449 lines
11 KiB
C++
449 lines
11 KiB
C++
//
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// Compile with: make helmholtz
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//
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// Sample runs: helmholtz -m ../data/one-hex.mesh
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// helmholtz -m ../data/fichera.mesh
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// helmholtz -m ../data/fichera-mixed.mesh
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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 Helmholtz problem
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// -Delta p - omega^2 p = 1 with impedance boundary condition.
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//
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#include "mfem.hpp"
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#include <fstream>
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#include <iostream>
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#include "pml.hpp"
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// #include "PST.hpp"
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#include "ST.hpp"
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using namespace std;
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using namespace mfem;
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// Exact solution and r.h.s., see below for implementation.
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double f_exact_Re(const Vector &x);
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double f_exact_Im(const Vector &x);
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double wavespeed(const Vector &x);
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int dim;
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double omega;
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int sol = 1;
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bool pml = false;
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double length = 1.0;
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double pml_length = 0.25;
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bool scatter = false;
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Array2D<double>comp_bdr;
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#ifndef MFEM_USE_SUPERLU
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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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int main(int argc, char *argv[])
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{
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// 2. 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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// finite element order of approximation
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int order = 1;
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// static condensation flag
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bool static_cond = false;
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bool visualization = 1;
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// number of wavelengths
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double k = 0.5;
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// number of mg levels
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int ref = 1;
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// dimension
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int nd = 2;
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// optional command line inputs
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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(&nd, "-nd", "--dim","Problem space dimension");
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args.AddOption(&sol, "-sol", "--exact",
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"Exact solution flag - 0:polynomial, 1: plane wave, -1: unknown exact");
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args.AddOption(&k, "-k", "--wavelengths",
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"Number of wavelengths.");
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args.AddOption(&pml, "-pml", "--pml", "-no-pml",
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"--no-pml", "Enable PML.");
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args.AddOption(&pml_length, "-pml_length", "--pml_length",
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"Length of the PML region in each direction");
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args.AddOption(&length, "-length", "--length",
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"length of the domainin in each direction.");
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args.AddOption(&ref, "-ref", "--ref",
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"Number of Refinements.");
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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(&scatter, "-scat", "--scattering-prob", "-no-scat",
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"--no-scattering", "Solve a scattering problem");
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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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// check if the inputs are correct
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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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// Angular frequency
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omega = 2.0 * M_PI * k;
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// 3. Read the mesh from the given mesh file.
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Mesh *mesh;
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if (nd == 2)
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{
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// mesh = new Mesh(mesh_file,1,1);
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mesh = new Mesh(1, 1, Element::QUADRILATERAL, true, length, length, false);
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}
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else
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{
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mesh = new Mesh(1, 1, 1, Element::HEXAHEDRON, true, length, length, length,false);
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}
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// 3. Executing uniform h-refinement
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for (int i = 0; i < ref; i++ )
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{
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mesh->UniformRefinement();
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}
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dim = mesh->Dimension();
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double hl = GetUniformMeshElementSize(mesh);
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Vector pmin, pmax;
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mesh->GetBoundingBox(pmin,pmax);
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double domain_length = pmax[0] - pmin[0];
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double pml_thickness = 0.25/domain_length;
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int nrlayers = pml_thickness/hl;
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// int nrlayers = 4;
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Array<int> directions;
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for (int i = 0; i<nrlayers; i++)
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{
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for (int comp=0; comp<dim; ++comp)
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{
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directions.Append(comp+1);
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directions.Append(-comp-1);
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}
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}
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// Find uniform h size of the original mesh
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cout << "pml layers = " << nrlayers << endl;
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cout << "pml length = " << hl*nrlayers << endl;
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Mesh *mesh_ext = ExtendMesh(mesh,directions);
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Array2D<double> lengths(dim,2);
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lengths = hl*nrlayers;
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// lengths[0][1] = 0.0;
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// lengths[1][1] = 0.0;
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// lengths[1][0] = 0.0;
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// lengths[0][0] = 0.0;
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CartesianPML pml(mesh_ext,lengths);
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pml.SetOmega(omega);
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comp_bdr.SetSize(dim,2);
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comp_bdr = pml.GetCompDomainBdr();
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// 6. Define a finite element space on the mesh.
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FiniteElementCollection *fec = new H1_FECollection(order, dim);
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FiniteElementSpace *fespace = new FiniteElementSpace(mesh_ext, fec);
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// 6. Set up the linear form (Real and Imaginary part)
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FunctionCoefficient f_Re(f_exact_Re);
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FunctionCoefficient f_Im(f_exact_Im);
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// ParLinearForm *b_Re(new ParLinearForm);
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ComplexLinearForm b(fespace, ComplexOperator::HERMITIAN);
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b.AddDomainIntegrator(new DomainLFIntegrator(f_Re),
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new DomainLFIntegrator(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. Set up the bilinear form (Real and Imaginary part)
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ConstantCoefficient one(1.0);
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ConstantCoefficient sigma(-pow(omega, 2));
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FunctionCoefficient ws(wavespeed);
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PmlMatrixCoefficient c1_re(dim,pml_detJ_JT_J_inv_Re,&pml);
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PmlMatrixCoefficient c1_im(dim,pml_detJ_JT_J_inv_Im,&pml);
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PmlCoefficient detJ_re(pml_detJ_Re,&pml);
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PmlCoefficient detJ_im(pml_detJ_Im,&pml);
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ProductCoefficient c2_re0(sigma, detJ_re);
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ProductCoefficient c2_im0(sigma, detJ_im);
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ProductCoefficient c2_re(c2_re0, ws);
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ProductCoefficient c2_im(c2_im0, ws);
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SesquilinearForm a(fespace,ComplexOperator::HERMITIAN);
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a.AddDomainIntegrator(new DiffusionIntegrator(c1_re),
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new DiffusionIntegrator(c1_im));
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a.AddDomainIntegrator(new MassIntegrator(c2_re),new MassIntegrator(c2_im));
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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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Array<int> ess_bdr(mesh_ext->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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// Solution grid function
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ComplexGridFunction p_gf(fespace);
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OperatorHandle Ah;
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Vector X, B;
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a.FormLinearSystem(ess_tdof_list, p_gf, b, Ah, X, B);
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ComplexSparseMatrix * AZ = Ah.As<ComplexSparseMatrix>();
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SparseMatrix * A = AZ->GetSystemMatrix();
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cout << "Size of fine grid system: "
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<< A->Height() << " x " << A->Width() << endl;
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// PSTP S(&a,lengths, omega, &ws, nrlayers);
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STP S(&a,lengths, omega, &ws, nrlayers);
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S.SetOperator(*A);
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// S.SetLoadVector(B);
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X = 0.0;
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GMRESSolver gmres;
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gmres.SetPreconditioner(S);
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gmres.SetOperator(*A);
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gmres.SetRelTol(1e-8);
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gmres.SetMaxIter(50);
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gmres.SetPrintLevel(1);
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gmres.Mult(B, X);
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int n= 50;
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X = 0.0;
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Vector z(X.Size()); z = 0.0;
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Vector r(B);
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Vector ztemp(r.Size());
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Vector Ax(X.Size());
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double tol = 1e-8;
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cout << endl;
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for (int i = 0; i<n; i++)
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{
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A->Mult(X,Ax); Ax *=-1.0;
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r = b; r+=Ax;
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cout << " ST Solver Iteration : " << i <<" || r || = " << r.Norml2() << endl;
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if (r.Norml2() < tol)
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{
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// cout << "Convergence in " << i+1 << " iterations" << endl;
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break;
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}
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S.Mult(r,z);
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X += z;
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// p_gf = 0.0;
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// a.RecoverFEMSolution(X,B,p_gf);
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// char vishost[] = "localhost";
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// int visport = 19916;
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// string keys;
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// if (dim ==2 )
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// {
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// keys = "keys mrRljc\n";
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// }
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// else
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// {
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// keys = "keys mc\n";
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// }
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// socketstream sol1_sock_re(vishost, visport);
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// sol1_sock_re.precision(8);
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// sol1_sock_re << "solution\n" << *mesh_ext << p_gf.real() <<
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// "window_title 'Numerical Pressure (real part)' "
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// << keys << flush;
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}
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// KLUSolver klu(*A);
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// klu.Mult(B,X);
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a.RecoverFEMSolution(X,B,p_gf);
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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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string keys;
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if (dim ==2 )
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{
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keys = "keys mrRljc\n";
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}
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else
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{
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keys = "keys mc\n";
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}
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socketstream sol_sock_re(vishost, visport);
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sol_sock_re.precision(8);
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sol_sock_re << "solution\n" << *mesh_ext << p_gf.real() <<
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"window_title 'Numerical Pressure (real part from KLU)' "
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<< keys << flush;
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// socketstream diff_sock_re(vishost, visport);
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// diff_sock_re.precision(8);
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// diff_sock_re << "solution\n" << *mesh_ext << p_gf1.real() <<
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// "window_title 'Numerical Pressure (real part from KLU)' "
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// << keys << flush;
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}
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delete fespace;
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delete fec;
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delete mesh_ext;
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delete mesh;
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return 0;
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}
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//calculate RHS from exact solution f = - \Delta u
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double f_exact_Re(const Vector &x)
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{
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double f_re = 0.0;
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double x0 = length/2.0;
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double x1 = length/2.0;
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double x2 = length/2.0;
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x0 = 0.1;
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x1 = 0.5;
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double alpha,beta;
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double n = 5.0*omega/M_PI;
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// double n = 1.0;
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double coeff = pow(n,2)/M_PI;
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beta = pow(x0-x(0),2) + pow(x1-x(1),2);
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if (dim == 3) { beta += pow(x2-x(2),2); }
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alpha = -pow(n,2) * beta;
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f_re = coeff*exp(alpha);
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// x0 = 0.9;
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// x1 = 0.5;
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// beta = pow(x0-x(0),2) + pow(x1-x(1),2);
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// if (dim == 3) { beta += pow(x2-x(2),2); }
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// alpha = -pow(n,2) * beta;
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// f_re += coeff*exp(alpha);
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// x0 = 0.5;
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// x1 = 0.8;
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// beta = pow(x0-x(0),2) + pow(x1-x(1),2);
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// if (dim == 3) { beta += pow(x2-x(2),2); }
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// alpha = -pow(n,2) * beta;
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// f_re += coeff*exp(alpha);
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bool in_pml = false;
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for (int i = 0; i<dim; i++)
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{
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if (x(i)<=comp_bdr(i,0) || x(i)>=comp_bdr(i,1))
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{
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in_pml = true;
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break;
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}
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}
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if (in_pml) f_re = 0.0;
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return f_re;
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}
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double f_exact_Im(const Vector &x)
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{
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double f_im;
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f_im = 0.0;
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return f_im;
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}
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double wavespeed(const Vector &x)
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{
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double ws;
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// if (x(0) <= 0.25)
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// {
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// ws = 1.0;
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// }
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// else if(x(0)<=0.5)
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// {
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// ws = 1.0;
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// }
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// else if(x(0)<=0.75)
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// {
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// ws = 0.75;
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// // ws = 0.5;
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// }
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// else
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// {
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// ws = 0.75;
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// // ws = 1.0;
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// }
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// if (x(1) <= 1.0/3.0)
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// {
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// ws = 2.0;
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// }
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// else if(x(1)<=2.0/3.0)
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// {
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// ws = 1.0;
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// }
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// else
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// {
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// // ws = 0.75;
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// ws = 0.25;
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// }
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// if (x(0) <= 0.33)
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// {
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// ws = 1.0;
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// }
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// else if(x(0)<=0.66)
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// {
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// ws = -0.65 + 5.0*x(0);
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// }
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// else
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// {
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// ws = 2.65;
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// // ws = 0.5;
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// }
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ws = 1.0;
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return ws;
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}
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