151 lines
4.5 KiB
C++
151 lines
4.5 KiB
C++
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#include "mfem.hpp"
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#include <fstream>
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#include <iostream>
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#include "additive_schwarz.hpp"
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#include "schwarz.hpp"
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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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// const char *mesh_file = "../../../data/beam-quad.mesh";
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int order = 1;
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int ref_levels = 1;
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bool visualization = true;
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StopWatch chrono;
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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(&ref_levels, "-ref", "--ref_levels",
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"Number of uniform h-refinements");
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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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Mesh *mesh;
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// mesh = new Mesh(mesh_file, 1, 1);
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mesh = new Mesh(1, 1, Element::QUADRILATERAL, true, 1, 1, false);
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int dim = mesh->Dimension();
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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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FiniteElementCollection *fec = new H1_FECollection(order, dim);
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// FiniteElementCollection *fec = new ND_FECollection(order, dim);
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FiniteElementSpace * fespace = new FiniteElementSpace(mesh, fec);
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Array<int> ess_tdof_list;
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Array<int> ess_bdr;
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if (mesh->bdr_attributes.Size())
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{
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ess_bdr.SetSize(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 = new LinearForm(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 = 1.0;
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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 = new BilinearForm(fespace);
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a->SetDiagonalPolicy(mfem::Matrix::DIAG_ONE);
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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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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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AddSchwarz * prec = new AddSchwarz(a,ess_tdof_list, 0);
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prec->SetOperator((SparseMatrix&)(*A));
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prec->SetNumSmoothSteps(1);
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prec->SetDumpingParam(0.5);
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SchwarzSmoother * prec2 = new SchwarzSmoother(mesh,0,fespace,&(SparseMatrix&)(*A),ess_bdr);
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prec2->SetNumSmoothSteps(1);
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prec2->SetDumpingParam(0.5);
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int maxit = 2000;
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double rtol = 1e-8;
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double atol = 1e-8;
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Vector X0(X);
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CGSolver pcg;
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pcg.iterative_mode = false;
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pcg.SetPrintLevel(1);
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pcg.SetMaxIter(maxit);
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pcg.SetRelTol(rtol);
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pcg.SetAbsTol(atol);
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pcg.SetPreconditioner(*prec);
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pcg.SetOperator((SparseMatrix&)(*A));
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pcg.Mult(B, X0);
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X0 = X;
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pcg.SetPreconditioner(*prec2);
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pcg.Mult(B, X0);
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// 12. Recover the solution as a finite element grid function.
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a->RecoverFEMSolution(X0, *b, x);
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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 mesh_sock(vishost, visport);
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mesh_sock.precision(8);
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mesh_sock << "mesh\n" << *mesh << flush;
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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 << "keys rRjmc" << flush;
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}
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// 15. Free the used memory.
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delete prec;
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delete a;
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delete b;
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delete fespace;
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delete fec;
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delete mesh;
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return 0;
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}
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