255 lines
9.4 KiB
C++
255 lines
9.4 KiB
C++
// MFEM Example 1
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//
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// Compile with: make ex1
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//
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// Sample runs: ex1 -m ../data/square-disc.mesh
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// ex1 -m ../data/star.mesh
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// ex1 -m ../data/escher.mesh
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// ex1 -m ../data/fichera.mesh
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// ex1 -m ../data/square-disc-p2.vtk -o 2
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// ex1 -m ../data/square-disc-p3.mesh -o 3
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// ex1 -m ../data/square-disc-nurbs.mesh -o -1
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// ex1 -m ../data/disc-nurbs.mesh -o -1
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// ex1 -m ../data/pipe-nurbs.mesh -o -1
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// ex1 -m ../data/star-surf.mesh
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// ex1 -m ../data/square-disc-surf.mesh
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// ex1 -m ../data/inline-segment.mesh
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// ex1 -m ../data/amr-quad.mesh
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// ex1 -m ../data/amr-hex.mesh
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// ex1 -m ../data/fichera-amr.mesh
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// ex1 -m ../data/mobius-strip.mesh
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// ex1 -m ../data/mobius-strip.mesh -o -1 -sc
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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 Laplace 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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#include "/home/camier1/home/stk/stk.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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stkIni(argv[0]);
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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 gpu = false;
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bool visualization = 1;
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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(&gpu, "-g", "--gpu", "-no-g", "--no-gpu", "Enable GPU.");
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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. 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 = new Mesh(mesh_file, 1, 1);
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int dim = mesh->Dimension();
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// 3. 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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/*
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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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}
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dbg("4. 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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if (order > 0)
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{
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fec = new H1_FECollection(order, dim);
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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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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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}
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FiniteElementSpace *fespace = new FiniteElementSpace(mesh, fec);
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cout << "Number of finite element unknowns: "
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<< fespace->GetTrueVSize() << endl;
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dbg("5. 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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dbg("6. 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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dbg("LinearForm b=");
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b->Print();
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//0.297205 0.118882 0.118882 0.0594411 0.118881 0.059441 0.118881 0.0594409
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//0.118882 0.0594411 0.0594411 0.237765 0.118882 0.118882 0.237764 0.118882
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//0.118882 0.237764 0.118881 0.118881 0.237763 0.118882 0.118882 0.237764
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//0.118882 0.118882 0.237765 0.237764 0.237763 0.237764 0.237765
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//mesh->SetNodalFESpace(fespace);
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//GridFunction *nodes = mesh->GetNodes();
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//dbg("nodes:");
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//nodes->Print();
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//0 1 0.309017 1.30902 -0.809017 -0.5 -0.809017 -1.61803
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//0.309017 -0.5 1.30902 0.5 1.15451 0.809019 0.154508 -0.0954915
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//-0.654508 -0.404508 -1.21352 -1.21352 -0.404508 -0.654508 -0.0954915 0.154508
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//0.809019 1.15451 0.654509 -0.25 -0.809016 -0.25 0.654509
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//assert(false);
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if (gpu){
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//#warning Need to do this before before switching to get the Nodes ready for kgeom
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//mesh->SetNodalFESpace(fespace);
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mesh->SetCurvature(1, false, -1, Ordering::byVDIM);
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config::Get().Cuda(true);
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config::Get().PA(true);
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dbg("\033[32;7mSwitched to GPU & PA!");
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}
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dbg("7. 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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dbg("8. 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->AddDomainIntegrator(new DiffusionIntegrator(one));
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if (config::Get().PA()){
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dbg("Add PA DiffusionIntegrator");
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a->AddDomainIntegrator(new PADiffusionIntegrator(one));
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}else{
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dbg("Add FA DiffusionIntegrator");
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a->AddDomainIntegrator(new DiffusionIntegrator(one));
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}
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dbg("9. 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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dbg("9. PA:BilinearForm / FA:SparseMatrix");
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PABilinearForm paA(fespace);
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SparseMatrix faA;
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//Operator A = config::Get().PA() ? paA : faA;
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//Operator &A = config::Get().PA() ? Operator(0) : SparseMatrix();
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Vector B, X;
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if (config::Get().PA())
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a->FormLinearSystem(ess_tdof_list, x, *b, paA, X, B);
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else
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a->FormLinearSystem(ess_tdof_list, x, *b, faA, X, B);
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if (config::Get().PA())
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cout << "Size of linear system: " << paA.Height() << endl;
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else
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cout << "Size of linear system: " << faA.Height() << endl;
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//config::Get().Cuda(gpu);
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#ifndef MFEM_USE_SUITESPARSE
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//dbg("10. Define a simple symmetric Gauss-Seidel preconditioner");// and use it to
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dbg("10. Solve the system A X = B with PCG.");
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//GSSmoother M(A);
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//PCG(A, M, B, X, 1, 200, 1e-12, 0.0);
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if (config::Get().PA())
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CG(paA, B, X, 3, 1000, 1e-12, 0.0);
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else
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CG(faA, B, X, 3, 1000, 1e-12, 0.0);
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#else
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// 10. 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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// 11. Recover the solution as a finite element grid function.
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a->RecoverFEMSolution(X, *b, x);
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// 12. 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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// 13. 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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// 14. Free the used memory.
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delete a;
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delete b;
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delete fespace;
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if (order > 0) { delete fec; }
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delete mesh;
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return 0;
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}
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