MFEM  v4.5.0
Finite element discretization library
ex21p.cpp
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1 // MFEM Example 21 - Parallel Version
2 //
3 // Compile with: make ex21p
4 //
5 // Sample runs: mpirun -np 4 ex21p
6 // mpirun -np 4 ex21p -o 3
7 // mpirun -np 4 ex21p -m ../data/beam-quad.mesh
8 // mpirun -np 4 ex21p -m ../data/beam-quad.mesh -o 3
9 // mpirun -np 4 ex21p -m ../data/beam-tet.mesh
10 // mpirun -np 4 ex21p -m ../data/beam-tet.mesh -o 2
11 // mpirun -np 4 ex21p -m ../data/beam-hex.mesh
12 // mpirun -np 4 ex21p -m ../data/beam-hex.mesh -o 2
13 //
14 // Description: This is a version of Example 2p with a simple adaptive mesh
15 // refinement loop. The problem being solved is again the linear
16 // elasticity describing a multi-material cantilever beam.
17 // The problem is solved on a sequence of meshes which
18 // are locally refined in a conforming (triangles, tetrahedrons)
19 // or non-conforming (quadrilaterals, hexahedra) manner according
20 // to a simple ZZ error estimator.
21 //
22 // The example demonstrates MFEM's capability to work with both
23 // conforming and nonconforming refinements, in 2D and 3D, on
24 // linear and curved meshes. Interpolation of functions from
25 // coarse to fine meshes, as well as persistent GLVis
26 // visualization are also illustrated.
27 //
28 // We recommend viewing Examples 2p and 6p before viewing this
29 // example.
30 
31 #include "mfem.hpp"
32 #include <fstream>
33 #include <iostream>
34 
35 using namespace std;
36 using namespace mfem;
37 
38 int main(int argc, char *argv[])
39 {
40  // 0. Initialize MPI and HYPRE.
41  Mpi::Init(argc, argv);
42  int num_procs = Mpi::WorldSize();
43  int myid = Mpi::WorldRank();
44  Hypre::Init();
45 
46  // 1. Parse command-line options.
47  const char *mesh_file = "../data/beam-tri.mesh";
48  int serial_ref_levels = 0;
49  int order = 1;
50  bool static_cond = false;
51  bool visualization = 1;
52 
53  OptionsParser args(argc, argv);
54  args.AddOption(&mesh_file, "-m", "--mesh",
55  "Mesh file to use.");
56  args.AddOption(&serial_ref_levels, "-rs", "--refine-serial",
57  "Number of uniform serial refinements (before parallel"
58  " partitioning)");
59  args.AddOption(&order, "-o", "--order",
60  "Finite element order (polynomial degree).");
61  args.AddOption(&static_cond, "-sc", "--static-condensation", "-no-sc",
62  "--no-static-condensation", "Enable static condensation.");
63  args.AddOption(&visualization, "-vis", "--visualization", "-no-vis",
64  "--no-visualization",
65  "Enable or disable GLVis visualization.");
66  args.Parse();
67  if (!args.Good())
68  {
69  if (myid == 0)
70  {
71  args.PrintUsage(cout);
72  }
73  return 1;
74  }
75  if (myid == 0)
76  {
77  args.PrintOptions(cout);
78  }
79 
80  // 2. Read the mesh from the given mesh file. We can handle triangular,
81  // quadrilateral, tetrahedral, and hexahedral meshes with the same code.
82  Mesh mesh(mesh_file, 1, 1);
83  int dim = mesh.Dimension();
84  MFEM_VERIFY(mesh.SpaceDimension() == dim, "invalid mesh");
85 
86  if (mesh.attributes.Max() < 2 || mesh.bdr_attributes.Max() < 2)
87  {
88  cerr << "\nInput mesh should have at least two materials and "
89  << "two boundary attributes! (See schematic in ex2.cpp)\n"
90  << endl;
91  return 3;
92  }
93 
94  // 3. Refine the mesh before parallel partitioning. Since a NURBS mesh can
95  // currently only be refined uniformly, we need to convert it to a
96  // piecewise-polynomial curved mesh. First we refine the NURBS mesh a bit
97  // more and then project the curvature to quadratic Nodes.
98  if (mesh.NURBSext && serial_ref_levels == 0)
99  {
100  serial_ref_levels = 2;
101  }
102  for (int i = 0; i < serial_ref_levels; i++)
103  {
104  mesh.UniformRefinement();
105  }
106  if (mesh.NURBSext)
107  {
108  mesh.SetCurvature(2);
109  }
110  mesh.EnsureNCMesh();
111 
112  ParMesh pmesh(MPI_COMM_WORLD, mesh);
113  mesh.Clear();
114 
115  // 4. Define a finite element space on the mesh. The polynomial order is
116  // one (linear) by default, but this can be changed on the command line.
117  H1_FECollection fec(order, dim);
118  ParFiniteElementSpace fespace(&pmesh, &fec, dim);
119 
120  // 5. As in Example 2, we set up the linear form b(.) which corresponds to
121  // the right-hand side of the FEM linear system. In this case, b_i equals
122  // the boundary integral of f*phi_i where f represents a "pull down"
123  // force on the Neumann part of the boundary and phi_i are the basis
124  // functions in the finite element fespace. The force is defined by the
125  // VectorArrayCoefficient object f, which is a vector of Coefficient
126  // objects. The fact that f is non-zero on boundary attribute 2 is
127  // indicated by the use of piece-wise constants coefficient for its last
128  // component. We don't assemble the discrete problem yet, this will be
129  // done in the main loop.
131  for (int i = 0; i < dim-1; i++)
132  {
133  f.Set(i, new ConstantCoefficient(0.0));
134  }
135  {
136  Vector pull_force(pmesh.bdr_attributes.Max());
137  pull_force = 0.0;
138  pull_force(1) = -1.0e-2;
139  f.Set(dim-1, new PWConstCoefficient(pull_force));
140  }
141 
142  ParLinearForm b(&fespace);
143  b.AddDomainIntegrator(new VectorBoundaryLFIntegrator(f));
144 
145  // 6. Set up the bilinear form a(.,.) on the finite element space
146  // corresponding to the linear elasticity integrator with piece-wise
147  // constants coefficient lambda and mu.
148  Vector lambda(pmesh.attributes.Max());
149  lambda = 1.0;
150  lambda(0) = lambda(1)*50;
151  PWConstCoefficient lambda_func(lambda);
152  Vector mu(pmesh.attributes.Max());
153  mu = 1.0;
154  mu(0) = mu(1)*50;
155  PWConstCoefficient mu_func(mu);
156 
157  ParBilinearForm a(&fespace);
158  BilinearFormIntegrator *integ =
159  new ElasticityIntegrator(lambda_func,mu_func);
160  a.AddDomainIntegrator(integ);
161  if (static_cond) { a.EnableStaticCondensation(); }
162 
163  // 7. The solution vector x and the associated finite element grid function
164  // will be maintained over the AMR iterations. We initialize it to zero.
165  Vector zero_vec(dim);
166  zero_vec = 0.0;
167  VectorConstantCoefficient zero_vec_coeff(zero_vec);
168  ParGridFunction x(&fespace);
169  x = 0.0;
170 
171  // 8. Determine the list of true (i.e. conforming) essential boundary dofs.
172  // In this example, the boundary conditions are defined by marking only
173  // boundary attribute 1 from the mesh as essential and converting it to a
174  // list of true dofs. The conversion to true dofs will be done in the
175  // main loop.
176  Array<int> ess_bdr(pmesh.bdr_attributes.Max());
177  ess_bdr = 0;
178  ess_bdr[0] = 1;
179 
180  // 9. GLVis visualization.
181  char vishost[] = "localhost";
182  int visport = 19916;
183  socketstream sol_sock;
184 
185  // 10. Set up an error estimator. Here we use the Zienkiewicz-Zhu estimator
186  // that uses the ComputeElementFlux method of the ElasticityIntegrator to
187  // recover a smoothed flux (stress) that is subtracted from the element
188  // flux to get an error indicator. We need to supply the space for the
189  // smoothed flux: an (H1)^tdim (i.e., vector-valued) space is used here.
190  // Here, tdim represents the number of components for a symmetric (dim x
191  // dim) tensor.
192  const int tdim = dim*(dim+1)/2;
193  L2_FECollection flux_fec(order, dim);
194  ParFiniteElementSpace flux_fespace(&pmesh, &flux_fec, tdim);
195  ParFiniteElementSpace smooth_flux_fespace(&pmesh, &fec, tdim);
196  L2ZienkiewiczZhuEstimator estimator(*integ, x, flux_fespace,
197  smooth_flux_fespace);
198 
199  // 11. A refiner selects and refines elements based on a refinement strategy.
200  // The strategy here is to refine elements with errors larger than a
201  // fraction of the maximum element error. Other strategies are possible.
202  // The refiner will call the given error estimator.
203  ThresholdRefiner refiner(estimator);
204  refiner.SetTotalErrorFraction(0.7);
205 
206  // 12. The main AMR loop. In each iteration we solve the problem on the
207  // current mesh, visualize the solution, and refine the mesh.
208  const int max_dofs = 50000;
209  const int max_amr_itr = 20;
210  for (int it = 0; it <= max_amr_itr; it++)
211  {
212  HYPRE_BigInt global_dofs = fespace.GlobalTrueVSize();
213  if (myid == 0)
214  {
215  cout << "\nAMR iteration " << it << endl;
216  cout << "Number of unknowns: " << global_dofs << endl;
217  }
218 
219  // 13. Assemble the stiffness matrix and the right-hand side.
220  a.Assemble();
221  b.Assemble();
222 
223  // 14. Set Dirichlet boundary values in the GridFunction x.
224  // Determine the list of Dirichlet true DOFs in the linear system.
225  Array<int> ess_tdof_list;
226  x.ProjectBdrCoefficient(zero_vec_coeff, ess_bdr);
227  fespace.GetEssentialTrueDofs(ess_bdr, ess_tdof_list);
228 
229  // 15. Create the linear system: eliminate boundary conditions, constrain
230  // hanging nodes and possibly apply other transformations. The system
231  // will be solved for true (unconstrained) DOFs only.
232 
233  HypreParMatrix A;
234  Vector B, X;
235  const int copy_interior = 1;
236  a.FormLinearSystem(ess_tdof_list, x, b, A, X, B, copy_interior);
237 
238  // 16. Define and apply a parallel PCG solver for AX=B with the BoomerAMG
239  // preconditioner from hypre.
240  HypreBoomerAMG amg;
241  amg.SetPrintLevel(0);
242  // amg.SetSystemsOptions(dim); // optional
243  CGSolver pcg(A.GetComm());
244  pcg.SetPreconditioner(amg);
245  pcg.SetOperator(A);
246  pcg.SetRelTol(1e-6);
247  pcg.SetMaxIter(500);
248  pcg.SetPrintLevel(3); // print the first and the last iterations only
249  pcg.Mult(B, X);
250 
251  // 17. After solving the linear system, reconstruct the solution as a
252  // finite element GridFunction. Constrained nodes are interpolated
253  // from true DOFs (it may therefore happen that x.Size() >= X.Size()).
254  a.RecoverFEMSolution(X, b, x);
255 
256  // 18. Send solution by socket to the GLVis server.
257  if (visualization && it == 0)
258  {
259  sol_sock.open(vishost, visport);
260  sol_sock.precision(8);
261  }
262  if (visualization && sol_sock.good())
263  {
264  GridFunction nodes(&fespace), *nodes_p = &nodes;
265  pmesh.GetNodes(nodes);
266  nodes += x;
267  int own_nodes = 0;
268  pmesh.SwapNodes(nodes_p, own_nodes);
269  x.Neg(); // visualize the backward displacement
270  sol_sock << "parallel " << num_procs << ' ' << myid << '\n';
271  sol_sock << "solution\n" << pmesh << x << flush;
272  x.Neg();
273  pmesh.SwapNodes(nodes_p, own_nodes);
274  if (it == 0)
275  {
276  sol_sock << "keys '" << ((dim == 2) ? "Rjl" : "") << "m'" << endl;
277  }
278  sol_sock << "window_title 'AMR iteration: " << it << "'\n"
279  << "pause" << endl;
280  if (myid == 0)
281  {
282  cout << "Visualization paused. "
283  "Press <space> in the GLVis window to continue." << endl;
284  }
285  }
286 
287  if (global_dofs > max_dofs)
288  {
289  if (myid == 0)
290  {
291  cout << "Reached the maximum number of dofs. Stop." << endl;
292  }
293  break;
294  }
295 
296  // 19. Call the refiner to modify the mesh. The refiner calls the error
297  // estimator to obtain element errors, then it selects elements to be
298  // refined and finally it modifies the mesh. The Stop() method can be
299  // used to determine if a stopping criterion was met.
300  refiner.Apply(pmesh);
301  if (refiner.Stop())
302  {
303  if (myid == 0)
304  {
305  cout << "Stopping criterion satisfied. Stop." << endl;
306  }
307  break;
308  }
309 
310  // 20. Update the space to reflect the new state of the mesh. Also,
311  // interpolate the solution x so that it lies in the new space but
312  // represents the same function. This saves solver iterations later
313  // since we'll have a good initial guess of x in the next step.
314  // Internally, FiniteElementSpace::Update() calculates an
315  // interpolation matrix which is then used by GridFunction::Update().
316  fespace.Update();
317  x.Update();
318 
319  // 21. Load balance the mesh, and update the space and solution. Currently
320  // available only for nonconforming meshes.
321  if (pmesh.Nonconforming())
322  {
323  pmesh.Rebalance();
324 
325  // Update the space and the GridFunction. This time the update matrix
326  // redistributes the GridFunction among the processors.
327  fespace.Update();
328  x.Update();
329  }
330 
331  // 21. Inform also the bilinear and linear forms that the space has
332  // changed.
333  a.Update();
334  b.Update();
335  }
336 
337  {
338  ostringstream mref_name, mesh_name, sol_name;
339  mref_name << "ex21p_reference_mesh." << setfill('0') << setw(6) << myid;
340  mesh_name << "ex21p_deformed_mesh." << setfill('0') << setw(6) << myid;
341  sol_name << "ex21p_displacement." << setfill('0') << setw(6) << myid;
342 
343  ofstream mesh_ref_out(mref_name.str().c_str());
344  mesh_ref_out.precision(16);
345  pmesh.Print(mesh_ref_out);
346 
347  ofstream mesh_out(mesh_name.str().c_str());
348  mesh_out.precision(16);
349  GridFunction nodes(&fespace), *nodes_p = &nodes;
350  pmesh.GetNodes(nodes);
351  nodes += x;
352  int own_nodes = 0;
353  pmesh.SwapNodes(nodes_p, own_nodes);
354  pmesh.Print(mesh_out);
355  pmesh.SwapNodes(nodes_p, own_nodes);
356 
357  ofstream x_out(sol_name.str().c_str());
358  x_out.precision(16);
359  x.Save(x_out);
360  }
361 
362  return 0;
363 }
virtual void GetEssentialTrueDofs(const Array< int > &bdr_attr_is_ess, Array< int > &ess_tdof_list, int component=-1)
Definition: pfespace.cpp:1032
Conjugate gradient method.
Definition: solvers.hpp:465
Vector coefficient defined by an array of scalar coefficients. Coefficients that are not set will eva...
Class for grid function - Vector with associated FE space.
Definition: gridfunc.hpp:30
int main(int argc, char *argv[])
Definition: ex21p.cpp:38
A coefficient that is constant across space and time.
Definition: coefficient.hpp:84
void PrintOptions(std::ostream &out) const
Print the options.
Definition: optparser.cpp:324
int Dimension() const
Definition: mesh.hpp:1006
void PrintUsage(std::ostream &out) const
Print the usage message.
Definition: optparser.cpp:454
Vector coefficient that is constant in space and time.
void SwapNodes(GridFunction *&nodes, int &own_nodes_)
Definition: mesh.cpp:7943
virtual void Update(bool want_transform=true)
Definition: pfespace.cpp:3287
bool Nonconforming() const
Definition: mesh.hpp:1651
T Max() const
Find the maximal element in the array, using the comparison operator < for class T.
Definition: array.cpp:68
bool Good() const
Return true if the command line options were parsed successfully.
Definition: optparser.hpp:150
Abstract parallel finite element space.
Definition: pfespace.hpp:28
STL namespace.
The L2ZienkiewiczZhuEstimator class implements the Zienkiewicz-Zhu error estimation procedure where t...
Definition: estimators.hpp:328
The BoomerAMG solver in hypre.
Definition: hypre.hpp:1579
bool Apply(Mesh &mesh)
Perform the mesh operation.
void Rebalance()
Definition: pmesh.cpp:3989
Class for parallel linear form.
Definition: plinearform.hpp:26
void Parse()
Parse the command-line options. Note that this function expects all the options provided through the ...
Definition: optparser.cpp:151
constexpr char vishost[]
void EnsureNCMesh(bool simplices_nonconforming=false)
Definition: mesh.cpp:9459
virtual void Update()
Transform by the Space UpdateMatrix (e.g., on Mesh change).
Definition: pgridfunc.cpp:81
double b
Definition: lissajous.cpp:42
void UniformRefinement(int i, const DSTable &, int *, int *, int *)
Definition: mesh.cpp:9802
void SetPrintLevel(int print_level)
Definition: hypre.hpp:1659
constexpr int visport
Mesh refinement operator using an error threshold.
virtual void SetCurvature(int order, bool discont=false, int space_dim=-1, int ordering=1)
Definition: mesh.cpp:5343
HYPRE_BigInt GlobalTrueVSize() const
Definition: pfespace.hpp:285
MPI_Comm GetComm() const
MPI communicator.
Definition: hypre.hpp:534
Abstract base class BilinearFormIntegrator.
Definition: bilininteg.hpp:35
Array< int > bdr_attributes
A list of all unique boundary attributes used by the Mesh.
Definition: mesh.hpp:270
void ProjectBdrCoefficient(Coefficient *coeff[], VectorCoefficient *vcoeff, Array< int > &attr)
Definition: pgridfunc.cpp:633
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
HYPRE_Int HYPRE_BigInt
int SpaceDimension() const
Definition: mesh.hpp:1007
virtual void Save(std::ostream &out) const
Definition: pgridfunc.cpp:873
double a
Definition: lissajous.cpp:41
NURBSExtension * NURBSext
Optional NURBS mesh extension.
Definition: mesh.hpp:272
A piecewise constant coefficient with the constants keyed off the element attribute numbers...
double mu
Definition: ex25.cpp:139
int dim
Definition: ex24.cpp:53
Class for parallel bilinear form.
int open(const char hostname[], int port)
Open the socket stream on &#39;port&#39; at &#39;hostname&#39;.
void Clear()
Clear the contents of the Mesh.
Definition: mesh.hpp:899
Vector data type.
Definition: vector.hpp:60
virtual void SetPreconditioner(Solver &pr)
This should be called before SetOperator.
Definition: solvers.cpp:173
Arbitrary order H1-conforming (continuous) finite elements.
Definition: fe_coll.hpp:220
void GetNodes(Vector &node_coord) const
Definition: mesh.cpp:7894
void Print(std::ostream &out=mfem::out) const override
Definition: pmesh.cpp:4770
Class for parallel grid function.
Definition: pgridfunc.hpp:32
void SetTotalErrorFraction(double fraction)
Set the total fraction used in the computation of the threshold. The default value is 1/2...
Wrapper for hypre&#39;s ParCSR matrix class.
Definition: hypre.hpp:343
bool Stop() const
Check if STOP action is requested, e.g. stopping criterion is satisfied.
Class for parallel meshes.
Definition: pmesh.hpp:32
Array< int > attributes
A list of all unique element attributes used by the Mesh.
Definition: mesh.hpp:268
Arbitrary order "L2-conforming" discontinuous finite elements.
Definition: fe_coll.hpp:288
double f(const Vector &p)
void Neg()
(*this) = -(*this)
Definition: vector.cpp:305