformly.");
81  "Finite element order (polynomial degree).");
83  "--serial-format",
84  "Format to use when saving the results for VisIt.");
86  "--no-partial-assembly", "Enable Partial Assembly.");
88  "Device configuration string, see Device::Configure().");
90  "--no-visualization",
91  "Enable or disable GLVis visualization.");
94  "Save data using adios2 streams.");
95  args.Parse();
96  if (!args.Good())
97  {
98  if (verbose)
99  {
100  args.PrintUsage(cout);
101  }
102  return 1;
103  }
104  if (verbose)
105  {
106  args.PrintOptions(cout);
107  }
108
109  // 3. Enable hardware devices such as GPUs, and programming models such as
110  // CUDA, OCCA, RAJA and OpenMP based on command line options.
111  Device device(device_config);
112  if (myid == 0) { device.Print(); }
113
114  // 4. Read the (serial) mesh from the given mesh file on all processors. We
115  // can handle triangular, quadrilateral, tetrahedral, hexahedral, surface
116  // and volume meshes with the same code.
117  Mesh *mesh = new Mesh(mesh_file, 1, 1);
118  int dim = mesh->Dimension();
119
120  // 5. Refine the serial mesh on all processors to increase the resolution. In
121  // this example we do 'ref_levels' of uniform refinement. We choose
122  // 'ref_levels' to be the largest number that gives a final mesh with no
123  // more than 10,000 elements, unless the user specifies it as input.
124  {
125  if (ref_levels == -1)
126  {
127  ref_levels = (int)floor(log(10000./mesh->GetNE())/log(2.)/dim);
128  }
129
130  for (int l = 0; l < ref_levels; l++)
131  {
132  mesh->UniformRefinement();
133  }
134  }
135
136  // 6. Define a parallel mesh by a partitioning of the serial mesh. Refine
137  // this mesh further in parallel to increase the resolution. Once the
138  // parallel mesh is defined, the serial mesh can be deleted.
139  ParMesh *pmesh = new ParMesh(MPI_COMM_WORLD, *mesh);
140  delete mesh;
141  {
142  int par_ref_levels = 2;
143  for (int l = 0; l < par_ref_levels; l++)
144  {
145  pmesh->UniformRefinement();
146  }
147  }
148
149  // 7. Define a parallel finite element space on the parallel mesh. Here we
150  // use the Raviart-Thomas finite elements of the specified order.
151  FiniteElementCollection *hdiv_coll(new RT_FECollection(order, dim));
152  FiniteElementCollection *l2_coll(new L2_FECollection(order, dim));
153
154  ParFiniteElementSpace *R_space = new ParFiniteElementSpace(pmesh, hdiv_coll);
155  ParFiniteElementSpace *W_space = new ParFiniteElementSpace(pmesh, l2_coll);
156
157  HYPRE_BigInt dimR = R_space->GlobalTrueVSize();
158  HYPRE_BigInt dimW = W_space->GlobalTrueVSize();
159
160  if (verbose)
161  {
162  std::cout << "***********************************************************\n";
163  std::cout << "dim(R) = " << dimR << "\n";
164  std::cout << "dim(W) = " << dimW << "\n";
165  std::cout << "dim(R+W) = " << dimR + dimW << "\n";
166  std::cout << "***********************************************************\n";
167  }
168
169  // 8. Define the two BlockStructure of the problem. block_offsets is used
170  // for Vector based on dof (like ParGridFunction or ParLinearForm),
171  // block_trueOffstes is used for Vector based on trueDof (HypreParVector
172  // for the rhs and solution of the linear system). The offsets computed
173  // here are local to the processor.
174  Array<int> block_offsets(3); // number of variables + 1
175  block_offsets[0] = 0;
176  block_offsets[1] = R_space->GetVSize();
177  block_offsets[2] = W_space->GetVSize();
178  block_offsets.PartialSum();
179
180  Array<int> block_trueOffsets(3); // number of variables + 1
181  block_trueOffsets[0] = 0;
182  block_trueOffsets[1] = R_space->TrueVSize();
183  block_trueOffsets[2] = W_space->TrueVSize();
184  block_trueOffsets.PartialSum();
185
186  // 9. Define the coefficients, analytical solution, and rhs of the PDE.
187  ConstantCoefficient k(1.0);
188
189  VectorFunctionCoefficient fcoeff(dim, fFun);
190  FunctionCoefficient fnatcoeff(f_natural);
191  FunctionCoefficient gcoeff(gFun);
192
193  VectorFunctionCoefficient ucoeff(dim, uFun_ex);
195
196  // 10. Define the parallel grid function and parallel linear forms, solution
197  // vector and rhs.
198  MemoryType mt = device.GetMemoryType();
199  BlockVector x(block_offsets, mt), rhs(block_offsets, mt);
200  BlockVector trueX(block_trueOffsets, mt), trueRhs(block_trueOffsets, mt);
201
202  ParLinearForm *fform(new ParLinearForm);
203  fform->Update(R_space, rhs.GetBlock(0), 0);
206  fform->Assemble();
207  fform->SyncAliasMemory(rhs);
208  fform->ParallelAssemble(trueRhs.GetBlock(0));
209  trueRhs.GetBlock(0).SyncAliasMemory(trueRhs);
210
211  ParLinearForm *gform(new ParLinearForm);
212  gform->Update(W_space, rhs.GetBlock(1), 0);
214  gform->Assemble();
215  gform->SyncAliasMemory(rhs);
216  gform->ParallelAssemble(trueRhs.GetBlock(1));
217  trueRhs.GetBlock(1).SyncAliasMemory(trueRhs);
218
219  // 11. Assemble the finite element matrices for the Darcy operator
220  //
221  // D = [ M B^T ]
222  // [ B 0 ]
223  // where:
224  //
225  // M = \int_\Omega k u_h \cdot v_h d\Omega u_h, v_h \in R_h
226  // B = -\int_\Omega \div u_h q_h d\Omega u_h \in R_h, q_h \in W_h
227  ParBilinearForm *mVarf(new ParBilinearForm(R_space));
228  ParMixedBilinearForm *bVarf(new ParMixedBilinearForm(R_space, W_space));
229
230  HypreParMatrix *M = NULL;
231  HypreParMatrix *B = NULL;
232
233  if (pa) { mVarf->SetAssemblyLevel(AssemblyLevel::PARTIAL); }
235  mVarf->Assemble();
236  if (!pa) { mVarf->Finalize(); }
237
238  if (pa) { bVarf->SetAssemblyLevel(AssemblyLevel::PARTIAL); }
240  bVarf->Assemble();
241  if (!pa) { bVarf->Finalize(); }
242
243  BlockOperator *darcyOp = new BlockOperator(block_trueOffsets);
244
245  Array<int> empty_tdof_list; // empty
246  OperatorPtr opM, opB;
247
248  TransposeOperator *Bt = NULL;
249
250  if (pa)
251  {
252  mVarf->FormSystemMatrix(empty_tdof_list, opM);
253  bVarf->FormRectangularSystemMatrix(empty_tdof_list, empty_tdof_list, opB);
254  Bt = new TransposeOperator(opB.Ptr());
255
256  darcyOp->SetBlock(0,0, opM.Ptr());
257  darcyOp->SetBlock(0,1, Bt, -1.0);
258  darcyOp->SetBlock(1,0, opB.Ptr(), -1.0);
259  }
260  else
261  {
262  M = mVarf->ParallelAssemble();
263  B = bVarf->ParallelAssemble();
264  (*B) *= -1;
265  Bt = new TransposeOperator(B);
266
267  darcyOp->SetBlock(0,0, M);
268  darcyOp->SetBlock(0,1, Bt);
269  darcyOp->SetBlock(1,0, B);
270  }
271
272  // 12. Construct the operators for preconditioner
273  //
274  // P = [ diag(M) 0 ]
275  // [ 0 B diag(M)^-1 B^T ]
276  //
277  // Here we use Symmetric Gauss-Seidel to approximate the inverse of the
278  // pressure Schur Complement.
279  HypreParMatrix *MinvBt = NULL;
280  HypreParVector *Md = NULL;
281  HypreParMatrix *S = NULL;
282  Vector Md_PA;
283  Solver *invM, *invS;
284
285  if (pa)
286  {
287  Md_PA.SetSize(R_space->GetTrueVSize());
288  mVarf->AssembleDiagonal(Md_PA);
290  Vector invMd(Md_PA.Size());
291  for (int i=0; i<Md_PA.Size(); ++i)
292  {
293  invMd(i) = 1.0 / Md_host[i];
294  }
295
296  Vector BMBt_diag(W_space->GetTrueVSize());
298
299  Array<int> ess_tdof_list; // empty
300
301  invM = new OperatorJacobiSmoother(Md_PA, ess_tdof_list);
302  invS = new OperatorJacobiSmoother(BMBt_diag, ess_tdof_list);
303  }
304  else
305  {
306  Md = new HypreParVector(MPI_COMM_WORLD, M->GetGlobalNumRows(),
307  M->GetRowStarts());
308  M->GetDiag(*Md);
309
310  MinvBt = B->Transpose();
311  MinvBt->InvScaleRows(*Md);
312  S = ParMult(B, MinvBt);
313
314  invM = new HypreDiagScale(*M);
315  invS = new HypreBoomerAMG(*S);
316  }
317
318  invM->iterative_mode = false;
319  invS->iterative_mode = false;
320
322  block_trueOffsets);
323  darcyPr->SetDiagonalBlock(0, invM);
324  darcyPr->SetDiagonalBlock(1, invS);
325
326  // 13. Solve the linear system with MINRES.
327  // Check the norm of the unpreconditioned residual.
328  int maxIter(pa ? 1000 : 500);
329  double rtol(1.e-6);
330  double atol(1.e-10);
331
332  chrono.Clear();
333  chrono.Start();
334  MINRESSolver solver(MPI_COMM_WORLD);
335  solver.SetAbsTol(atol);
336  solver.SetRelTol(rtol);
337  solver.SetMaxIter(maxIter);
338  solver.SetOperator(*darcyOp);
339  solver.SetPreconditioner(*darcyPr);
340  solver.SetPrintLevel(verbose);
341  trueX = 0.0;
342  solver.Mult(trueRhs, trueX);
343  if (device.IsEnabled()) { trueX.HostRead(); }
344  chrono.Stop();
345
346  if (verbose)
347  {
348  if (solver.GetConverged())
349  std::cout << "MINRES converged in " << solver.GetNumIterations()
350  << " iterations with a residual norm of " << solver.GetFinalNorm() << ".\n";
351  else
352  std::cout << "MINRES did not converge in " << solver.GetNumIterations()
353  << " iterations. Residual norm is " << solver.GetFinalNorm() << ".\n";
354  std::cout << "MINRES solver took " << chrono.RealTime() << "s. \n";
355  }
356
357  // 14. Extract the parallel grid function corresponding to the finite element
358  // approximation X. This is the local solution on each processor. Compute
359  // L2 error norms.
362  u->MakeRef(R_space, x.GetBlock(0), 0);
363  p->MakeRef(W_space, x.GetBlock(1), 0);
364  u->Distribute(&(trueX.GetBlock(0)));
365  p->Distribute(&(trueX.GetBlock(1)));
366
367  int order_quad = max(2, 2*order+1);
368  const IntegrationRule *irs[Geometry::NumGeom];
369  for (int i=0; i < Geometry::NumGeom; ++i)
370  {
372  }
373
374  double err_u = u->ComputeL2Error(ucoeff, irs);
375  double norm_u = ComputeGlobalLpNorm(2, ucoeff, *pmesh, irs);
376  double err_p = p->ComputeL2Error(pcoeff, irs);
377  double norm_p = ComputeGlobalLpNorm(2, pcoeff, *pmesh, irs);
378
379  if (verbose)
380  {
381  std::cout << "|| u_h - u_ex || / || u_ex || = " << err_u / norm_u << "\n";
382  std::cout << "|| p_h - p_ex || / || p_ex || = " << err_p / norm_p << "\n";
383  }
384
385  // 15. Save the refined mesh and the solution in parallel. This output can be
386  // viewed later using GLVis: "glvis -np <np> -m mesh -g sol_*".
387  {
388  ostringstream mesh_name, u_name, p_name;
389  mesh_name << "mesh." << setfill('0') << setw(6) << myid;
390  u_name << "sol_u." << setfill('0') << setw(6) << myid;
391  p_name << "sol_p." << setfill('0') << setw(6) << myid;
392
393  ofstream mesh_ofs(mesh_name.str().c_str());
394  mesh_ofs.precision(8);
395  pmesh->Print(mesh_ofs);
396
397  ofstream u_ofs(u_name.str().c_str());
398  u_ofs.precision(8);
399  u->Save(u_ofs);
400
401  ofstream p_ofs(p_name.str().c_str());
402  p_ofs.precision(8);
403  p->Save(p_ofs);
404  }
405
406  // 16. Save data in the VisIt format
407  VisItDataCollection visit_dc("Example5-Parallel", pmesh);
408  visit_dc.RegisterField("velocity", u);
409  visit_dc.RegisterField("pressure", p);
410  visit_dc.SetFormat(!par_format ?
411  DataCollection::SERIAL_FORMAT :
412  DataCollection::PARALLEL_FORMAT);
413  visit_dc.Save();
414
415  // 17. Save data in the ParaView format
416  ParaViewDataCollection paraview_dc("Example5P", pmesh);
417  paraview_dc.SetPrefixPath("ParaView");
418  paraview_dc.SetLevelsOfDetail(order);
419  paraview_dc.SetDataFormat(VTKFormat::BINARY);
420  paraview_dc.SetHighOrderOutput(true);
421  paraview_dc.SetCycle(0);
422  paraview_dc.SetTime(0.0);
423  paraview_dc.RegisterField("velocity",u);
424  paraview_dc.RegisterField("pressure",p);
425  paraview_dc.Save();
426
427  // 18. Optionally output a BP (binary pack) file using ADIOS2. This can be
428  // visualized with the ParaView VTX reader.
431  {
432  std::string postfix(mesh_file);
433  postfix.erase(0, std::string("../data/").size() );
434  postfix += "_o" + std::to_string(order);
435  const std::string collection_name = "ex5-p_" + postfix + ".bp";
436
444  }
445 #endif
446
447  // 19. Send the solution by socket to a GLVis server.
448  if (visualization)
449  {
450  char vishost[] = "localhost";
451  int visport = 19916;
452  socketstream u_sock(vishost, visport);
453  u_sock << "parallel " << num_procs << " " << myid << "\n";
454  u_sock.precision(8);
455  u_sock << "solution\n" << *pmesh << *u << "window_title 'Velocity'"
456  << endl;
457  // Make sure all ranks have sent their 'u' solution before initiating
458  // another set of GLVis connections (one from each rank):
459  MPI_Barrier(pmesh->GetComm());
460  socketstream p_sock(vishost, visport);
461  p_sock << "parallel " << num_procs << " " << myid << "\n";
462  p_sock.precision(8);
463  p_sock << "solution\n" << *pmesh << *p << "window_title 'Pressure'"
464  << endl;
465  }
466
467  // 20. Free the used memory.
468  delete fform;
469  delete gform;
470  delete u;
471  delete p;
472  delete darcyOp;
473  delete darcyPr;
474  delete invM;
475  delete invS;
476  delete S;
477  delete Md;
478  delete MinvBt;
479  delete Bt;
480  delete B;
481  delete M;
482  delete mVarf;
483  delete bVarf;
484  delete W_space;
485  delete R_space;
486  delete l2_coll;
487  delete hdiv_coll;
488  delete pmesh;
489
490  return 0;
491 }
492
493
494 void uFun_ex(const Vector & x, Vector & u)
495 {
496  double xi(x(0));
497  double yi(x(1));
498  double zi(0.0);
499  if (x.Size() == 3)
500  {
501  zi = x(2);
502  }
503
504  u(0) = - exp(xi)*sin(yi)*cos(zi);
505  u(1) = - exp(xi)*cos(yi)*cos(zi);
506
507  if (x.Size() == 3)
508  {
509  u(2) = exp(xi)*sin(yi)*sin(zi);
510  }
511 }
512
513 // Change if needed
514 double pFun_ex(const Vector & x)
515 {
516  double xi(x(0));
517  double yi(x(1));
518  double zi(0.0);
519
520  if (x.Size() == 3)
521  {
522  zi = x(2);
523  }
524
525  return exp(xi)*sin(yi)*cos(zi);
526 }
527
528 void fFun(const Vector & x, Vector & f)
529 {
530  f = 0.0;
531 }
532
533 double gFun(const Vector & x)
534 {
535  if (x.Size() == 3)
536  {
537  return -pFun_ex(x);
538  }
539  else
540  {
541  return 0;
542  }
543 }
544
545 double f_natural(const Vector & x)
546 {
547  return (-pFun_ex(x));
548 }
Class for domain integration L(v) := (f, v)
Definition: lininteg.hpp:108
int GetVSize() const
Return the number of vector dofs, i.e. GetNDofs() x GetVDim().
Definition: fespace.hpp:587
Class for an integration rule - an Array of IntegrationPoint.
Definition: intrules.hpp:90
virtual void AssembleDiagonal(Vector &diag) const
Assemble the diagonal of the bilinear form into diag. Note that diag is a true-dof Vector...
int GetNumIterations() const
Definition: solvers.hpp:246
void SetCycle(int c)
Set time cycle (for time-dependent simulations)
const IntegrationRule & Get(int GeomType, int Order)
Returns an integration rule for given GeomType and Order.
Definition: intrules.cpp:923
void fFun(const Vector &x, Vector &f)
Definition: ex5.cpp:426
A class to handle Vectors in a block fashion.
Definition: blockvector.hpp:30
void SetDataFormat(VTKFormat fmt)
A coefficient that is constant across space and time.
Definition: coefficient.hpp:84
void SetSize(int s)
Resize the vector to size s.
Definition: vector.hpp:513
Helper class for ParaView visualization data.
int TrueVSize() const
Obsolete, kept for backward compatibility.
Definition: pfespace.hpp:434
Pointer to an Operator of a specified type.
Definition: handle.hpp:33
HYPRE_BigInt GlobalTrueVSize() const
Definition: pfespace.hpp:285
int Size() const
Returns the size of the vector.
Definition: vector.hpp:200
int GetNE() const
Returns number of elements.
Definition: mesh.hpp:923
virtual void Save(std::ostream &out) const
Definition: pgridfunc.cpp:873
void Print(std::ostream &out=mfem::out)
Print the configuration of the MFEM virtual device object.
Definition: device.cpp:279
void SetAssemblyLevel(AssemblyLevel assembly_level)
Set the desired assembly level.
double RealTime()
Definition: tic_toc.cpp:426
Abstract parallel finite element space.
Definition: pfespace.hpp:28
bool iterative_mode
If true, use the second argument of Mult() as an initial guess.
Definition: operator.hpp:659
virtual void Finalize(int skip_zeros=1)
Finalizes the matrix initialization.
MINRES method.
Definition: solvers.hpp:575
void SyncAliasMemory(const Vector &v) const
Update the alias memory location of the vector to match v.
Definition: vector.hpp:245
static bool IsEnabled()
Return true if any backend other than Backend::CPU is enabled.
Definition: device.hpp:246
bool GetConverged() const
Definition: solvers.hpp:247
HypreParMatrix * ParMult(const HypreParMatrix *A, const HypreParMatrix *B, bool own_matrix)
Definition: hypre.cpp:2849
void Update(ParFiniteElementSpace *pf=NULL)
Update the object according to the given new FE space *pf.
Definition: plinearform.cpp:21
HypreParMatrix * ParallelAssemble()
Returns the matrix assembled on the true dofs, i.e. P^t A P.
double GetFinalNorm() const
Definition: solvers.hpp:248
virtual int GetTrueVSize() const
Return the number of local vector true dofs.
Definition: pfespace.hpp:289
void Stop()
Stop the stopwatch.
Definition: tic_toc.cpp:416
HypreParMatrix * ParallelAssemble()
Returns the matrix assembled on the true dofs, i.e. P_test^t A P_trial.
Adds a domain integrator. Assumes ownership of bfi.
virtual void MakeRef(FiniteElementSpace *f, double *v)
Make the ParGridFunction reference external data on a new FiniteElementSpace.
Definition: pgridfunc.cpp:102
HYPRE_BigInt * GetRowStarts() const
Return the parallel row partitioning array.
Definition: hypre.hpp:645
The BoomerAMG solver in hypre.
Definition: hypre.hpp:1579
virtual void Mult(const Vector &b, Vector &x) const
Operator application: y=A(x).
Definition: solvers.cpp:1609
Class for parallel linear form.
Definition: plinearform.hpp:26
virtual void RegisterField(const std::string &field_name, GridFunction *gf)
Add a grid function to the collection.
virtual void SetPrintLevel(int print_lvl)
Legacy method to set the level of verbosity of the solver output.
Definition: solvers.cpp:71
virtual void SetPreconditioner(Solver &pr)
This should be called before SetOperator.
Definition: solvers.hpp:588
void Parse()
Parse the command-line options. Note that this function expects all the options provided through the ...
Definition: optparser.cpp:151
A class to handle Block diagonal preconditioners in a matrix-free implementation. ...
constexpr char vishost[]
Jacobi preconditioner in hypre.
Definition: hypre.hpp:1410
Jacobi smoothing for a given bilinear form (no matrix necessary).
Definition: solvers.hpp:274
double f_natural(const Vector &x)
Definition: ex5.cpp:443
void Assemble()
Assembles the ParLinearForm i.e. sums over all domain/bdr integrators.
Definition: plinearform.cpp:46
void UniformRefinement(int i, const DSTable &, int *, int *, int *)
Definition: mesh.cpp:9816
constexpr int visport
Timing object.
Definition: tic_toc.hpp:34
static MemoryType GetMemoryType()
(DEPRECATED) Equivalent to GetDeviceMemoryType().
Definition: device.hpp:277
Data collection with VisIt I/O routines.
void SetMaxIter(int max_it)
Definition: solvers.hpp:200
virtual double ComputeL2Error(Coefficient *exsol[], const IntegrationRule *irs[]=NULL, const Array< int > *elems=NULL) const
Definition: pgridfunc.hpp:281
void Assemble(int skip_zeros=1)
void Assemble(int skip_zeros=1)
Assemble the local matrix.
virtual void SetFormat(int fmt)
Set the desired output mesh and data format.
double pFun_ex(const Vector &x)
Definition: ex5.cpp:412
virtual void FormRectangularSystemMatrix(const Array< int > &trial_tdof_list, const Array< int > &test_tdof_list, OperatorHandle &A)
Return in A a parallel (on truedofs) version of this operator.
HypreParMatrix * Transpose() const
Returns the transpose of *this.
Definition: hypre.cpp:1607
void SetHighOrderOutput(bool high_order_output_)
void GetDiag(Vector &diag) const
Get the local diagonal of the matrix.
Definition: hypre.cpp:1480
void AssembleDiagonal_ADAt(const Vector &D, Vector &diag) const
Assemble the diagonal of ADA^T into diag, where A is this mixed bilinear form and D is a diagonal...
virtual void SetOperator(const Operator &op)
Also calls SetOperator for the preconditioner if there is one.
Definition: solvers.cpp:1588
Adds new Boundary Integrator. Assumes ownership of lfi.
Definition: linearform.cpp:72
int Dimension() const
Definition: mesh.hpp:1006
void PrintUsage(std::ostream &out) const
Print the usage message.
Definition: optparser.cpp:454
void SetTime(double t)
Set physical time (for time-dependent simulations)
virtual const double * HostRead() const
Definition: vector.hpp:453
Operator * Ptr() const
Access the underlying Operator pointer.
Definition: handle.hpp:87
void Start()
Start the stopwatch. The elapsed time is not cleared.
Definition: tic_toc.cpp:411
Arbitrary order H(div)-conforming Raviart-Thomas finite elements.
Definition: fe_coll.hpp:341
A general vector function coefficient.
void SetAssemblyLevel(AssemblyLevel assembly_level)
Set the desired assembly level. The default is AssemblyLevel::LEGACY.
Wrapper for hypre&#39;s parallel vector class.
Definition: hypre.hpp:161
Adds new Domain Integrator. Assumes ownership of lfi.
Definition: linearform.cpp:41
void SetAbsTol(double atol)
Definition: solvers.hpp:199
void SetRelTol(double rtol)
Definition: solvers.hpp:198
MPI_Comm GetComm() const
Definition: pmesh.hpp:351
Collection of finite elements from the same family in multiple dimensions. This class is used to matc...
Definition: fe_coll.hpp:26
virtual void Save() override
Save the collection and a VisIt root file.
MemoryType
Memory types supported by MFEM.
Definition: mem_manager.hpp:31
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
void PartialSum()
Fill the entries of the array with the cumulative sum of the entries.
Definition: array.cpp:103
HYPRE_Int HYPRE_BigInt
double ComputeGlobalLpNorm(double p, Coefficient &coeff, ParMesh &pmesh, const IntegrationRule *irs[])
Compute the global Lp norm of a function f. .
void Distribute(const Vector *tv)
Definition: pgridfunc.cpp:132
The transpose of a given operator. Switches the roles of the methods Mult() and MultTranspose().
Definition: operator.hpp:722
virtual void FormSystemMatrix(const Array< int > &ess_tdof_list, OperatorHandle &A)
Form the linear system matrix A, see FormLinearSystem() for details.
void uFun_ex(const Vector &x, Vector &u)
Definition: ex5.cpp:392
double gFun(const Vector &x)
Definition: ex5.cpp:431
Class for parallel bilinear form using different test and trial FE spaces.
virtual void Finalize(int skip_zeros=1)
Finalizes the matrix initialization.
HYPRE_BigInt GetGlobalNumRows() const
Return the global number of rows.
Definition: hypre.hpp:635
void InvScaleRows(const Vector &s)
Scale the local row i by 1./s(i)
Definition: hypre.cpp:2052
int dim
Definition: ex24.cpp:53
Adds new Domain Integrator. Assumes ownership of bfi.
void PrintOptions(std::ostream &out) const
Print the options.
Definition: optparser.cpp:324
Class for parallel bilinear form.
void SetLevelsOfDetail(int levels_of_detail_)
for VectorFiniteElements (Nedelec, Raviart-Thomas)
Definition: lininteg.hpp:346
A general function coefficient.
Vector data type.
Definition: vector.hpp:60
void SetLevelsOfDetail(const int levels_of_detail) noexcept
virtual void Save() override
void Print(std::ostream &out=mfem::out) const override
Definition: pmesh.cpp:4770
double u(const Vector &xvec)
Definition: lor_mms.hpp:24
Base class for solvers.
Definition: operator.hpp:655
Class for parallel grid function.
Definition: pgridfunc.hpp:32
The MFEM Device class abstracts hardware devices such as GPUs, as well as programming models such as ...
Definition: device.hpp:121
Wrapper for hypre&#39;s ParCSR matrix class.
Definition: hypre.hpp:343
A class to handle Block systems in a matrix-free implementation.
Class for parallel meshes.
Definition: pmesh.hpp:32
A global object with all integration rules (defined in intrules.cpp)
Definition: intrules.hpp:379
void ParallelAssemble(Vector &tv)
Assemble the vector on the true dofs, i.e. P^t v.
Definition: plinearform.cpp:95
int main()
void SetPrefixPath(const std::string &prefix)
Set the path where the DataCollection will be saved.
void Clear()
Clear the elapsed time on the stopwatch and restart it if it&#39;s running.
Definition: tic_toc.cpp:406
void SetBlock(int iRow, int iCol, Operator *op, double c=1.0)
Add a block op in the block-entry (iblock, jblock).
void SetDiagonalBlock(int iblock, Operator *op)
Add a square block op in the block-entry (iblock, iblock).
Vector & GetBlock(int i)
Get the i-th vector in the block.
Definition: blockvector.hpp:90
Arbitrary order &quot;L2-conforming&quot; discontinuous finite elements.
Definition: fe_coll.hpp:288
double f(const Vector &p)
virtual void RegisterField(const std::string &field_name, GridFunction *gf) override
Add a grid function to the collection and update the root file.
bool Good() const
Return true if the command line options were parsed successfully.
Definition: optparser.hpp:150