MFEM  v4.6.0
Finite element discretization library
ex1.cpp
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1 // MFEM Example 1 - High-Performance Version
2 //
3 // Compile with: make ex1
4 //
5 // Sample runs: ex1 -m ../../data/fichera.mesh -perf -mf -pc lor
6 // ex1 -m ../../data/fichera.mesh -perf -asm -pc ho
7 // ex1 -m ../../data/fichera.mesh -perf -asm -pc ho -sc
8 // ex1 -m ../../data/fichera.mesh -std -asm -pc ho
9 // ex1 -m ../../data/fichera.mesh -std -asm -pc ho -sc
10 // ex1 -m ../../data/amr-hex.mesh -perf -asm -pc ho -sc
11 // ex1 -m ../../data/amr-hex.mesh -std -asm -pc ho -sc
12 // ex1 -m ../../data/ball-nurbs.mesh -perf -asm -pc ho -sc
13 // ex1 -m ../../data/ball-nurbs.mesh -std -asm -pc ho -sc
14 // ex1 -m ../../data/pipe-nurbs.mesh -perf -mf -pc lor
15 // ex1 -m ../../data/pipe-nurbs.mesh -std -asm -pc ho -sc
16 // ex1 -m ../../data/star.mesh -perf -mf -pc lor
17 // ex1 -m ../../data/star.mesh -perf -asm -pc ho
18 // ex1 -m ../../data/star.mesh -perf -asm -pc ho -sc
19 // ex1 -m ../../data/star.mesh -std -asm -pc ho
20 // ex1 -m ../../data/star.mesh -std -asm -pc ho -sc
21 // ex1 -m ../../data/amr-quad.mesh -perf -asm -pc ho -sc
22 // ex1 -m ../../data/amr-quad.mesh -std -asm -pc ho -sc
23 // ex1 -m ../../data/disc-nurbs.mesh -perf -asm -pc ho -sc
24 // ex1 -m ../../data/disc-nurbs.mesh -std -asm -pc ho -sc
25 //
26 // Description: This example code demonstrates the use of MFEM to define a
27 // simple finite element discretization of the Laplace problem
28 // -Delta u = 1 with homogeneous Dirichlet boundary conditions.
29 // Specifically, we discretize using a FE space of the specified
30 // order, or if order < 1 using an isoparametric/isogeometric
31 // space (i.e. quadratic for quadratic curvilinear mesh, NURBS for
32 // NURBS mesh, etc.)
33 //
34 // The example highlights the use of mesh refinement, finite
35 // element grid functions, as well as linear and bilinear forms
36 // corresponding to the left-hand side and right-hand side of the
37 // discrete linear system. We also cover the explicit elimination
38 // of essential boundary conditions, static condensation, and the
39 // optional connection to the GLVis tool for visualization.
40 
41 #include "mfem-performance.hpp"
42 #include <fstream>
43 #include <iostream>
44 
45 using namespace std;
46 using namespace mfem;
47 
48 enum class PCType { NONE, LOR, HO };
49 
50 // Define template parameters for optimized build.
51 template <int dim> struct geom_t { };
52 template <>
53 struct geom_t<2> { static const Geometry::Type value = Geometry::SQUARE; };
54 template <>
55 struct geom_t<3> { static const Geometry::Type value = Geometry::CUBE; };
56 
57 const int mesh_p = 3; // mesh curvature (default: 3)
58 const int sol_p = 3; // solution order (default: 3)
59 
60 template <int dim>
61 struct ex1_t
62 {
63  static const Geometry::Type geom = geom_t<dim>::value;
64  static const int rdim = Geometry::Constants<geom>::Dimension;
65  static const int ir_order = 2*sol_p+rdim-1;
66 
67  // Static mesh type
68  using mesh_fe_t = H1_FiniteElement<geom,mesh_p>;
69  using mesh_fes_t = H1_FiniteElementSpace<mesh_fe_t>;
70  using mesh_t = TMesh<mesh_fes_t>;
71 
72  // Static solution finite element space type
73  using sol_fe_t = H1_FiniteElement<geom,sol_p>;
74  using sol_fes_t = H1_FiniteElementSpace<sol_fe_t>;
75 
76  // Static quadrature, coefficient and integrator types
77  using int_rule_t = TIntegrationRule<geom,ir_order>;
78  using coeff_t = TConstantCoefficient<>;
80 
82 
83  static int run(Mesh *mesh, int ref_levels, int order, int basis,
84  bool static_cond, PCType pc_choice, bool perf,
85  bool matrix_free, bool visualization);
86 };
87 
88 int main(int argc, char *argv[])
89 {
90  // 1. Parse command-line options.
91  const char *mesh_file = "../../data/fichera.mesh";
92  int ref_levels = -1;
93  int order = sol_p;
94  const char *basis_type = "G"; // Gauss-Lobatto
95  bool static_cond = false;
96  const char *pc = "none";
97  bool perf = true;
98  bool matrix_free = true;
99  bool visualization = 1;
100 
101  OptionsParser args(argc, argv);
102  args.AddOption(&mesh_file, "-m", "--mesh",
103  "Mesh file to use.");
104  args.AddOption(&ref_levels, "-r", "--refine",
105  "Number of times to refine the mesh uniformly;"
106  " -1 = auto: <= 50,000 elements.");
107  args.AddOption(&order, "-o", "--order",
108  "Finite element order (polynomial degree) or -1 for"
109  " isoparametric space.");
110  args.AddOption(&basis_type, "-b", "--basis-type",
111  "Basis: G - Gauss-Lobatto, P - Positive, U - Uniform");
112  args.AddOption(&perf, "-perf", "--hpc-version", "-std", "--standard-version",
113  "Enable high-performance, tensor-based, assembly/evaluation.");
114  args.AddOption(&matrix_free, "-mf", "--matrix-free", "-asm", "--assembly",
115  "Use matrix-free evaluation or efficient matrix assembly in "
116  "the high-performance version.");
117  args.AddOption(&pc, "-pc", "--preconditioner",
118  "Preconditioner: lor - low-order-refined (matrix-free) GS, "
119  "ho - high-order (assembled) GS, none.");
120  args.AddOption(&static_cond, "-sc", "--static-condensation", "-no-sc",
121  "--no-static-condensation", "Enable static condensation.");
122  args.AddOption(&visualization, "-vis", "--visualization", "-no-vis",
123  "--no-visualization",
124  "Enable or disable GLVis visualization.");
125  args.Parse();
126  if (!args.Good())
127  {
128  args.PrintUsage(cout);
129  return 1;
130  }
131  if (static_cond && perf && matrix_free)
132  {
133  cout << "\nStatic condensation can not be used with matrix-free"
134  " evaluation!\n" << endl;
135  return 2;
136  }
137  MFEM_VERIFY(perf || !matrix_free,
138  "--standard-version is not compatible with --matrix-free");
139  args.PrintOptions(cout);
140 
141  PCType pc_choice;
142  if (!strcmp(pc, "ho")) { pc_choice = PCType::HO; }
143  else if (!strcmp(pc, "lor")) { pc_choice = PCType::LOR; }
144  else if (!strcmp(pc, "none")) { pc_choice = PCType::NONE; }
145  else
146  {
147  mfem_error("Invalid Preconditioner specified");
148  return 3;
149  }
150 
151  cout << "\nMFEM SIMD width: " << MFEM_SIMD_BYTES/sizeof(double)
152  << " doubles\n" << endl;
153 
154  // See class BasisType in fem/fe_coll.hpp for available basis types
155  int basis = BasisType::GetType(basis_type[0]);
156  cout << "Using " << BasisType::Name(basis) << " basis ..." << endl;
157 
158  // 2. Read the mesh from the given mesh file. We can handle triangular,
159  // quadrilateral, tetrahedral, hexahedral, surface and volume meshes with
160  // the same code.
161  Mesh *mesh = new Mesh(mesh_file, 1, 1);
162  int dim = mesh->Dimension();
163 
164  if (dim == 2)
165  {
166  return ex1_t<2>::run(mesh, ref_levels, order, basis, static_cond,
167  pc_choice, perf, matrix_free, visualization);
168  }
169  else if (dim == 3)
170  {
171  return ex1_t<3>::run(mesh, ref_levels, order, basis, static_cond,
172  pc_choice, perf, matrix_free, visualization);
173  }
174  else
175  {
176  MFEM_ABORT("Dimension must be 2 or 3.")
177  }
178 
179  return 0;
180 }
181 
182 template <int dim>
183 int ex1_t<dim>::run(Mesh *mesh, int ref_levels, int order, int basis,
184  bool static_cond, PCType pc_choice, bool perf,
185  bool matrix_free, bool visualization)
186 {
187  // 3. Check if the optimized version matches the given mesh
188  if (perf)
189  {
190  cout << "High-performance version using integration rule with "
191  << int_rule_t::qpts << " points ..." << endl;
192  if (!mesh_t::MatchesGeometry(*mesh))
193  {
194  cout << "The given mesh does not match the optimized 'geom' parameter.\n"
195  << "Recompile with suitable 'geom' value." << endl;
196  delete mesh;
197  return 4;
198  }
199  else if (!mesh_t::MatchesNodes(*mesh))
200  {
201  cout << "Switching the mesh curvature to match the "
202  << "optimized value (order " << mesh_p << ") ..." << endl;
203  mesh->SetCurvature(mesh_p, false, -1, Ordering::byNODES);
204  }
205  }
206 
207  // 4. Refine the mesh to increase the resolution. In this example we do
208  // 'ref_levels' of uniform refinement. We choose 'ref_levels' to be the
209  // largest number that gives a final mesh with no more than 50,000
210  // elements, or as specified on the command line with the option
211  // '--refine'.
212  {
213  ref_levels = (ref_levels != -1) ? ref_levels :
214  (int)floor(log(50000./mesh->GetNE())/log(2.)/dim);
215  for (int l = 0; l < ref_levels; l++)
216  {
217  mesh->UniformRefinement();
218  }
219  }
220  if (mesh->MeshGenerator() & 1) // simplex mesh
221  {
222  MFEM_VERIFY(pc_choice != PCType::LOR, "triangle and tet meshes do not "
223  " support the LOR preconditioner yet");
224  }
225 
226  // 5. Define a finite element space on the mesh. Here we use continuous
227  // Lagrange finite elements of the specified order. If order < 1, we
228  // instead use an isoparametric/isogeometric space.
230  if (order > 0)
231  {
232  fec = new H1_FECollection(order, dim, basis);
233  }
234  else if (mesh->GetNodes())
235  {
236  fec = mesh->GetNodes()->OwnFEC();
237  cout << "Using isoparametric FEs: " << fec->Name() << endl;
238  }
239  else
240  {
241  fec = new H1_FECollection(order = 1, dim, basis);
242  }
243  FiniteElementSpace *fespace = new FiniteElementSpace(mesh, fec);
244  cout << "Number of finite element unknowns: "
245  << fespace->GetTrueVSize() << endl;
246 
247  // Create the LOR mesh and finite element space. In the settings of this
248  // example, we can transfer between HO and LOR with the identity operator.
249  Mesh mesh_lor;
250  FiniteElementCollection *fec_lor = NULL;
251  FiniteElementSpace *fespace_lor = NULL;
252  if (pc_choice == PCType::LOR)
253  {
254  int basis_lor = basis;
255  if (basis == BasisType::Positive) { basis_lor=BasisType::ClosedUniform; }
256  mesh_lor = Mesh::MakeRefined(*mesh, order, basis_lor);
257  fec_lor = new H1_FECollection(1, dim);
258  fespace_lor = new FiniteElementSpace(&mesh_lor, fec_lor);
259  }
260 
261  // 6. Check if the optimized version matches the given space
262  if (perf && !sol_fes_t::Matches(*fespace))
263  {
264  cout << "The given order does not match the optimized parameter.\n"
265  << "Recompile with suitable 'sol_p' value." << endl;
266  delete fespace;
267  delete fec;
268  delete mesh;
269  return 5;
270  }
271 
272  // 7. Determine the list of true (i.e. conforming) essential boundary dofs.
273  // In this example, the boundary conditions are defined by marking all
274  // the boundary attributes from the mesh as essential (Dirichlet) and
275  // converting them to a list of true dofs.
276  Array<int> ess_tdof_list;
277  if (mesh->bdr_attributes.Size())
278  {
279  Array<int> ess_bdr(mesh->bdr_attributes.Max());
280  ess_bdr = 1;
281  fespace->GetEssentialTrueDofs(ess_bdr, ess_tdof_list);
282  }
283 
284  // 8. Set up the linear form b(.) which corresponds to the right-hand side of
285  // the FEM linear system, which in this case is (1,phi_i) where phi_i are
286  // the basis functions in the finite element fespace.
287  LinearForm *b = new LinearForm(fespace);
288  ConstantCoefficient one(1.0);
289  b->AddDomainIntegrator(new DomainLFIntegrator(one));
290  b->Assemble();
291 
292  // 9. Define the solution vector x as a finite element grid function
293  // corresponding to fespace. Initialize x with initial guess of zero,
294  // which satisfies the boundary conditions.
295  GridFunction x(fespace);
296  x = 0.0;
297 
298  // 10. Set up the bilinear form a(.,.) on the finite element space that will
299  // hold the matrix corresponding to the Laplacian operator -Delta.
300  // Optionally setup a form to be assembled for preconditioning (a_pc).
301  BilinearForm *a = new BilinearForm(fespace);
302  BilinearForm *a_pc = NULL;
303  if (pc_choice == PCType::LOR) { a_pc = new BilinearForm(fespace_lor); }
304  if (pc_choice == PCType::HO) { a_pc = new BilinearForm(fespace); }
305 
306  // 11. Assemble the bilinear form and the corresponding linear system,
307  // applying any necessary transformations such as: eliminating boundary
308  // conditions, applying conforming constraints for non-conforming AMR,
309  // static condensation, etc.
310  if (static_cond)
311  {
312  a->EnableStaticCondensation();
313  MFEM_VERIFY(pc_choice != PCType::LOR,
314  "cannot use LOR preconditioner with static condensation");
315  }
316 
317  cout << "Assembling the bilinear form ..." << flush;
318  tic_toc.Clear();
319  tic_toc.Start();
320  // Pre-allocate sparsity assuming dense element matrices
321  a->UsePrecomputedSparsity();
322 
323  HPCBilinearForm *a_hpc = NULL;
324  Operator *a_oper = NULL;
325 
326  if (!perf)
327  {
328  // Standard assembly using a diffusion domain integrator
329  a->AddDomainIntegrator(new DiffusionIntegrator(one));
330  a->Assemble();
331  }
332  else
333  {
334  // High-performance assembly/evaluation using the templated operator type
335  a_hpc = new HPCBilinearForm(integ_t(coeff_t(1.0)), *fespace);
336  if (matrix_free)
337  {
338  a_hpc->Assemble(); // partial assembly
339  }
340  else
341  {
342  a_hpc->AssembleBilinearForm(*a); // full matrix assembly
343  }
344  }
345  tic_toc.Stop();
346  cout << " done, " << tic_toc.RealTime() << "s." << endl;
347 
348  // 12. Solve the system A X = B with CG. In the standard case, use a simple
349  // symmetric Gauss-Seidel preconditioner.
350 
351  // Setup the operator matrix (if applicable)
352  SparseMatrix A;
353  Vector B, X;
354  if (perf && matrix_free)
355  {
356  a_hpc->FormLinearSystem(ess_tdof_list, x, *b, a_oper, X, B);
357  cout << "Size of linear system: " << a_hpc->Height() << endl;
358  }
359  else
360  {
361  a->FormLinearSystem(ess_tdof_list, x, *b, A, X, B);
362  cout << "Size of linear system: " << A.Height() << endl;
363  a_oper = &A;
364  }
365 
366  // Setup the matrix used for preconditioning
367  cout << "Assembling the preconditioning matrix ..." << flush;
368  tic_toc.Clear();
369  tic_toc.Start();
370 
371  SparseMatrix A_pc;
372  if (pc_choice == PCType::LOR)
373  {
374  // TODO: assemble the LOR matrix using the performance code
376  a_pc->UsePrecomputedSparsity();
377  a_pc->Assemble();
378  a_pc->FormSystemMatrix(ess_tdof_list, A_pc);
379  }
380  else if (pc_choice == PCType::HO)
381  {
382  if (!matrix_free)
383  {
384  A_pc.MakeRef(A); // matrix already assembled, reuse it
385  }
386  else
387  {
388  a_pc->UsePrecomputedSparsity();
389  a_hpc->AssembleBilinearForm(*a_pc);
390  a_pc->FormSystemMatrix(ess_tdof_list, A_pc);
391  }
392  }
393 
394  tic_toc.Stop();
395  cout << " done, " << tic_toc.RealTime() << "s." << endl;
396 
397  // Solve with CG or PCG, depending if the matrix A_pc is available
398  if (pc_choice != PCType::NONE)
399  {
400  GSSmoother M(A_pc);
401  PCG(*a_oper, M, B, X, 1, 500, 1e-12, 0.0);
402  }
403  else
404  {
405  CG(*a_oper, B, X, 1, 500, 1e-12, 0.0);
406  }
407 
408  // 13. Recover the solution as a finite element grid function.
409  if (perf && matrix_free)
410  {
411  a_hpc->RecoverFEMSolution(X, *b, x);
412  }
413  else
414  {
415  a->RecoverFEMSolution(X, *b, x);
416  }
417 
418  // 14. Save the refined mesh and the solution. This output can be viewed later
419  // using GLVis: "glvis -m refined.mesh -g sol.gf".
420  ofstream mesh_ofs("refined.mesh");
421  mesh_ofs.precision(8);
422  mesh->Print(mesh_ofs);
423  ofstream sol_ofs("sol.gf");
424  sol_ofs.precision(8);
425  x.Save(sol_ofs);
426 
427  // 15. Send the solution by socket to a GLVis server.
428  if (visualization)
429  {
430  char vishost[] = "localhost";
431  int visport = 19916;
432  socketstream sol_sock(vishost, visport);
433  sol_sock.precision(8);
434  sol_sock << "solution\n" << *mesh << x << flush;
435  }
436 
437  // 16. Free the used memory.
438  delete a;
439  delete a_hpc;
440  if (a_oper != &A) { delete a_oper; }
441  delete a_pc;
442  delete b;
443  delete fespace;
444  delete fespace_lor;
445  delete fec_lor;
446  if (order > 0) { delete fec; }
447  delete mesh;
448 
449  return 0;
450 }
Class for domain integration L(v) := (f, v)
Definition: lininteg.hpp:108
int visport
Templated bilinear form class, cf. bilinearform.?pp.
Class for grid function - Vector with associated FE space.
Definition: gridfunc.hpp:30
void Assemble(int skip_zeros=1)
Assembles the form i.e. sums over all domain/bdr integrators.
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:331
int Dimension() const
Dimension of the reference space used within the elements.
Definition: mesh.hpp:1020
void MakeRef(const SparseMatrix &master)
Clear the contents of the SparseMatrix and make it a reference to master.
Definition: sparsemat.cpp:313
void PrintUsage(std::ostream &out) const
Print the usage message.
Definition: optparser.cpp:462
StopWatch tic_toc
Definition: tic_toc.cpp:447
T Max() const
Find the maximal element in the array, using the comparison operator < for class T.
Definition: array.cpp:68
virtual void GetEssentialTrueDofs(const Array< int > &bdr_attr_is_ess, Array< int > &ess_tdof_list, int component=-1)
Get a list of essential true dofs, ess_tdof_list, corresponding to the boundary attributes marked in ...
Definition: fespace.cpp:587
double RealTime()
Return the number of real seconds elapsed since the stopwatch was started.
Definition: tic_toc.cpp:429
bool Good() const
Return true if the command line options were parsed successfully.
Definition: optparser.hpp:159
STL namespace.
PCType
Definition: ex1.cpp:48
int main(int argc, char *argv[])
Definition: ex1.cpp:74
The Integrator class combines a kernel and a coefficient.
Definition: tbilininteg.hpp:26
Data type for Gauss-Seidel smoother of sparse matrix.
void Stop()
Stop the stopwatch.
Definition: tic_toc.cpp:419
void Parse()
Parse the command-line options. Note that this function expects all the options provided through the ...
Definition: optparser.cpp:151
char vishost[]
Data type sparse matrix.
Definition: sparsemat.hpp:50
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:154
double b
Definition: lissajous.cpp:42
void UniformRefinement(int i, const DSTable &, int *, int *, int *)
Definition: mesh.cpp:10232
const int sol_p
Definition: ex1.cpp:58
virtual void SetCurvature(int order, bool discont=false, int space_dim=-1, int ordering=1)
Set the curvature of the mesh nodes using the given polynomial degree.
Definition: mesh.cpp:5635
int MeshGenerator()
Get the mesh generator/type.
Definition: mesh.hpp:1047
virtual const char * Name() const
Definition: fe_coll.hpp:80
void CG(const Operator &A, const Vector &b, Vector &x, int print_iter, int max_num_iter, double RTOLERANCE, double ATOLERANCE)
Conjugate gradient method. (tolerances are squared)
Definition: solvers.cpp:898
virtual void FormSystemMatrix(const Array< int > &ess_tdof_list, OperatorHandle &A)
Form the linear system matrix A, see FormLinearSystem() for details.
void PCG(const Operator &A, Solver &B, const Vector &b, Vector &x, int print_iter, int max_num_iter, double RTOLERANCE, double ATOLERANCE)
Preconditioned conjugate gradient method. (tolerances are squared)
Definition: solvers.cpp:913
void Start()
Start the stopwatch. The elapsed time is not cleared.
Definition: tic_toc.cpp:408
virtual int GetTrueVSize() const
Return the number of vector true (conforming) dofs.
Definition: fespace.hpp:712
Array< int > bdr_attributes
A list of all unique boundary attributes used by the Mesh.
Definition: mesh.hpp:275
void UsePrecomputedSparsity(int ps=1)
For scalar FE spaces, precompute the sparsity pattern of the matrix (assuming dense element matrices)...
Class FiniteElementSpace - responsible for providing FEM view of the mesh, mainly managing the set of...
Definition: fespace.hpp:219
Collection of finite elements from the same family in multiple dimensions. This class is used to matc...
Definition: fe_coll.hpp:26
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
int Height() const
Get the height (size of output) of the Operator. Synonym with NumRows().
Definition: operator.hpp:66
int GetNE() const
Returns number of elements.
Definition: mesh.hpp:1086
double a
Definition: lissajous.cpp:41
A "square matrix" operator for the associated FE space and BLFIntegrators The sum of all the BLFInteg...
const int mesh_p
Definition: ex1.cpp:57
int dim
Definition: ex24.cpp:53
void AddDomainIntegrator(BilinearFormIntegrator *bfi)
Adds new Domain Integrator. Assumes ownership of bfi.
int Size() const
Return the logical size of the array.
Definition: array.hpp:141
Vector data type.
Definition: vector.hpp:58
virtual void Print(std::ostream &os=mfem::out) const
Definition: mesh.hpp:2011
Arbitrary order H1-conforming (continuous) finite elements.
Definition: fe_coll.hpp:259
Vector with associated FE space and LinearFormIntegrators.
Definition: linearform.hpp:24
void GetNodes(Vector &node_coord) const
Definition: mesh.cpp:8302
Abstract operator.
Definition: operator.hpp:24
void Clear()
Clear the elapsed time on the stopwatch and restart it if it&#39;s running.
Definition: tic_toc.cpp:403