MFEM v4.7.0 Finite element discretization library
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ex28p.cpp
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1// MFEM Example 28 - Parallel Version
2//
3// Compile with: make ex28p
4//
5// Sample runs: ex28p
6// ex28p --visit-datafiles
7// ex28p --order 4
8// ex28p --penalty 1e+5
9//
10// mpirun -np 4 ex28p
11// mpirun -np 4 ex28p --penalty 1e+5
12//
13// Description: Demonstrates a sliding boundary condition in an elasticity
14// problem. A trapezoid, roughly as pictured below, is pushed
15// from the right into a rigid notch. Normal displacement is
16// restricted, but tangential movement is allowed, so the
17// trapezoid compresses into the notch.
18//
19// /-------+
20// normal constrained --->/ | <--- boundary force (2)
21// boundary (4) /---------+
22// ^
23// |
24// normal constrained boundary (1)
25//
26// This example demonstrates the use of the ConstrainedSolver
27// framework.
28//
29// We recommend viewing Example 2 before viewing this example.
30
31#include "mfem.hpp"
32#include <fstream>
33#include <iostream>
34
35using namespace std;
36using namespace mfem;
37
38// Return a mesh with a single element with vertices (0, 0), (1, 0), (1, 1),
39// (offset, 1) to demonstrate boundary conditions on a surface that is not
40// axis-aligned.
42{
43 MFEM_VERIFY(offset < 0.9, "offset is too large!");
44
45 const int dimension = 2;
46 const int nvt = 4; // vertices
47 const int nbe = 4; // num boundary elements
48 Mesh * mesh = new Mesh(dimension, nvt, 1, nbe);
49
50 // vertices
51 real_t vc[dimension];
52 vc[0] = 0.0; vc[1] = 0.0;
54 vc[0] = 1.0; vc[1] = 0.0;
56 vc[0] = offset; vc[1] = 1.0;
58 vc[0] = 1.0; vc[1] = 1.0;
60
61 // element
62 Array<int> vert(4);
63 vert[0] = 0; vert[1] = 1; vert[2] = 3; vert[3] = 2;
65
66 // boundary
67 Array<int> sv(2);
68 sv[0] = 0; sv[1] = 1;
70 sv[0] = 1; sv[1] = 3;
72 sv[0] = 2; sv[1] = 3;
74 sv[0] = 0; sv[1] = 2;
76
78
79 return mesh;
80}
81
82int main(int argc, char *argv[])
83{
84#ifdef HYPRE_USING_GPU
85 cout << "\nAs of mfem-4.3 and hypre-2.22.0 (July 2021) this example\n"
86 << "is NOT supported with the GPU version of hypre.\n\n";
87 return MFEM_SKIP_RETURN_VALUE;
88#endif
89
90 // 1. Initialize MPI and HYPRE.
91 Mpi::Init(argc, argv);
92 int num_procs = Mpi::WorldSize();
93 int myid = Mpi::WorldRank();
95
96 // 2. Parse command-line options.
97 int order = 1;
98 bool visualization = 1;
99 bool reorder_space = false;
100 real_t offset = 0.3;
101 bool visit = false;
102 real_t penalty = 0.0;
103
104 OptionsParser args(argc, argv);
106 "Finite element order (polynomial degree).");
108 "--no-visualization",
109 "Enable or disable GLVis visualization.");
110 args.AddOption(&reorder_space, "-nodes", "--by-nodes", "-vdim", "--by-vdim",
111 "Use byNODES ordering of vector space instead of byVDIM");
113 "How much to offset the trapezoid.");
115 "--no-visit-datafiles",
116 "Save data files for VisIt (visit.llnl.gov) visualization.");
118 "Penalty parameter; 0 means use elimination solver.");
119 args.Parse();
120 if (!args.Good())
121 {
122 if (myid == 0)
123 {
124 args.PrintUsage(cout);
125 }
126 return 1;
127 }
128 if (myid == 0)
129 {
130 args.PrintOptions(cout);
131 }
132
133 // 3. Build a trapezoidal mesh with a single quadrilateral element, where
134 // 'offset' determines how far off it is from a rectangle.
135 Mesh *mesh = build_trapezoid_mesh(offset);
136 int dim = mesh->Dimension();
137
138 // 4. Refine the serial mesh on all processors to increase the resolution. In
139 // this example we do 'ref_levels' of uniform refinement. We choose
140 // 'ref_levels' to be the largest number that gives a final mesh with no
141 // more than 1,000 elements.
142 {
143 int ref_levels =
144 (int)floor(log(1000./mesh->GetNE())/log(2.)/dim);
145 for (int l = 0; l < ref_levels; l++)
146 {
147 mesh->UniformRefinement();
148 }
149 }
150
151 // 5. Define a parallel mesh by a partitioning of the serial mesh. Refine
152 // this mesh further in parallel to increase the resolution. Once the
153 // parallel mesh is defined, the serial mesh can be deleted.
154 ParMesh *pmesh = new ParMesh(MPI_COMM_WORLD, *mesh);
155 delete mesh;
156 {
157 int par_ref_levels = 1;
158 for (int l = 0; l < par_ref_levels; l++)
159 {
160 pmesh->UniformRefinement();
161 }
162 }
163
164 // 6. Define a parallel finite element space on the parallel mesh. Here we
165 // use vector finite elements, i.e. dim copies of a scalar finite element
166 // space. We use the ordering by vector dimension (the last argument of
167 // the FiniteElementSpace constructor) which is expected in the systems
168 // version of BoomerAMG preconditioner. For NURBS meshes, we use the
169 // (degree elevated) NURBS space associated with the mesh nodes.
171 ParFiniteElementSpace *fespace;
172 const bool use_nodal_fespace = pmesh->NURBSext;
173 if (use_nodal_fespace)
174 {
175 fec = NULL;
176 fespace = (ParFiniteElementSpace *)pmesh->GetNodes()->FESpace();
177 }
178 else
179 {
180 fec = new H1_FECollection(order, dim);
181 if (reorder_space)
182 {
183 fespace = new ParFiniteElementSpace(pmesh, fec, dim, Ordering::byNODES);
184 }
185 else
186 {
187 fespace = new ParFiniteElementSpace(pmesh, fec, dim, Ordering::byVDIM);
188 }
189 }
190 HYPRE_BigInt size = fespace->GlobalTrueVSize();
191 if (myid == 0)
192 {
193 cout << "Number of finite element unknowns: " << size << endl
194 << "Assembling matrix and r.h.s... " << flush;
195 }
196
197 // 7. Determine the list of true (i.e. parallel conforming) essential
198 // boundary dofs. In this example, there are no essential boundary
199 // conditions in the usual sense, but we leave the machinery here for
200 // users to modify if they wish.
201 Array<int> ess_tdof_list, ess_bdr(pmesh->bdr_attributes.Max());
202 ess_bdr = 0;
203 fespace->GetEssentialTrueDofs(ess_bdr, ess_tdof_list);
204
205 // 8. Set up the parallel linear form b(.) which corresponds to the
206 // right-hand side of the FEM linear system. In this case, b_i equals the
207 // boundary integral of f*phi_i where f represents a "pull down" force on
208 // the Neumann part of the boundary and phi_i are the basis functions in
209 // the finite element fespace. The force is defined by the object f, which
210 // is a vector of Coefficient objects. The fact that f is non-zero on
211 // boundary attribute 2 is indicated by the use of piece-wise constants
212 // coefficient for its last component.
214 for (int i = 0; i < dim-1; i++)
215 {
216 f.Set(i, new ConstantCoefficient(0.0));
217 }
218
219 // 9. Put a leftward force on the right side of the trapezoid
220 {
221 Vector push_force(pmesh->bdr_attributes.Max());
222 push_force = 0.0;
223 push_force(1) = -5.0e-2; // index 1 attribute 2
224 f.Set(0, new PWConstCoefficient(push_force));
225 }
226
227 ParLinearForm *b = new ParLinearForm(fespace);
229 b->Assemble();
230
231 // 10. Define the solution vector x as a parallel finite element grid
232 // function corresponding to fespace. Initialize x with initial guess of
233 // zero, which satisfies the boundary conditions.
234 ParGridFunction x(fespace);
235 x = 0.0;
236
237 // 11. Set up the parallel bilinear form a(.,.) on the finite element space
238 // corresponding to the linear elasticity integrator with piece-wise
239 // constants coefficient lambda and mu. We use constant coefficients,
240 // but see ex2 for how to set up piecewise constant coefficients based
241 // on attribute.
242 Vector lambda(pmesh->attributes.Max());
243 lambda = 1.0;
244 PWConstCoefficient lambda_func(lambda);
245 Vector mu(pmesh->attributes.Max());
246 mu = 1.0;
247 PWConstCoefficient mu_func(mu);
248 ParBilinearForm *a = new ParBilinearForm(fespace);
250
251 // 12. Assemble the parallel bilinear form and the corresponding linear
252 // system, applying any necessary transformations such as: parallel
253 // assembly, eliminating boundary conditions, applying conforming
254 // constraints for non-conforming AMR, etc.
255 a->Assemble();
256
258 Vector B, X;
259 a->FormLinearSystem(ess_tdof_list, x, *b, A, X, B);
260 if (myid == 0)
261 {
262 cout << "done." << endl;
263 cout << "Size of linear system: " << A.GetGlobalNumRows() << endl;
264 }
265
266 // 13. Set up constraint matrix to constrain normal displacement (but
267 // allow tangential displacement) on specified boundaries.
268 Array<int> constraint_atts(2);
269 constraint_atts[0] = 1; // attribute 1 bottom
270 constraint_atts[1] = 4; // attribute 4 left side
271 Array<int> constraint_rowstarts;
272 SparseMatrix* local_constraints =
273 ParBuildNormalConstraints(*fespace, constraint_atts,
274 constraint_rowstarts);
275
276 // 14. Define and apply a parallel PCG solver for the constrained system
277 // where the normal boundary constraints have been separately eliminated
278 // from the system.
279 ConstrainedSolver * solver;
280 if (penalty == 0.0)
281 {
282 solver = new EliminationCGSolver(A, *local_constraints,
283 constraint_rowstarts, dim,
284 reorder_space);
285 }
286 else
287 {
288 solver = new PenaltyPCGSolver(A, *local_constraints, penalty,
289 dim, reorder_space);
290 }
291
292 solver->SetRelTol(1e-8);
293 solver->SetMaxIter(500);
294 solver->SetPrintLevel(1);
295 solver->Mult(B, X);
296
297 // 15. Recover the parallel grid function corresponding to X. This is the
298 // local finite element solution on each processor.
299 a->RecoverFEMSolution(X, *b, x);
300
301 // 16. For non-NURBS meshes, make the mesh curved based on the finite element
302 // space. This means that we define the mesh elements through a fespace
303 // based transformation of the reference element. This allows us to save
304 // the displaced mesh as a curved mesh when using high-order finite
305 // element displacement field. We assume that the initial mesh (read from
306 // the file) is not higher order curved mesh compared to the chosen FE
307 // space.
308 if (!use_nodal_fespace)
309 {
310 pmesh->SetNodalFESpace(fespace);
311 }
312
313 GridFunction *nodes = pmesh->GetNodes();
314 *nodes += x;
315
316 // 17. Save the refined mesh and the solution in VisIt format.
317 if (visit)
318 {
319 VisItDataCollection visit_dc(MPI_COMM_WORLD, "ex28p", pmesh);
320 visit_dc.SetLevelsOfDetail(4);
321 visit_dc.RegisterField("displacement", &x);
322 visit_dc.Save();
323 }
324
325 // 18. Save in parallel the displaced mesh and the inverted solution (which
326 // gives the backward displacements to the original grid). This output
327 // can be viewed later using GLVis: "glvis -np <np> -m mesh -g sol".
328 {
329 x *= -1; // sign convention for GLVis displacements
330
331 ostringstream mesh_name, sol_name;
332 mesh_name << "mesh." << setfill('0') << setw(6) << myid;
333 sol_name << "sol." << setfill('0') << setw(6) << myid;
334
335 ofstream mesh_ofs(mesh_name.str().c_str());
336 mesh_ofs.precision(8);
337 pmesh->Print(mesh_ofs);
338
339 ofstream sol_ofs(sol_name.str().c_str());
340 sol_ofs.precision(8);
341 x.Save(sol_ofs);
342 }
343
344 // 19. Send the above data by socket to a GLVis server. Use the "n" and "b"
345 // keys in GLVis to visualize the displacements.
346 if (visualization)
347 {
348 char vishost[] = "localhost";
349 int visport = 19916;
350 socketstream sol_sock(vishost, visport);
351 sol_sock << "parallel " << num_procs << " " << myid << "\n";
352 sol_sock.precision(8);
353 sol_sock << "solution\n" << *pmesh << x << flush;
354 }
355
356 // 20. Free the used memory.
357 delete local_constraints;
358 delete solver;
359 delete a;
360 delete b;
361 if (fec)
362 {
363 delete fespace;
364 delete fec;
365 }
366 delete pmesh;
367
368 // HYPRE_Finalize();
369
370 return 0;
371}
T Max() const
Find the maximal element in the array, using the comparison operator < for class T.
Definition array.cpp:68
A coefficient that is constant across space and time.
An abstract class to solve the constrained system subject to the constraint .
virtual void Mult(const Vector &f, Vector &x) const override
Solve for given .
Collection of finite elements from the same family in multiple dimensions. This class is used to matc...
Definition fe_coll.hpp:27
Class for grid function - Vector with associated FE space.
Definition gridfunc.hpp:31
Arbitrary order H1-conforming (continuous) finite elements.
Definition fe_coll.hpp:260
Wrapper for hypre's ParCSR matrix class.
Definition hypre.hpp:388
HYPRE_BigInt GetGlobalNumRows() const
Return the global number of rows.
Definition hypre.hpp:679
static void Init()
Initialize hypre by calling HYPRE_Init() and set default options. After calling Hypre::Init(),...
Definition hypre.hpp:74
void SetRelTol(real_t rtol)
Definition solvers.hpp:209
virtual void SetPrintLevel(int print_lvl)
Legacy method to set the level of verbosity of the solver output.
Definition solvers.cpp:71
void SetMaxIter(int max_it)
Definition solvers.hpp:211
Mesh data type.
Definition mesh.hpp:56
Array< int > bdr_attributes
A list of all unique boundary attributes used by the Mesh.
Definition mesh.hpp:282
NURBSExtension * NURBSext
Optional NURBS mesh extension.
Definition mesh.hpp:290
Adds a quadrilateral to the mesh given by 4 vertices v1 through v4.
Definition mesh.cpp:1743
int AddVertex(real_t x, real_t y=0.0, real_t z=0.0)
Definition mesh.cpp:1658
int GetNE() const
Returns number of elements.
Definition mesh.hpp:1226
int Dimension() const
Dimension of the reference space used within the elements.
Definition mesh.hpp:1160
int AddBdrSegment(int v1, int v2, int attr=1)
Definition mesh.cpp:2035
void FinalizeQuadMesh(int generate_edges=0, int refine=0, bool fix_orientation=true)
Finalize the construction of a quadrilateral Mesh.
Definition mesh.cpp:2177
void GetNodes(Vector &node_coord) const
Definition mesh.cpp:8973
void UniformRefinement(int i, const DSTable &, int *, int *, int *)
Definition mesh.cpp:10970
Array< int > attributes
A list of all unique element attributes used by the Mesh.
Definition mesh.hpp:280
static int WorldRank()
Return the MPI rank in MPI_COMM_WORLD.
static int WorldSize()
Return the size of MPI_COMM_WORLD.
static void Init(int &argc, char **&argv, int required=default_thread_required, int *provided=nullptr)
Singleton creation with Mpi::Init(argc, argv).
void Parse()
Parse the command-line options. Note that this function expects all the options provided through the ...
void PrintUsage(std::ostream &out) const
Print the usage message.
void PrintOptions(std::ostream &out) const
Print the options.
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 'var' to receive the value. Enable/disable tags are used to set the bool...
Definition optparser.hpp:82
bool Good() const
Return true if the command line options were parsed successfully.
A piecewise constant coefficient with the constants keyed off the element attribute numbers.
Class for parallel bilinear form.
Abstract parallel finite element space.
Definition pfespace.hpp:29
void GetEssentialTrueDofs(const Array< int > &bdr_attr_is_ess, Array< int > &ess_tdof_list, int component=-1) const override
HYPRE_BigInt GlobalTrueVSize() const
Definition pfespace.hpp:285
Class for parallel grid function.
Definition pgridfunc.hpp:33
void Save(std::ostream &out) const override
Class for parallel linear form.
Class for parallel meshes.
Definition pmesh.hpp:34
void SetNodalFESpace(FiniteElementSpace *nfes) override
Definition pmesh.cpp:2028
void Print(std::ostream &out=mfem::out, const std::string &comments="") const override
Definition pmesh.cpp:4801
Data type sparse matrix.
Definition sparsemat.hpp:51
Vector coefficient defined by an array of scalar coefficients. Coefficients that are not set will eva...
Vector data type.
Definition vector.hpp:80
Vector & Set(const real_t a, const Vector &x)
(*this) = a * x
Definition vector.cpp:262
Data collection with VisIt I/O routines.
void SetLevelsOfDetail(int levels_of_detail)
Set VisIt parameter: default levels of detail for the MultiresControl.
virtual void Save() override
Save the collection and a VisIt root file.
virtual void RegisterField(const std::string &field_name, GridFunction *gf) override
Add a grid function to the collection and update the root file.
int dim
Definition ex24.cpp:53
real_t mu
Definition ex25.cpp:140
Mesh * build_trapezoid_mesh(real_t offset)
Definition ex28p.cpp:41
int main()
constexpr int dimension
This example only works in 3D. Kernels for 2D are not implemented.
Definition hooke.cpp:45
HYPRE_Int HYPRE_BigInt
real_t b
Definition lissajous.cpp:42
real_t a
Definition lissajous.cpp:41
const int visport
SparseMatrix * ParBuildNormalConstraints(ParFiniteElementSpace &fespace, Array< int > &constrained_att, Array< int > &constraint_rowstarts)
Parallel wrapper for BuildNormalConstraints.
float real_t
Definition config.hpp:43
std::function< real_t(const Vector &)> f(real_t mass_coeff)
Definition lor_mms.hpp:30
const char vishost[]