MFEM  v3.4 Finite element discretization library
ex9p.cpp
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1 // MFEM Example 9 - Parallel Version
2 // PETSc Modification
3 //
4 // Compile with: make ex9p
5 //
6 // Sample runs:
7 // mpirun -np 4 ex9p -m ../../data/periodic-hexagon.mesh --petscopts rc_ex9p_expl
8 // mpirun -np 4 ex9p -m ../../data/periodic-hexagon.mesh --petscopts rc_ex9p_impl -implicit
9 //
10 // Description: This example code solves the time-dependent advection equation
11 // du/dt + v.grad(u) = 0, where v is a given fluid velocity, and
12 // u0(x)=u(0,x) is a given initial condition.
13 //
14 // The example demonstrates the use of Discontinuous Galerkin (DG)
15 // bilinear forms in MFEM (face integrators), the use of explicit
16 // ODE time integrators, the definition of periodic boundary
17 // conditions through periodic meshes, as well as the use of GLVis
18 // for persistent visualization of a time-evolving solution. The
19 // saving of time-dependent data files for external visualization
20 // with VisIt (visit.llnl.gov) is also illustrated.
21 //
22 // The example also demonstrates how to use PETSc ODE solvers and
23 // customize them by command line (see rc_ex9p_expl and
24 // rc_ex9p_impl). The split in left-hand side and right-hand side
25 // of the TimeDependentOperator is amenable for IMEX methods.
26 // When using fully implicit methods, just the left-hand side of
27 // the operator should be provided for efficiency reasons when
28 // assembling the Jacobians. Here, we provide two Jacobian
29 // routines just to illustrate the capabilities of the
30 // PetscODESolver class. We also show how to monitor the time
31 // dependent solution inside a call to PetscODESolver:Mult.
32
33 #include "mfem.hpp"
34 #include <fstream>
35 #include <iostream>
36
37 #ifndef MFEM_USE_PETSC
38 #error This example requires that MFEM is built with MFEM_USE_PETSC=YES
39 #endif
40
41 using namespace std;
42 using namespace mfem;
43
44 // Choice for the problem setup. The fluid velocity, initial condition and
45 // inflow boundary condition are chosen based on this parameter.
46 int problem;
47
48 // Velocity coefficient
49 void velocity_function(const Vector &x, Vector &v);
50
51 // Initial condition
52 double u0_function(const Vector &x);
53
54 // Inflow boundary condition
55 double inflow_function(const Vector &x);
56
57 // Mesh bounding box
59
60
61 /** A time-dependent operator for the ODE as F(u,du/dt,t) = G(u,t)
62  The DG weak form of du/dt = -v.grad(u) is M du/dt = K u + b, where M and K are the mass
63  and advection matrices, and b describes the flow on the boundary. This can
64  be also written as a general ODE with the right-hand side only as
65  du/dt = M^{-1} (K u + b).
66  This class is used to evaluate the right-hand side and the left-hand side. */
68 {
69 private:
70  HypreParMatrix &M, &K;
71  const Vector &b;
72  HypreSmoother M_prec;
73  CGSolver M_solver;
74
75  mutable Vector z;
76  mutable PetscParMatrix* iJacobian;
77  mutable PetscParMatrix* rJacobian;
78
79 public:
81  bool M_in_lhs);
82
83  virtual void ExplicitMult(const Vector &x, Vector &y) const;
84  virtual void ImplicitMult(const Vector &x, const Vector &xp, Vector &y) const;
85  virtual void Mult(const Vector &x, Vector &y) const;
86  virtual Operator& GetExplicitGradient(const Vector &x) const;
87  virtual Operator& GetImplicitGradient(const Vector &x, const Vector &xp,
88  double shift) const;
89  virtual ~FE_Evolution() { delete iJacobian; delete rJacobian; }
90 };
91
92
93 // Monitor the solution at time step "step", explicitly in the time loop
94 class UserMonitor : public PetscSolverMonitor
95 {
96 private:
97  socketstream& sout;
98  ParMesh* pmesh;
99  ParGridFunction* u;
100  int vt;
101  bool pause;
102
103 public:
104  UserMonitor(socketstream& _s, ParMesh* _m, ParGridFunction* _u, int _vt) :
105  PetscSolverMonitor(true,false), sout(_s), pmesh(_m), u(_u), vt(_vt),
106  pause(true) {}
107
108  void MonitorSolution(PetscInt step, PetscReal norm, const Vector &X)
109  {
110  if (step % vt == 0)
111  {
112  int num_procs, myid;
113
114  *u = X;
115  MPI_Comm_size(pmesh->GetComm(),&num_procs);
116  MPI_Comm_rank(pmesh->GetComm(),&myid);
117  sout << "parallel " << num_procs << " " << myid << "\n";
118  sout << "solution\n" << *pmesh << *u;
119  if (pause) { sout << "pause\n"; }
120  sout << flush;
121  if (pause)
122  {
123  pause = false;
124  if (myid == 0)
125  {
126  cout << "GLVis visualization paused."
127  << " Press space (in the GLVis window) to resume it.\n";
128  }
129  }
130  }
131  }
132 };
133
134
135 int main(int argc, char *argv[])
136 {
137  // 1. Initialize MPI.
138  int num_procs, myid;
139  MPI_Init(&argc, &argv);
140  MPI_Comm_size(MPI_COMM_WORLD, &num_procs);
141  MPI_Comm_rank(MPI_COMM_WORLD, &myid);
142
143  // 2. Parse command-line options.
144  problem = 0;
145  const char *mesh_file = "../../data/periodic-hexagon.mesh";
146  int ser_ref_levels = 2;
147  int par_ref_levels = 0;
148  int order = 3;
149  int ode_solver_type = 4;
150  double t_final = 10.0;
151  double dt = 0.01;
152  bool visualization = true;
153  bool visit = false;
154  bool binary = false;
155  int vis_steps = 5;
156  bool use_petsc = true;
157  bool implicit = false;
158  bool use_step = true;
159  const char *petscrc_file = "";
160
161  int precision = 8;
162  cout.precision(precision);
163
164  OptionsParser args(argc, argv);
166  "Mesh file to use.");
168  "Problem setup to use. See options in velocity_function().");
170  "Number of times to refine the mesh uniformly in serial.");
172  "Number of times to refine the mesh uniformly in parallel.");
174  "Order (degree) of the finite elements.");
176  "ODE solver: 1 - Forward Euler,\n\t"
177  " 2 - RK2 SSP, 3 - RK3 SSP, 4 - RK4, 6 - RK6.");
179  "Final time; start time is 0.");
181  "Time step.");
183  "--no-visualization",
184  "Enable or disable GLVis visualization.");
186  "--no-visit-datafiles",
187  "Save data files for VisIt (visit.llnl.gov) visualization.");
189  "--ascii-datafiles",
190  "Use binary (Sidre) or ascii format for VisIt data files.");
192  "Visualize every n-th timestep.");
194  "--no-petsc",
195  "Use or not PETSc to solve the ODE system.");
197  "PetscOptions file to use.");
199  "--no-step",
200  "Use the Step() or Run() method to solve the ODE system.");
202  "--no-implicit",
203  "Use or not an implicit method in PETSc to solve the ODE system.");
204  args.Parse();
205  if (!args.Good())
206  {
207  if (myid == 0)
208  {
209  args.PrintUsage(cout);
210  }
211  MPI_Finalize();
212  return 1;
213  }
214  if (myid == 0)
215  {
216  args.PrintOptions(cout);
217  }
218
219  // 3. Read the serial mesh from the given mesh file on all processors. We can
220  // handle geometrically periodic meshes in this code.
221  Mesh *mesh = new Mesh(mesh_file, 1, 1);
222  int dim = mesh->Dimension();
223
224  // 4. Define the ODE solver used for time integration. Several explicit
225  // Runge-Kutta methods are available.
226  ODESolver *ode_solver = NULL;
227  PetscODESolver *pode_solver = NULL;
228  UserMonitor *pmon = NULL;
229  if (!use_petsc)
230  {
231  switch (ode_solver_type)
232  {
233  case 1: ode_solver = new ForwardEulerSolver; break;
234  case 2: ode_solver = new RK2Solver(1.0); break;
235  case 3: ode_solver = new RK3SSPSolver; break;
236  case 4: ode_solver = new RK4Solver; break;
237  case 6: ode_solver = new RK6Solver; break;
238  default:
239  if (myid == 0)
240  {
241  cout << "Unknown ODE solver type: " << ode_solver_type << '\n';
242  }
243  MPI_Finalize();
244  return 3;
245  }
246  }
247  else
248  {
249  // When using PETSc, we just create the ODE solver. We use command line
250  // customization to select a specific solver.
251  PetscInitialize(NULL, NULL, petscrc_file, NULL);
252  ode_solver = pode_solver = new PetscODESolver(MPI_COMM_WORLD);
253  }
254
255  // 5. Refine the mesh in serial to increase the resolution. In this example
256  // we do 'ser_ref_levels' of uniform refinement, where 'ser_ref_levels' is
257  // a command-line parameter. If the mesh is of NURBS type, we convert it
258  // to a (piecewise-polynomial) high-order mesh.
259  for (int lev = 0; lev < ser_ref_levels; lev++)
260  {
261  mesh->UniformRefinement();
262  }
263  if (mesh->NURBSext)
264  {
265  mesh->SetCurvature(max(order, 1));
266  }
267  mesh->GetBoundingBox(bb_min, bb_max, max(order, 1));
268
269  // 6. Define the parallel mesh by a partitioning of the serial mesh. Refine
270  // this mesh further in parallel to increase the resolution. Once the
271  // parallel mesh is defined, the serial mesh can be deleted.
272  ParMesh *pmesh = new ParMesh(MPI_COMM_WORLD, *mesh);
273  delete mesh;
274  for (int lev = 0; lev < par_ref_levels; lev++)
275  {
276  pmesh->UniformRefinement();
277  }
278
279  // 7. Define the parallel discontinuous DG finite element space on the
280  // parallel refined mesh of the given polynomial order.
281  DG_FECollection fec(order, dim);
282  ParFiniteElementSpace *fes = new ParFiniteElementSpace(pmesh, &fec);
283
284  HYPRE_Int global_vSize = fes->GlobalTrueVSize();
285  if (myid == 0)
286  {
287  cout << "Number of unknowns: " << global_vSize << endl;
288  }
289
290  // 8. Set up and assemble the parallel bilinear and linear forms (and the
291  // parallel hypre matrices) corresponding to the DG discretization. The
292  // DGTraceIntegrator involves integrals over mesh interior faces.
296
297  ParBilinearForm *m = new ParBilinearForm(fes);
299  ParBilinearForm *k = new ParBilinearForm(fes);
302  new TransposeIntegrator(new DGTraceIntegrator(velocity, 1.0, -0.5)));
304  new TransposeIntegrator(new DGTraceIntegrator(velocity, 1.0, -0.5)));
305
306  ParLinearForm *b = new ParLinearForm(fes);
308  new BoundaryFlowIntegrator(inflow, velocity, -1.0, -0.5));
309
310  m->Assemble();
311  m->Finalize();
312  int skip_zeros = 0;
313  k->Assemble(skip_zeros);
314  k->Finalize(skip_zeros);
315  b->Assemble();
316
320
321  // 9. Define the initial conditions, save the corresponding grid function to
322  // a file and (optionally) save data in the VisIt format and initialize
323  // GLVis visualization.
324  ParGridFunction *u = new ParGridFunction(fes);
325  u->ProjectCoefficient(u0);
326  HypreParVector *U = u->GetTrueDofs();
327
328  {
329  ostringstream mesh_name, sol_name;
330  mesh_name << "ex9-mesh." << setfill('0') << setw(6) << myid;
331  sol_name << "ex9-init." << setfill('0') << setw(6) << myid;
332  ofstream omesh(mesh_name.str().c_str());
333  omesh.precision(precision);
334  pmesh->Print(omesh);
335  ofstream osol(sol_name.str().c_str());
336  osol.precision(precision);
337  u->Save(osol);
338  }
339
340  // Create data collection for solution output: either VisItDataCollection for
341  // ascii data files, or SidreDataCollection for binary data files.
342  DataCollection *dc = NULL;
343  if (visit)
344  {
345  if (binary)
346  {
347 #ifdef MFEM_USE_SIDRE
348  dc = new SidreDataCollection("Example9-Parallel", pmesh);
349 #else
350  MFEM_ABORT("Must build with MFEM_USE_SIDRE=YES for binary output.");
351 #endif
352  }
353  else
354  {
355  dc = new VisItDataCollection("Example9-Parallel", pmesh);
356  dc->SetPrecision(precision);
357  }
358  dc->RegisterField("solution", u);
359  dc->SetCycle(0);
360  dc->SetTime(0.0);
361  dc->Save();
362  }
363
364  socketstream sout;
365  if (visualization)
366  {
367  char vishost[] = "localhost";
368  int visport = 19916;
369  sout.open(vishost, visport);
370  if (!sout)
371  {
372  if (myid == 0)
373  cout << "Unable to connect to GLVis server at "
374  << vishost << ':' << visport << endl;
375  visualization = false;
376  if (myid == 0)
377  {
378  cout << "GLVis visualization disabled.\n";
379  }
380  }
381  else if (use_step)
382  {
383  sout << "parallel " << num_procs << " " << myid << "\n";
384  sout.precision(precision);
385  sout << "solution\n" << *pmesh << *u;
386  sout << "pause\n";
387  sout << flush;
388  if (myid == 0)
389  cout << "GLVis visualization paused."
390  << " Press space (in the GLVis window) to resume it.\n";
391  }
392  else if (use_petsc)
393  {
394  // Set the monitoring routine for the PetscODESolver.
395  sout.precision(precision);
396  pmon = new UserMonitor(sout,pmesh,u,vis_steps);
397  pode_solver->SetMonitor(pmon);
398  }
399  }
400
401  // 10. Define the time-dependent evolution operator describing the ODE
402  FE_Evolution *adv = new FE_Evolution(*M, *K, *B, implicit);
403
404  double t = 0.0;
406  if (use_petsc)
407  {
409  }
410  else
411  {
413  }
414
415  // Explicitly perform time-integration (looping over the time iterations, ti,
416  // with a time-step dt), or use the Run method of the ODE solver class.
417  if (use_step)
418  {
419  bool done = false;
420  for (int ti = 0; !done; )
421  {
422  double dt_real = min(dt, t_final - t);
423  ode_solver->Step(*U, t, dt_real);
424  ti++;
425
426  done = (t >= t_final - 1e-8*dt);
427
428  if (done || ti % vis_steps == 0)
429  {
430  if (myid == 0)
431  {
432  cout << "time step: " << ti << ", time: " << t << endl;
433  }
434  // 11. Extract the parallel grid function corresponding to the finite
435  // element approximation U (the local solution on each processor).
436  *u = *U;
437
438  if (visualization)
439  {
440  sout << "parallel " << num_procs << " " << myid << "\n";
441  sout << "solution\n" << *pmesh << *u << flush;
442  }
443
444  if (visit)
445  {
446  dc->SetCycle(ti);
447  dc->SetTime(t);
448  dc->Save();
449  }
450  }
451  }
452  }
453  else { ode_solver->Run(*U, t, dt, t_final); }
454
455  // 12. Save the final solution in parallel. This output can be viewed later
456  // using GLVis: "glvis -np <np> -m ex9-mesh -g ex9-final".
457  {
458  *u = *U;
459  ostringstream sol_name;
460  sol_name << "ex9-final." << setfill('0') << setw(6) << myid;
461  ofstream osol(sol_name.str().c_str());
462  osol.precision(precision);
463  u->Save(osol);
464  }
465
466  // 13. Free the used memory.
467  delete U;
468  delete u;
469  delete B;
470  delete b;
471  delete K;
472  delete k;
473  delete M;
474  delete m;
475  delete fes;
476  delete pmesh;
477  delete ode_solver;
478  delete dc;
480
481  delete pmon;
482
483  // We finalize PETSc
484  if (use_petsc) { PetscFinalize(); }
485
486  MPI_Finalize();
487  return 0;
488 }
489
490
491 // Implementation of class FE_Evolution
493  const Vector &_b,bool M_in_lhs)
494  : TimeDependentOperator(_M.Height(), 0.0,
495  M_in_lhs ? TimeDependentOperator::IMPLICIT
496  : TimeDependentOperator::EXPLICIT),
497  M(_M), K(_K), b(_b), M_solver(M.GetComm()), z(_M.Height()),
498  iJacobian(NULL), rJacobian(NULL)
499 {
500  if (isExplicit())
501  {
502  M_prec.SetType(HypreSmoother::Jacobi);
503  M_solver.SetPreconditioner(M_prec);
504  M_solver.SetOperator(M);
505
506  M_solver.iterative_mode = false;
507  M_solver.SetRelTol(1e-9);
508  M_solver.SetAbsTol(0.0);
509  M_solver.SetMaxIter(100);
510  M_solver.SetPrintLevel(0);
511  }
512 }
513
514 // RHS evaluation
515 void FE_Evolution::ExplicitMult(const Vector &x, Vector &y) const
516 {
517  if (isExplicit())
518  {
519  // y = M^{-1} (K x + b)
520  K.Mult(x, z);
521  z += b;
522  M_solver.Mult(z, y);
523  }
524  else
525  {
526  // y = K x + b
527  K.Mult(x, y);
528  y += b;
529  }
530 }
531
532 // LHS evaluation
533 void FE_Evolution::ImplicitMult(const Vector &x, const Vector &xp,
534  Vector &y) const
535 {
536  if (isImplicit())
537  {
538  M.Mult(xp, y);
539  }
540  else
541  {
542  y = xp;
543  }
544 }
545
546 void FE_Evolution::Mult(const Vector &x, Vector &y) const
547 {
548  // y = M^{-1} (K x + b)
549  K.Mult(x, z);
550  z += b;
551  M_solver.Mult(z, y);
552 }
553
554 // RHS Jacobian
556 {
557  delete rJacobian;
558  if (isImplicit())
559  {
560  rJacobian = new PetscParMatrix(&K, Operator::PETSC_MATAIJ);
561  }
562  else
563  {
565  }
566  return *rJacobian;
567 }
568
569 // LHS Jacobian, evaluated as shift*F_du/dt + F_u
571  double shift) const
572 {
573  delete iJacobian;
574  if (isImplicit())
575  {
576  iJacobian = new PetscParMatrix(&M, Operator::PETSC_MATAIJ);
577  *iJacobian *= shift;
578  }
579  else
580  {
582  " Capability not coded!");
583  }
584  return *iJacobian;
585 }
586
587 // Velocity coefficient
588 void velocity_function(const Vector &x, Vector &v)
589 {
590  int dim = x.Size();
591
592  // map to the reference [-1,1] domain
593  Vector X(dim);
594  for (int i = 0; i < dim; i++)
595  {
596  double center = (bb_min[i] + bb_max[i]) * 0.5;
597  X(i) = 2 * (x(i) - center) / (bb_max[i] - bb_min[i]);
598  }
599
600  switch (problem)
601  {
602  case 0:
603  {
604  // Translations in 1D, 2D, and 3D
605  switch (dim)
606  {
607  case 1: v(0) = 1.0; break;
608  case 2: v(0) = sqrt(2./3.); v(1) = sqrt(1./3.); break;
609  case 3: v(0) = sqrt(3./6.); v(1) = sqrt(2./6.); v(2) = sqrt(1./6.);
610  break;
611  }
612  break;
613  }
614  case 1:
615  case 2:
616  {
617  // Clockwise rotation in 2D around the origin
618  const double w = M_PI/2;
619  switch (dim)
620  {
621  case 1: v(0) = 1.0; break;
622  case 2: v(0) = w*X(1); v(1) = -w*X(0); break;
623  case 3: v(0) = w*X(1); v(1) = -w*X(0); v(2) = 0.0; break;
624  }
625  break;
626  }
627  case 3:
628  {
629  // Clockwise twisting rotation in 2D around the origin
630  const double w = M_PI/2;
631  double d = max((X(0)+1.)*(1.-X(0)),0.) * max((X(1)+1.)*(1.-X(1)),0.);
632  d = d*d;
633  switch (dim)
634  {
635  case 1: v(0) = 1.0; break;
636  case 2: v(0) = d*w*X(1); v(1) = -d*w*X(0); break;
637  case 3: v(0) = d*w*X(1); v(1) = -d*w*X(0); v(2) = 0.0; break;
638  }
639  break;
640  }
641  }
642 }
643
644 // Initial condition
645 double u0_function(const Vector &x)
646 {
647  int dim = x.Size();
648
649  // map to the reference [-1,1] domain
650  Vector X(dim);
651  for (int i = 0; i < dim; i++)
652  {
653  double center = (bb_min[i] + bb_max[i]) * 0.5;
654  X(i) = 2 * (x(i) - center) / (bb_max[i] - bb_min[i]);
655  }
656
657  switch (problem)
658  {
659  case 0:
660  case 1:
661  {
662  switch (dim)
663  {
664  case 1:
665  return exp(-40.*pow(X(0)-0.5,2));
666  case 2:
667  case 3:
668  {
669  double rx = 0.45, ry = 0.25, cx = 0., cy = -0.2, w = 10.;
670  if (dim == 3)
671  {
672  const double s = (1. + 0.25*cos(2*M_PI*X(2)));
673  rx *= s;
674  ry *= s;
675  }
676  return ( erfc(w*(X(0)-cx-rx))*erfc(-w*(X(0)-cx+rx)) *
677  erfc(w*(X(1)-cy-ry))*erfc(-w*(X(1)-cy+ry)) )/16;
678  }
679  }
680  }
681  case 2:
682  {
683  double x_ = X(0), y_ = X(1), rho, phi;
684  rho = hypot(x_, y_);
685  phi = atan2(y_, x_);
686  return pow(sin(M_PI*rho),2)*sin(3*phi);
687  }
688  case 3:
689  {
690  const double f = M_PI;
691  return sin(f*X(0))*sin(f*X(1));
692  }
693  }
694  return 0.0;
695 }
696
697 // Inflow boundary condition (zero for the problems considered in this example)
698 double inflow_function(const Vector &x)
699 {
700  switch (problem)
701  {
702  case 0:
703  case 1:
704  case 2:
705  case 3: return 0.0;
706  }
707  return 0.0;
708 }
virtual void ImplicitMult(const Vector &x, const Vector &xp, Vector &y) const
Perform the action of the implicit part of the operator, F: y = F(x, k, t) where t is the current tim...
Definition: ex9p.cpp:533
Vector bb_max
Definition: ex9.cpp:52
void SetPrecision(int prec)
Set the precision (number of digits) used for the text output of doubles.
Definition: solvers.hpp:111
bool isImplicit() const
True if type is IMPLICIT or HOMOGENEOUS.
Definition: operator.hpp:186
void SetCycle(int c)
Set time cycle (for time-dependent simulations)
virtual void Mult(const Vector &b, Vector &x) const
Operator application: y=A(x).
Definition: solvers.cpp:295
virtual void Init(TimeDependentOperator &f)
Associate a TimeDependentOperator with the ODE solver.
Definition: ode.hpp:37
Wrapper for PETSc&#39;s matrix class.
Definition: petsc.hpp:133
Base abstract class for time dependent operators.
Definition: operator.hpp:151
void Mult(const Table &A, const Table &B, Table &C)
C = A * B (as boolean matrices)
Definition: table.cpp:478
void GetBoundingBox(Vector &min, Vector &max, int ref=2)
Definition: mesh.cpp:108
void Assemble()
Assembles the linear form i.e. sums over all domain/bdr integrators.
Definition: linearform.cpp:51
virtual void Step(Vector &x, double &t, double &dt)=0
Perform a time step from time t [in] to time t [out] based on the requested step size dt [in]...
virtual void SetTime(const double _t)
Set the current time.
Definition: operator.hpp:181
int Size() const
Returns the size of the vector.
Definition: vector.hpp:120
Abstract class for solving systems of ODEs: dx/dt = f(x,t)
Definition: ode.hpp:22
virtual void Save(std::ostream &out) const
Definition: pgridfunc.cpp:398
Abstract parallel finite element space.
Definition: pfespace.hpp:28
virtual void ProjectCoefficient(Coefficient &coeff)
Definition: pgridfunc.cpp:290
bool iterative_mode
If true, use the second argument of Mult() as an initial guess.
Definition: operator.hpp:272
void SetMonitor(PetscSolverMonitor *ctx)
Sets user-defined monitoring routine.
Definition: petsc.cpp:1479
int main(int argc, char *argv[])
Definition: ex1.cpp:45
Abstract class for PETSc&#39;s ODE solvers.
Definition: petsc.hpp:629
HypreParMatrix * ParallelAssemble()
Returns the matrix assembled on the true dofs, i.e. P^t A P.
FE_Evolution(FiniteElementSpace &_vfes, Operator &_A, SparseMatrix &_Aflux)
Definition: ex18.hpp:104
Data collection with Sidre routines following the Conduit mesh blueprint specification.
Class for parallel linear form.
Definition: plinearform.hpp:26
virtual void Init(TimeDependentOperator &f_, enum PetscODESolver::Type type)
Initialize the ODE solver.
Definition: petsc.cpp:2725
virtual void RegisterField(const std::string &field_name, GridFunction *gf)
Add a grid function to the collection.
int dim
Definition: ex3.cpp:47
void SetPrintLevel(int print_lvl)
Definition: solvers.cpp:72
Abstract class for monitoring PETSc&#39;s solvers.
Definition: petsc.hpp:661
virtual void Save()
Save the collection to disk.
void mfem_error(const char *msg)
Function called when an error is encountered. Used by the macros MFEM_ABORT, MFEM_ASSERT, MFEM_VERIFY.
Definition: error.cpp:146
void UniformRefinement(int i, const DSTable &, int *, int *, int *)
Definition: mesh.cpp:6741
Data collection with VisIt I/O routines.
void SetMaxIter(int max_it)
Definition: solvers.hpp:63
void SetCurvature(int order, bool discont=false, int space_dim=-1, int ordering=1)
Definition: mesh.cpp:3355
HYPRE_Int GlobalTrueVSize() const
Definition: pfespace.hpp:247
void Assemble(int skip_zeros=1)
Assemble the local matrix.
virtual void Print(std::ostream &out=mfem::out) const
Definition: pmesh.cpp:3428
Parallel smoothers in hypre.
Definition: hypre.hpp:517
Definition: linearform.cpp:38
bool isExplicit() const
True if type is EXPLICIT.
Definition: operator.hpp:184
int Dimension() const
Definition: mesh.hpp:645
void PrintUsage(std::ostream &out) const
Definition: optparser.cpp:434
void SetTime(double t)
Set physical time (for time-dependent simulations)
Vector bb_min
Definition: ex9.cpp:52
Wrapper for hypre&#39;s parallel vector class.
Definition: hypre.hpp:73
The classical explicit forth-order Runge-Kutta method, RK4.
Definition: ode.hpp:147
void SetAbsTol(double atol)
Definition: solvers.hpp:62
void SetRelTol(double rtol)
Definition: solvers.hpp:61
void velocity_function(const Vector &x, Vector &v)
Definition: ex9.cpp:340
virtual void Mult(const Vector &x, Vector &y) const
Matrix vector multiplication.
Definition: sparsemat.cpp:486
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)
Definition: optparser.hpp:74
int problem
Definition: ex15.cpp:57
Third-order, strong stability preserving (SSP) Runge-Kutta method.
Definition: ode.hpp:134
virtual Operator & GetExplicitGradient(const Vector &x) const
Return an Operator representing dG/dx at the given point x and the currently set time.
Definition: ex9p.cpp:555
virtual ~FE_Evolution()
Definition: ex9p.cpp:89
virtual void Mult(const Vector &x, Vector &y) const
Perform the action of the operator: y = k = f(x, t), where k solves the algebraic equation F(x...
Definition: ex18.hpp:130
NURBSExtension * NURBSext
Optional NURBS mesh extension.
Definition: mesh.hpp:176
virtual Operator & GetImplicitGradient(const Vector &x, const Vector &xp, double shift) const
Return an Operator representing (dF/dk shift + dF/dx) at the given x, k, and the currently set time...
Definition: ex9p.cpp:570
virtual void Finalize(int skip_zeros=1)
Finalizes the matrix initialization.
void PrintOptions(std::ostream &out) const
Definition: optparser.cpp:304
HypreParVector * GetTrueDofs() const
Returns the true dofs in a new HypreParVector.
Definition: pgridfunc.cpp:141
Class for parallel bilinear form.
int open(const char hostname[], int port)
double u0_function(const Vector &x)
Definition: ex9.cpp:397
virtual void SetOperator(const Operator &op)
Also calls SetOperator for the preconditioner if there is one.
Definition: solvers.hpp:125
class for C-function coefficient
Vector data type.
Definition: vector.hpp:48
virtual void SetPreconditioner(Solver &pr)
This should be called before SetOperator.
Definition: solvers.cpp:93
virtual void Run(Vector &x, double &t, double &dt, double tf)
Perform time integration from time t [in] to time tf [in].
Definition: ode.hpp:91
Class for parallel grid function.
Definition: pgridfunc.hpp:32
The classical forward Euler method.
Definition: ode.hpp:101
Abstract operator.
Definition: operator.hpp:21
Wrapper for hypre&#39;s ParCSR matrix class.
Definition: hypre.hpp:175
Class for parallel meshes.
Definition: pmesh.hpp:32
virtual void ExplicitMult(const Vector &x, Vector &y) const
Perform the action of the explicit part of the operator, G: y = G(x, t) where t is the current time...
Definition: ex9p.cpp:515
void ParallelAssemble(Vector &tv)
Assemble the vector on the true dofs, i.e. P^t v.
Definition: plinearform.cpp:34
double inflow_function(const Vector &x)
Definition: ex9.cpp:450