 MFEM  v4.3.0 Finite element discretization library
ex1.cpp
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1 // MFEM Example 1
2 // AmgX Modification
3 //
4 // Compile with: make ex1
5 //
6 // AmgX sample runs:
7 // ex1
8 // ex1 -d cuda
9 // ex1 --amgx-file multi_gs.json --amgx-solver
10 // ex1 --amgx-file precon.json --amgx-preconditioner
11 // ex1 --amgx-file multi_gs.json --amgx-solver -d cuda
12 // ex1 --amgx-file precon.json --amgx-preconditioner -d cuda
13 //
14 // Description: This example code demonstrates the use of MFEM to define a
15 // simple finite element discretization of the Laplace problem
16 // -Delta u = 1 with homogeneous Dirichlet boundary conditions.
17 // Specifically, we discretize using a FE space of the specified
18 // order, or if order < 1 using an isoparametric/isogeometric
20 // NURBS mesh, etc.)
21 //
22 // The example highlights the use of mesh refinement, finite
23 // element grid functions, as well as linear and bilinear forms
24 // corresponding to the left-hand side and right-hand side of the
25 // discrete linear system. We also cover the explicit elimination
26 // of essential boundary conditions, static condensation, and the
27 // optional connection to the GLVis tool for visualization.
28
29 #include "mfem.hpp"
30 #include <fstream>
31 #include <iostream>
32
33 #ifndef MFEM_USE_AMGX
34 #error This example requires that MFEM is built with MFEM_USE_AMGX=YES
35 #endif
36
37 using namespace std;
38 using namespace mfem;
39
40 int main(int argc, char *argv[])
41 {
42  // 1. Parse command-line options.
43  const char *mesh_file = "../../data/star.mesh";
44  int order = 1;
45  bool static_cond = false;
46  bool pa = false;
47  const char *device_config = "cpu";
48  bool visualization = true;
49  bool amgx_lib = true;
50  bool amgx_solver = true;
51  const char* amgx_json_file = ""; // JSON file for AmgX
52
53  OptionsParser args(argc, argv);
55  "Mesh file to use.");
57  "Finite element order (polynomial degree) or -1 for"
58  " isoparametric space.");
60  "--no-static-condensation", "Enable static condensation.");
62  "--no-partial-assembly", "Enable Partial Assembly.");
64  "--no-amgx-lib", "Use AmgX in example.");
66  "AMGX solver config file (overrides --amgx-solver, --amgx-verbose)");
68  "--amgx-preconditioner", "--amgx-preconditioner",
69  "Configure AMGX as solver or preconditioner.");
71  "Device configuration string, see Device::Configure().");
73  "--no-visualization",
74  "Enable or disable GLVis visualization.");
75  args.Parse();
76  if (!args.Good())
77  {
78  args.PrintUsage(cout);
79  return 1;
80  }
81  args.PrintOptions(cout);
82
83  // 2. Enable hardware devices such as GPUs, and programming models such as
84  // CUDA, OCCA, RAJA and OpenMP based on command line options.
85  Device device(device_config);
86  device.Print();
87
88  // 3. Read the mesh from the given mesh file. We can handle triangular,
89  // quadrilateral, tetrahedral, hexahedral, surface and volume meshes with
90  // the same code.
91  Mesh mesh(mesh_file, 1, 1);
92  int dim = mesh.Dimension();
93
94  // 4. Refine the mesh to increase the resolution. In this example we do
95  // 'ref_levels' of uniform refinement. We choose 'ref_levels' to be the
96  // largest number that gives a final mesh with no more than 50,000
97  // elements.
98  {
99  int ref_levels =
100  (int)floor(log(50000./mesh.GetNE())/log(2.)/dim);
101  for (int l = 0; l < ref_levels; l++)
102  {
103  mesh.UniformRefinement();
104  }
105  }
106
107  // 5. Define a finite element space on the mesh. Here we use continuous
108  // Lagrange finite elements of the specified order. If order < 1, we
109  // instead use an isoparametric/isogeometric space.
111  bool delete_fec;
112  if (order > 0)
113  {
114  fec = new H1_FECollection(order, dim);
115  delete_fec = true;
116  }
117  else if (mesh.GetNodes())
118  {
119  fec = mesh.GetNodes()->OwnFEC();
120  delete_fec = false;
121  cout << "Using isoparametric FEs: " << fec->Name() << endl;
122  }
123  else
124  {
125  fec = new H1_FECollection(order = 1, dim);
126  delete_fec = true;
127  }
128  FiniteElementSpace fespace(&mesh, fec);
129  cout << "Number of finite element unknowns: "
130  << fespace.GetTrueVSize() << endl;
131
132  // 6. Determine the list of true (i.e. conforming) essential boundary dofs.
133  // In this example, the boundary conditions are defined by marking all
134  // the boundary attributes from the mesh as essential (Dirichlet) and
135  // converting them to a list of true dofs.
136  Array<int> ess_tdof_list;
137  if (mesh.bdr_attributes.Size())
138  {
139  Array<int> ess_bdr(mesh.bdr_attributes.Max());
140  ess_bdr = 1;
141  fespace.GetEssentialTrueDofs(ess_bdr, ess_tdof_list);
142  }
143
144  // 7. Set up the linear form b(.) which corresponds to the right-hand side of
145  // the FEM linear system, which in this case is (1,phi_i) where phi_i are
146  // the basis functions in the finite element fespace.
147  LinearForm b(&fespace);
148  ConstantCoefficient one(1.0);
150  b.Assemble();
151
152  // 8. Define the solution vector x as a finite element grid function
153  // corresponding to fespace. Initialize x with initial guess of zero,
154  // which satisfies the boundary conditions.
155  GridFunction x(&fespace);
156  x = 0.0;
157
158  // 9. Set up the bilinear form a(.,.) on the finite element space
159  // corresponding to the Laplacian operator -Delta, by adding the Diffusion
160  // domain integrator.
161  BilinearForm a(&fespace);
162  if (pa) { a.SetAssemblyLevel(AssemblyLevel::PARTIAL); }
164
165  // 10. Assemble the bilinear form and the corresponding linear system,
166  // applying any necessary transformations such as: eliminating boundary
167  // conditions, applying conforming constraints for non-conforming AMR,
168  // static condensation, etc.
169  if (static_cond) { a.EnableStaticCondensation(); }
170  a.Assemble();
171
172  OperatorPtr A;
173  Vector B, X;
174  a.FormLinearSystem(ess_tdof_list, x, b, A, X, B);
175
176  cout << "Size of linear system: " << A->Height() << endl;
177
178  // 11. Solve the linear system A X = B.
179  if (pa)
180  {
181  // Jacobi preconditioning in partial assembly mode
182  if (UsesTensorBasis(fespace))
183  {
184  OperatorJacobiSmoother M(a, ess_tdof_list);
185  PCG(*A, M, B, X, 1, 400, 1e-12, 0.0);
186  }
187  else
188  {
189  CG(*A, B, X, 1, 400, 1e-12, 0.0);
190  }
191  }
192  else if (amgx_lib && strcmp(amgx_json_file,"") == 0)
193  {
194  bool amgx_verbose = false;
195  AmgXSolver amgx(AmgXSolver::PRECONDITIONER, amgx_verbose);
196  amgx.SetOperator(*A.As<SparseMatrix>());
197  PCG(*A, amgx, B, X, 1, 200, 1e-12, 0.0);
198  }
199  else if (amgx_lib && strcmp(amgx_json_file,"") != 0)
200  {
201  AmgXSolver amgx;
203  amgx.InitSerial();
204  amgx.SetOperator(*A.As<SparseMatrix>());
205
206  if (amgx_solver)
207  {
208  amgx.SetConvergenceCheck(true);
209  amgx.Mult(B,X);
210  }
211  else
212  {
213  // Omit convergence check at the AmgX level when using as a
214  // preconditioner.
215  amgx.SetConvergenceCheck(false);
216  PCG(*A.As<SparseMatrix>(), amgx, B, X, 3, 40, 1e-12, 0.0);
217  }
218  }
219  else
220  {
221 #ifndef MFEM_USE_SUITESPARSE
222  // Use a simple symmetric Gauss-Seidel preconditioner with PCG.
223  GSSmoother M((SparseMatrix&)(*A));
224  PCG(*A, M, B, X, 1, 200, 1e-12, 0.0);
225 #else
226  // If MFEM was compiled with SuiteSparse, use UMFPACK to solve the system.
227  UMFPackSolver umf_solver;
228  umf_solver.Control[UMFPACK_ORDERING] = UMFPACK_ORDERING_METIS;
229  umf_solver.SetOperator(*A);
230  umf_solver.Mult(B, X);
231 #endif
232  }
233
234  // 12. Recover the solution as a finite element grid function.
235  a.RecoverFEMSolution(X, b, x);
236
237  // 13. Save the refined mesh and the solution. This output can be viewed later
238  // using GLVis: "glvis -m refined.mesh -g sol.gf".
239  ofstream mesh_ofs("refined.mesh");
240  mesh_ofs.precision(8);
241  mesh.Print(mesh_ofs);
242  ofstream sol_ofs("sol.gf");
243  sol_ofs.precision(8);
244  x.Save(sol_ofs);
245
246  // 14. Send the solution by socket to a GLVis server.
247  if (visualization)
248  {
249  char vishost[] = "localhost";
250  int visport = 19916;
251  socketstream sol_sock(vishost, visport);
252  sol_sock.precision(8);
253  sol_sock << "solution\n" << mesh << x << flush;
254  }
255
256  // 15. Free the used memory.
257  if (delete_fec)
258  {
259  delete fec;
260  }
261
262  return 0;
263 }
int Size() const
Return the logical size of the array.
Definition: array.hpp:134
Class for domain integration L(v) := (f, v)
Definition: lininteg.hpp:97
virtual void Print(std::ostream &out=mfem::out) const
Definition: mesh.hpp:1387
OpType * As() const
Return the Operator pointer statically cast to a specified OpType. Similar to the method Get()...
Definition: handle.hpp:99
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:78
void Assemble()
Assembles the linear form i.e. sums over all domain/bdr integrators.
Definition: linearform.cpp:102
Pointer to an Operator of a specified type.
Definition: handle.hpp:33
virtual void FormLinearSystem(const Array< int > &ess_tdof_list, Vector &x, Vector &b, OperatorHandle &A, Vector &X, Vector &B, int copy_interior=0)
Form the linear system A X = B, corresponding to this bilinear form and the linear form b(...
virtual void RecoverFEMSolution(const Vector &X, const Vector &b, Vector &x)
Recover the solution of a linear system formed with FormLinearSystem().
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:506
int GetNE() const
Returns number of elements.
Definition: mesh.hpp:846
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.
bool UsesTensorBasis(const FiniteElementSpace &fes)
Definition: fespace.hpp:957
void ReadParameters(const std::string config, CONFIG_SRC source)
Definition: amgxsolver.cpp:186
Data type for Gauss-Seidel smoother of sparse matrix.
virtual void Mult(const Vector &b, Vector &x) const
Operator application: y=A(x).
Definition: amgxsolver.cpp:897
Direct sparse solver using UMFPACK.
Definition: solvers.hpp:839
virtual void Save(std::ostream &out) const
Save the GridFunction to an output stream.
Definition: gridfunc.cpp:3484
void SetConvergenceCheck(bool setConvergenceCheck_=true)
Add a check for convergence after applying Mult.
Definition: amgxsolver.cpp:193
void Parse()
Parse the command-line options. Note that this function expects all the options provided through the ...
Definition: optparser.cpp:150
Data type sparse matrix.
Definition: sparsemat.hpp:41
int Height() const
Get the height (size of output) of the Operator. Synonym with NumRows().
Definition: operator.hpp:66
constexpr char vishost[]
Jacobi smoothing for a given bilinear form (no matrix necessary).
Definition: solvers.hpp:130
double b
Definition: lissajous.cpp:42
void UniformRefinement(int i, const DSTable &, int *, int *, int *)
Definition: mesh.cpp:9143
constexpr int visport
T Max() const
Find the maximal element in the array, using the comparison operator &lt; for class T.
Definition: array.cpp:68
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:802
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:817
virtual int GetTrueVSize() const
Return the number of vector true (conforming) dofs.
Definition: fespace.hpp:543
int Dimension() const
Definition: mesh.hpp:911
void PrintUsage(std::ostream &out) const
Print the usage message.
Definition: optparser.cpp:457
Adds new Domain Integrator. Assumes ownership of lfi.
Definition: linearform.cpp:39
Array< int > bdr_attributes
A list of all unique boundary attributes used by the Mesh.
Definition: mesh.hpp:204
double Control[UMFPACK_CONTROL]
Definition: solvers.hpp:850
Class FiniteElementSpace - responsible for providing FEM view of the mesh, mainly managing the set of...
Definition: fespace.hpp:87
Collection of finite elements from the same family in multiple dimensions. This class is used to matc...
Definition: fe_coll.hpp:26
virtual void SetOperator(const Operator &op)
Definition: amgxsolver.cpp:854
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
double a
Definition: lissajous.cpp:41
A &quot;square matrix&quot; operator for the associated FE space and BLFIntegrators The sum of all the BLFInteg...
virtual const char * Name() const
Definition: fe_coll.hpp:61
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:327
Vector data type.
Definition: vector.hpp:60
void GetNodes(Vector &node_coord) const
Definition: mesh.cpp:7343
Arbitrary order H1-conforming (continuous) finite elements.
Definition: fe_coll.hpp:216
Vector with associated FE space and LinearFormIntegrators.
Definition: linearform.hpp:23
The MFEM Device class abstracts hardware devices such as GPUs, as well as programming models such as ...
Definition: device.hpp:121
int main()
virtual void Mult(const Vector &b, Vector &x) const
Operator application: y=A(x).
Definition: solvers.cpp:2999
void EnableStaticCondensation()
Enable the use of static condensation. For details see the description for class StaticCondensation i...
virtual void SetOperator(const Operator &op)
Factorize the given Operator op which must be a SparseMatrix.
Definition: solvers.cpp:2904
bool Good() const
Return true if the command line options were parsed successfully.
Definition: optparser.hpp:150