264 lines
9.2 KiB
C++
264 lines
9.2 KiB
C++
// MFEM Example 1
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// AmgX Modification
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//
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// Compile with: make ex1
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//
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// AmgX sample runs:
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// ex1
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// ex1 -d cuda
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// ex1 --amgx-file multi_gs.json --amgx-solver
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// ex1 --amgx-file precon.json --amgx-preconditioner
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// ex1 --amgx-file multi_gs.json --amgx-solver -d cuda
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// ex1 --amgx-file precon.json --amgx-preconditioner -d cuda
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//
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// Description: This example code demonstrates the use of MFEM to define a
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// simple finite element discretization of the Poisson problem
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// -Delta u = 1 with homogeneous Dirichlet boundary conditions.
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// Specifically, we discretize using a FE space of the specified
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// order, or if order < 1 using an isoparametric/isogeometric
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// space (i.e. quadratic for quadratic curvilinear mesh, NURBS for
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// NURBS mesh, etc.)
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//
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// The example highlights the use of mesh refinement, finite
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// element grid functions, as well as linear and bilinear forms
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// corresponding to the left-hand side and right-hand side of the
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// discrete linear system. We also cover the explicit elimination
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// of essential boundary conditions, static condensation, and the
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// optional connection to the GLVis tool for visualization.
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#include "mfem.hpp"
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#include <fstream>
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#include <iostream>
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#ifndef MFEM_USE_AMGX
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#error This example requires that MFEM is built with MFEM_USE_AMGX=YES
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#endif
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using namespace std;
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using namespace mfem;
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int main(int argc, char *argv[])
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{
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// 1. Parse command-line options.
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const char *mesh_file = "../../data/star.mesh";
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int order = 1;
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bool static_cond = false;
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bool pa = false;
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const char *device_config = "cpu";
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bool visualization = true;
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bool amgx_lib = true;
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bool amgx_solver = true;
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const char* amgx_json_file = ""; // JSON file for AmgX
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OptionsParser args(argc, argv);
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args.AddOption(&mesh_file, "-m", "--mesh",
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"Mesh file to use.");
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args.AddOption(&order, "-o", "--order",
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"Finite element order (polynomial degree) or -1 for"
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" isoparametric space.");
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args.AddOption(&static_cond, "-sc", "--static-condensation", "-no-sc",
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"--no-static-condensation", "Enable static condensation.");
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args.AddOption(&pa, "-pa", "--partial-assembly", "-no-pa",
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"--no-partial-assembly", "Enable Partial Assembly.");
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args.AddOption(&amgx_lib, "-amgx", "--amgx-lib", "-no-amgx",
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"--no-amgx-lib", "Use AmgX in example.");
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args.AddOption(&amgx_json_file, "--amgx-file", "--amgx-file",
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"AMGX solver config file (overrides --amgx-solver, --amgx-verbose)");
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args.AddOption(&amgx_solver, "--amgx-solver", "--amgx-solver",
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"--amgx-preconditioner", "--amgx-preconditioner",
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"Configure AMGX as solver or preconditioner.");
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args.AddOption(&device_config, "-d", "--device",
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"Device configuration string, see Device::Configure().");
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args.AddOption(&visualization, "-vis", "--visualization", "-no-vis",
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"--no-visualization",
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"Enable or disable GLVis visualization.");
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args.Parse();
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if (!args.Good())
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{
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args.PrintUsage(cout);
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return 1;
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}
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args.PrintOptions(cout);
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// 2. Enable hardware devices such as GPUs, and programming models such as
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// CUDA, OCCA, RAJA and OpenMP based on command line options.
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Device device(device_config);
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device.Print();
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// 3. Read the mesh from the given mesh file. We can handle triangular,
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// quadrilateral, tetrahedral, hexahedral, surface and volume meshes with
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// the same code.
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Mesh mesh(mesh_file, 1, 1);
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int dim = mesh.Dimension();
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// 4. Refine the mesh to increase the resolution. In this example we do
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// 'ref_levels' of uniform refinement. We choose 'ref_levels' to be the
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// largest number that gives a final mesh with no more than 50,000
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// elements.
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{
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int ref_levels =
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(int)floor(log(50000./mesh.GetNE())/log(2.)/dim);
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for (int l = 0; l < ref_levels; l++)
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{
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mesh.UniformRefinement();
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}
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}
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// 5. Define a finite element space on the mesh. Here we use continuous
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// Lagrange finite elements of the specified order. If order < 1, we
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// instead use an isoparametric/isogeometric space.
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FiniteElementCollection *fec;
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bool delete_fec;
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if (order > 0)
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{
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fec = new H1_FECollection(order, dim);
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delete_fec = true;
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}
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else if (mesh.GetNodes())
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{
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fec = mesh.GetNodes()->OwnFEC();
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delete_fec = false;
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cout << "Using isoparametric FEs: " << fec->Name() << endl;
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}
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else
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{
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fec = new H1_FECollection(order = 1, dim);
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delete_fec = true;
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}
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FiniteElementSpace fespace(&mesh, fec);
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cout << "Number of finite element unknowns: "
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<< fespace.GetTrueVSize() << endl;
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// 6. Determine the list of true (i.e. conforming) essential boundary dofs.
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// In this example, the boundary conditions are defined by marking all
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// the boundary attributes from the mesh as essential (Dirichlet) and
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// converting them to a list of true dofs.
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Array<int> ess_tdof_list;
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if (mesh.bdr_attributes.Size())
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{
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Array<int> ess_bdr(mesh.bdr_attributes.Max());
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ess_bdr = 1;
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fespace.GetEssentialTrueDofs(ess_bdr, ess_tdof_list);
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}
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// 7. Set up the linear form b(.) which corresponds to the right-hand side of
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// the FEM linear system, which in this case is (1,phi_i) where phi_i are
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// the basis functions in the finite element fespace.
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LinearForm b(&fespace);
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ConstantCoefficient one(1.0);
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b.AddDomainIntegrator(new DomainLFIntegrator(one));
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b.Assemble();
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// 8. Define the solution vector x as a finite element grid function
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// corresponding to fespace. Initialize x with initial guess of zero,
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// which satisfies the boundary conditions.
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GridFunction x(&fespace);
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x = 0.0;
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// 9. Set up the bilinear form a(.,.) on the finite element space
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// corresponding to the Laplacian operator -Delta, by adding the Diffusion
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// domain integrator.
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BilinearForm a(&fespace);
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if (pa) { a.SetAssemblyLevel(AssemblyLevel::PARTIAL); }
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a.AddDomainIntegrator(new DiffusionIntegrator(one));
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// 10. Assemble the bilinear form and the corresponding linear system,
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// applying any necessary transformations such as: eliminating boundary
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// conditions, applying conforming constraints for non-conforming AMR,
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// static condensation, etc.
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if (static_cond) { a.EnableStaticCondensation(); }
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a.Assemble();
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OperatorPtr A;
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Vector B, X;
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a.FormLinearSystem(ess_tdof_list, x, b, A, X, B);
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cout << "Size of linear system: " << A->Height() << endl;
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// 11. Solve the linear system A X = B.
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if (pa)
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{
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// Jacobi preconditioning in partial assembly mode
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if (UsesTensorBasis(fespace))
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{
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OperatorJacobiSmoother M(a, ess_tdof_list);
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PCG(*A, M, B, X, 1, 400, 1e-12, 0.0);
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}
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else
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{
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CG(*A, B, X, 1, 400, 1e-12, 0.0);
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}
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}
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else if (amgx_lib && strcmp(amgx_json_file,"") == 0)
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{
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bool amgx_verbose = false;
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AmgXSolver amgx(AmgXSolver::PRECONDITIONER, amgx_verbose);
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amgx.SetOperator(*A.As<SparseMatrix>());
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PCG(*A, amgx, B, X, 1, 200, 1e-12, 0.0);
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}
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else if (amgx_lib && strcmp(amgx_json_file,"") != 0)
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{
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AmgXSolver amgx;
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amgx.ReadParameters(amgx_json_file, AmgXSolver::EXTERNAL);
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amgx.InitSerial();
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amgx.SetOperator(*A.As<SparseMatrix>());
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if (amgx_solver)
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{
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amgx.SetConvergenceCheck(true);
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amgx.Mult(B,X);
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}
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else
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{
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// Omit convergence check at the AmgX level when using as a
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// preconditioner.
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amgx.SetConvergenceCheck(false);
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PCG(*A.As<SparseMatrix>(), amgx, B, X, 3, 40, 1e-12, 0.0);
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}
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}
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else
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{
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#ifndef MFEM_USE_SUITESPARSE
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// Use a simple symmetric Gauss-Seidel preconditioner with PCG.
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GSSmoother M((SparseMatrix&)(*A));
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PCG(*A, M, B, X, 1, 200, 1e-12, 0.0);
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#else
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// If MFEM was compiled with SuiteSparse, use UMFPACK to solve the system.
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UMFPackSolver umf_solver;
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umf_solver.Control[UMFPACK_ORDERING] = UMFPACK_ORDERING_METIS;
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umf_solver.SetOperator(*A);
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umf_solver.Mult(B, X);
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#endif
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}
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// 12. Recover the solution as a finite element grid function.
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a.RecoverFEMSolution(X, b, x);
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// 13. Save the refined mesh and the solution. This output can be viewed later
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// using GLVis: "glvis -m refined.mesh -g sol.gf".
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ofstream mesh_ofs("refined.mesh");
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mesh_ofs.precision(8);
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mesh.Print(mesh_ofs);
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ofstream sol_ofs("sol.gf");
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sol_ofs.precision(8);
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x.Save(sol_ofs);
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// 14. Send the solution by socket to a GLVis server.
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if (visualization)
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{
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char vishost[] = "localhost";
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int visport = 19916;
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socketstream sol_sock(vishost, visport);
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sol_sock.precision(8);
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sol_sock << "solution\n" << mesh << x << flush;
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}
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// 15. Free the used memory.
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if (delete_fec)
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{
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delete fec;
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}
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return 0;
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}
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