497 lines
15 KiB
C++
497 lines
15 KiB
C++
// Copyright (c) 2010, Lawrence Livermore National Security, LLC. Produced at
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// the Lawrence Livermore National Laboratory. LLNL-CODE-443211. All Rights
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// reserved. See file COPYRIGHT for details.
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//
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// This file is part of the MFEM library. For more information and source code
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// availability see http://mfem.org.
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//
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// MFEM is free software; you can redistribute it and/or modify it under the
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// terms of the GNU Lesser General Public License (as published by the Free
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// Software Foundation) version 2.1 dated February 1999.
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#include "mfem.hpp"
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#include <fstream>
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#include <iostream>
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#include <cmath>
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#include <complex>
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using namespace std;
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using namespace mfem;
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// #define DEFINITE
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// #ifndef MFEM_USE_PETSC
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// #error This example requires that MFEM is built with MFEM_USE_PETSC=YES
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// #endif
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// Define exact solution
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void E_exact_Re(const Vector & x, Vector & E);
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void f_exact_Re(const Vector & x, Vector & f);
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void get_maxwell_solution_Re(const Vector & x, double E[], double curl2E[]);
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void E_exact_Im(const Vector & x, Vector & E);
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void f_exact_Im(const Vector & x, Vector & f);
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void get_maxwell_solution_Im(const Vector & x, double E[], double curl2E[]);
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// Mesh Size
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int dim;
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double omega;
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double complex_shift;
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int isol = 1;
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int main(int argc, char *argv[])
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{
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StopWatch chrono;
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// 1. Initialise MPI
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MPI_Session mpi(argc, argv);
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// 1. Parse command-line options.
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// geometry file
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const char *mesh_file = "../../data/one-hex.mesh";
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int order = 1;
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// number of wavelengths
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double k = 0.5;
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//
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const char *petscrc_file = "petscrc_mult_options";
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// visualization flag
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bool visualization = 1;
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// number of initial ref
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int initref = 1;
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// number of mg levels
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int maxref = 1;
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// solver
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int solver = 1;
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//
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complex_shift = 0.0;
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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).");
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args.AddOption(&k, "-k", "--wavelengths",
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"Number of wavelengths");
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args.AddOption(&complex_shift, "-cs", "--complex_shift",
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"Complex shift");
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args.AddOption(&isol, "-isol", "--exact",
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"Exact solution flag - 0:polynomial, 1: plane wave");
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args.AddOption(&initref, "-initref", "--initref",
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"Number of initial refinements.");
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args.AddOption(&maxref, "-maxref", "--maxref",
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"Number of 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.AddOption(&solver, "-s", "--solver",
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"Solver: 1 - GMG-GMRES, 2 - PETSC, 3 - SUPERLU, 4 - STRUMPACK, 5-HSS-GMRES");
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args.Parse();
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// check if the inputs are correct
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if (!args.Good())
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{
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if ( mpi.Root() )
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{
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args.PrintUsage(cout);
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}
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MPI_Finalize();
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return 1;
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}
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if ( mpi.Root() )
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{
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args.PrintOptions(cout);
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}
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enum SolverType
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{
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INVALID_SOL = -1,
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GMG_GMRES = 1,
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PETSC = 2,
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SUPERLU = 3,
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STRUMPACK = 4,
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HSS_GMRES = 5,
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};
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// Angular frequency
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omega = 2.0*k*M_PI;
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// Create serial mesh
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Mesh *mesh = new Mesh(mesh_file, 1, 1);
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dim = mesh->Dimension();
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// 3. Executing uniform h-refinement
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for (int i = 0; i < initref; i++ )
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{
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mesh->UniformRefinement();
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}
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// create parallel mesh and delete the serial one
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ParMesh *pmesh = new ParMesh(MPI_COMM_WORLD, *mesh);
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delete mesh;
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// Create H(curl) (Nedelec) Finite element space
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FiniteElementCollection *fec = new ND_FECollection(order, dim);
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ParFiniteElementSpace *ND_fespace = new ParFiniteElementSpace(pmesh, fec);
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std::vector<HypreParMatrix*> P(maxref);
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for (int i = 0; i < maxref; i++)
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{
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const ParFiniteElementSpace cfespace(*ND_fespace);
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pmesh->UniformRefinement();
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// Update fespace
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ND_fespace->Update();
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OperatorHandle Tr(Operator::Hypre_ParCSR);
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ND_fespace->GetTrueTransferOperator(cfespace, Tr);
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Tr.SetOperatorOwner(false);
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Tr.Get(P[i]);
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}
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// 7. Linear form b(.) (Right hand side)
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VectorFunctionCoefficient f_Re(dim, f_exact_Re);
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VectorFunctionCoefficient f_Im(dim, f_exact_Im);
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ParComplexLinearForm b(ND_fespace,ComplexOperator::HERMITIAN);
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b.AddDomainIntegrator(new VectorFEDomainLFIntegrator(f_Re),
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new VectorFEDomainLFIntegrator(f_Im));
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b.real().Vector::operator=(0.0);
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b.imag().Vector::operator=(0.0);
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b.Assemble();
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// 7. Bilinear form a(.,.) on the finite element space
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ConstantCoefficient muinv(1.0);
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ConstantCoefficient sigma(-pow(omega, 2));
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ConstantCoefficient alpha(complex_shift);
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ParSesquilinearForm a(ND_fespace, ComplexOperator::HERMITIAN);
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a.AddDomainIntegrator(new CurlCurlIntegrator(muinv),NULL);
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a.AddDomainIntegrator(new VectorFEMassIntegrator(sigma),NULL);
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a.AddDomainIntegrator(NULL,new VectorFEMassIntegrator(alpha));
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a.Assemble();
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a.Finalize();
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Array<int> ess_tdof_list;
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if (pmesh->bdr_attributes.Size())
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{
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Array<int> ess_bdr(pmesh->bdr_attributes.Max());
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ess_bdr = 1;
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ND_fespace->GetEssentialTrueDofs(ess_bdr, ess_tdof_list);
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}
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// Solution grid function
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ParComplexGridFunction E_gf(ND_fespace);
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VectorFunctionCoefficient E_Re(dim, E_exact_Re);
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VectorFunctionCoefficient E_Im(dim, E_exact_Im);
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E_gf.ProjectCoefficient(E_Re,E_Im);
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OperatorHandle Ah;
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Vector X, B;
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a.FormLinearSystem(ess_tdof_list, E_gf, b, Ah, X, B);
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ComplexHypreParMatrix * AZ = Ah.As<ComplexHypreParMatrix>();
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HypreParMatrix * A = AZ->GetSystemMatrix();
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if ( mpi.Root() )
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{
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cout << "Size of fine grid system: "
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<< A->GetGlobalNumRows() << " x " << A->GetGlobalNumCols() << endl;
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}
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chrono.Clear();
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chrono.Start();
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switch((SolverType)solver)
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{
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case GMG_GMRES:
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{
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if(mpi.Root()) {cout<< "Solver choice: GMG_GMRES" << endl;}
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#ifdef MFEM_USE_PETSC
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MFEMInitializePetsc(NULL, NULL, petscrc_file, NULL);
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#endif
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ComplexGMGSolver M(AZ, P, ComplexGMGSolver::CoarseSolver::PETSC);
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M.SetTheta(0.5);
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M.SetSmootherType(HypreSmoother::Jacobi);
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int maxit(5000);
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double rtol(1.e-6);
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double atol(0.0);
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X = 0.0;
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GMRESSolver gmres(MPI_COMM_WORLD);
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gmres.SetAbsTol(atol);
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gmres.SetRelTol(rtol);
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gmres.SetMaxIter(maxit);
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gmres.SetOperator(*AZ);
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gmres.SetPreconditioner(M);
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gmres.SetPrintLevel(1);
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gmres.Mult(B,X);
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#ifdef MFEM_USE_PETSC
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MFEMFinalizePetsc();
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#endif
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}
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break;
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case PETSC:
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{
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#ifndef MFEM_USE_PETSC
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MFEM_ABORT("Invalid choice of CoarseSolver. MFEM is not linked with STRUMPACK");
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#else
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if(mpi.Root()) {cout<< "Solver choice: PETSC" << endl;}
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MFEMInitializePetsc(NULL, NULL, petscrc_file, NULL);
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PetscLinearSolver * invA = new PetscLinearSolver(MPI_COMM_WORLD, "direct");
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PetscParMatrix *PA = new PetscParMatrix(A, Operator::PETSC_MATAIJ);
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invA->SetOperator(*PA);
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invA->Mult(B,X);
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delete PA;
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MFEMFinalizePetsc();
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#endif
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}
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break;
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case SUPERLU:
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{
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#ifndef MFEM_USE_SUPERLU
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MFEM_ABORT("Invalid choice of CoarseSolver. MFEM is not linked with STRUMPACK");
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#else
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if(mpi.Root()) {cout<< "Solver choice: SuperLU" << endl;}
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SuperLURowLocMatrix *SA = new SuperLURowLocMatrix(*A);
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SuperLUSolver * superlu = new SuperLUSolver(MPI_COMM_WORLD);
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// superlu->SetPrintStatistics(true);
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// superlu->SetSymmetricPattern(false);
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superlu->SetColumnPermutation(superlu::PARMETIS);
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superlu->SetOperator(*SA);
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superlu->Mult(B,X);
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delete SA;
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delete superlu;
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#endif
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}
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break;
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case STRUMPACK:
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{
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#ifndef MFEM_USE_STRUMPACK
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MFEM_ABORT("Invalid choice of CoarseSolver. MFEM is not linked with STRUMPACK");
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#else
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if(mpi.Root()) {cout<< "Solver choice: STRUMPACK" << endl;}
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STRUMPACKRowLocMatrix *SA = new STRUMPACKRowLocMatrix(*A);
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STRUMPACKSolver * strumpack = new STRUMPACKSolver(argc, argv, MPI_COMM_WORLD);
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strumpack->SetPrintFactorStatistics(false);
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strumpack->SetPrintSolveStatistics(true);
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strumpack->SetHSS(true);
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strumpack->SetHssAbsTol(0.0);
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strumpack->SetHssRelTol(1e-4);
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strumpack->SetAbsTol(0.0);
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strumpack->SetRelTol(1e-6);
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strumpack->SetKrylovSolver(strumpack::KrylovSolver::AUTO);
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strumpack->SetReorderingStrategy(strumpack::ReorderingStrategy::METIS);
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strumpack->DisableMatching();
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strumpack->SetOperator(*SA);
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strumpack->SetFromCommandLine();
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strumpack->Mult(B, X);
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delete SA;
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delete strumpack;
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#endif
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}
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break ;
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case HSS_GMRES:
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{
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#ifndef MFEM_USE_STRUMPACK
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MFEM_ABORT("Invalid choice of CoarseSolver. MFEM is not linked with STRUMPACK");
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#else
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if(mpi.Root()) {cout<< "Solver choice: STRUMPACK" << endl;}
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STRUMPACKRowLocMatrix *SA = new STRUMPACKRowLocMatrix(*A);
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STRUMPACKSolver * prec = new STRUMPACKSolver(argc, argv, MPI_COMM_WORLD);
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prec->SetPrintFactorStatistics(true);
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prec->SetPrintSolveStatistics(false);
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prec->SetHSS(true);
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prec->SetHssAbsTol(0.0);
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prec->SetHssRelTol(1e-4);
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prec->SetKrylovSolver(strumpack::KrylovSolver::DIRECT);
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prec->SetReorderingStrategy(strumpack::ReorderingStrategy::METIS);
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prec->DisableMatching();
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prec->SetOperator(*SA);
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prec->SetFromCommandLine();
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int maxit(50);
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double rtol(1.e-6);
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double atol(0.0);
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GMRESSolver gmres(MPI_COMM_WORLD);
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gmres.SetAbsTol(atol);
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gmres.SetRelTol(rtol);
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gmres.SetMaxIter(maxit);
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gmres.SetOperator(*A);
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gmres.SetPreconditioner(*prec);
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gmres.SetPrintLevel(1);
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gmres.Mult(B,X);
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delete SA;
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delete prec;
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#endif
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}
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break ;
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default:
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if(mpi.Root()) {cout<< "Solver choice not valid. Problem not solved" << endl;}
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}
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chrono.Stop();
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if (mpi.Root())
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{
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cout << "Solver time: " << chrono.RealTime() << endl;
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}
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a.RecoverFEMSolution(X,B,E_gf);
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// Compute error
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int order_quad = max(2, 2 * order + 1);
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const IntegrationRule *irs[Geometry::NumGeom];
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for (int i = 0; i < Geometry::NumGeom; ++i)
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{
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irs[i] = &(IntRules.Get(i, order_quad));
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}
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double L2Error_Re = E_gf.real().ComputeL2Error(E_Re, irs);
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double norm_E_Re = ComputeGlobalLpNorm(2, E_Re, *pmesh, irs);
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double L2Error_Im = E_gf.imag().ComputeL2Error(E_Im, irs);
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double norm_E_Im = ComputeGlobalLpNorm(2, E_Im, *pmesh, irs);
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if (mpi.Root())
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{
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cout << " Real Part: || E_h - E || / ||E|| = " << L2Error_Re / norm_E_Re << '\n' << endl;
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cout << " Imag Part: || E_h - E || / ||E|| = " << L2Error_Im / norm_E_Im << '\n' << endl;
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cout << " Real Part: || E_h - E || = " << L2Error_Re << '\n' << endl;
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cout << " Imag Part: || E_h - E || = " << L2Error_Im << '\n' << endl;
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}
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// visualization
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if (visualization)
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{
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int num_procs, myid;
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MPI_Comm_size(MPI_COMM_WORLD, &num_procs);
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MPI_Comm_rank(MPI_COMM_WORLD, &myid);
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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 << "parallel " << num_procs << " " << myid << "\n";
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sol_sock.precision(8);
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sol_sock << "solution\n" << *pmesh << E_gf.real() << "window_title 'Real part'" << flush;
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socketstream sol_sock_Im(vishost, visport);
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sol_sock_Im << "parallel " << num_procs << " " << myid << "\n";
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sol_sock_Im.precision(8);
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sol_sock_Im << "solution\n" << *pmesh << E_gf.imag() << "window_title 'Imaginary part'" << flush;
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}
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// // delete invA;
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delete fec;
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delete ND_fespace;
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delete pmesh;
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return 0;
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}
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//define exact solution
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void E_exact_Re(const Vector &x, Vector &E)
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{
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double curl2E[3];
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get_maxwell_solution_Re(x, E, curl2E);
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}
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//calculate RHS from exact solution
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void f_exact_Re(const Vector &x, Vector &f)
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{
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double E_Re[3], curl2E_Re[3];
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double E_Im[3], curl2E_Im[3];
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get_maxwell_solution_Re(x, E_Re, curl2E_Re);
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get_maxwell_solution_Re(x, E_Im, curl2E_Im);
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// curl ( curl E) - omega^2 E = f
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double coeff;
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coeff = -omega * omega;
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f(0) = curl2E_Re[0] + coeff * E_Re[0];
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f(1) = curl2E_Re[1] + coeff * E_Re[1];
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f(2) = curl2E_Re[2] + coeff * E_Re[2];
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// Account for the complex shift
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f(0) += -complex_shift*E_Im[0];
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f(1) += -complex_shift*E_Im[1];
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f(2) += -complex_shift*E_Im[2];
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}
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void get_maxwell_solution_Re(const Vector & x, double E[], double curl2E[])
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{
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if (isol == 0) // polynomial
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{
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E[0] = x[1] * x[2] * (1.0 - x[1]) * (1.0 - x[2]);
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E[1] = x[0] * x[1] * x[2] * (1.0 - x[0]) * (1.0 - x[2]);
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E[2] = x[0] * x[1] * (1.0 - x[0]) * (1.0 - x[1]);
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curl2E[0] = 2.0 * x[1] * (1.0 - x[1]) - (2.0 * x[0] - 3.0) * x[2] * (1 - x[2]);
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curl2E[1] = 2.0 * x[1] * (x[0] * (1.0 - x[0]) + (1.0 - x[2]) * x[2]);
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curl2E[2] = 2.0 * x[1] * (1.0 - x[1]) + x[0] * (3.0 - 2.0 * x[2]) * (1.0 - x[0]);
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}
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else
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{
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double alpha = omega / sqrt(3);
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E[0] = cos(alpha*(x(0) + x(1) + x(2)));
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E[1] = 0.0;
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E[2] = 0.0;
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curl2E[0] = 2.0 * alpha * alpha * E[0];
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curl2E[1] = -alpha * alpha * E[0];
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curl2E[2] = -alpha * alpha * E[0];
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}
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}
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//define exact solution
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void E_exact_Im(const Vector &x, Vector &E)
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{
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double curl2E[3];
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get_maxwell_solution_Re(x, E, curl2E);
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}
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//calculate RHS from exact solution
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void f_exact_Im(const Vector &x, Vector &f)
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{
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double E_Re[3], curl2E_Re[3];
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double E_Im[3], curl2E_Im[3];
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get_maxwell_solution_Re(x, E_Im, curl2E_Im);
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get_maxwell_solution_Re(x, E_Re, curl2E_Re);
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// curl ( curl E) - omega^2 E = f
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double coeff;
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coeff = -omega * omega;
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f(0) = curl2E_Im[0] + coeff * E_Im[0];
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f(1) = curl2E_Im[1] + coeff * E_Im[1];
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f(2) = curl2E_Im[2] + coeff * E_Im[2];
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// Acount for the complex shift
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f(0) += complex_shift*E_Re[0];
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f(1) += complex_shift*E_Re[1];
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f(2) += complex_shift*E_Re[2];
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}
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|
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void get_maxwell_solution_Im(const Vector & x, double E[], double curl2E[])
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{
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if (isol == 0) // polynomial
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{
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E[0] = x[1] * x[2] * (1.0 - x[1]) * (1.0 - x[2]);
|
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E[1] = x[0] * x[1] * x[2] * (1.0 - x[0]) * (1.0 - x[2]);
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E[2] = x[0] * x[1] * (1.0 - x[0]) * (1.0 - x[1]);
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curl2E[0] = 2.0 * x[1] * (1.0 - x[1]) - (2.0 * x[0] - 3.0) * x[2] * (1 - x[2]);
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curl2E[1] = 2.0 * x[1] * (x[0] * (1.0 - x[0]) + (1.0 - x[2]) * x[2]);
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|
curl2E[2] = 2.0 * x[1] * (1.0 - x[1]) + x[0] * (3.0 - 2.0 * x[2]) * (1.0 - x[0]);
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|
}
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|
else
|
|
{
|
|
double alpha = omega / sqrt(3);
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|
E[0] = sin(alpha * (x(0) + x(1) + x(2)));
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|
E[1] = 0.0;
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|
E[2] = 0.0;
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curl2E[0] = 2.0 * alpha * alpha * E[0];
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|
curl2E[1] = -alpha * alpha * E[0];
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curl2E[2] = -alpha * alpha * E[0];
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|
}
|
|
} |