452 lines
16 KiB
C++
452 lines
16 KiB
C++
// MFEM Example 1 - High-Performance Version
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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/fichera.mesh -perf -mf -pc lor
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// ex1 -m ../../data/fichera.mesh -perf -asm -pc ho
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// ex1 -m ../../data/fichera.mesh -perf -asm -pc ho -sc
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// ex1 -m ../../data/fichera.mesh -std -asm -pc ho
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// ex1 -m ../../data/fichera.mesh -std -asm -pc ho -sc
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// ex1 -m ../../data/amr-hex.mesh -perf -asm -pc ho -sc
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// ex1 -m ../../data/amr-hex.mesh -std -asm -pc ho -sc
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// ex1 -m ../../data/ball-nurbs.mesh -perf -asm -pc ho -sc
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// ex1 -m ../../data/ball-nurbs.mesh -std -asm -pc ho -sc
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// ex1 -m ../../data/pipe-nurbs.mesh -perf -mf -pc lor
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// ex1 -m ../../data/pipe-nurbs.mesh -std -asm -pc ho -sc
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// ex1 -m ../../data/star.mesh -perf -mf -pc lor
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// ex1 -m ../../data/star.mesh -perf -asm -pc ho
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// ex1 -m ../../data/star.mesh -perf -asm -pc ho -sc
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// ex1 -m ../../data/star.mesh -std -asm -pc ho
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// ex1 -m ../../data/star.mesh -std -asm -pc ho -sc
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// ex1 -m ../../data/amr-quad.mesh -perf -asm -pc ho -sc
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// ex1 -m ../../data/amr-quad.mesh -std -asm -pc ho -sc
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// ex1 -m ../../data/disc-nurbs.mesh -perf -asm -pc ho -sc
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// ex1 -m ../../data/disc-nurbs.mesh -std -asm -pc ho -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 Poisson problem
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// -Delta u = 1 with homogeneous Dirichlet boundary conditions.
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// Specifically, we discretize using a FE space of the specified
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// order, or if order < 1 using an isoparametric/isogeometric
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// space (i.e. quadratic for quadratic curvilinear mesh, NURBS for
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// NURBS mesh, etc.)
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//
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// The example highlights the use of mesh refinement, finite
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// element grid functions, as well as linear and bilinear forms
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// corresponding to the left-hand side and right-hand side of the
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// discrete linear system. We also cover the explicit elimination
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// of essential boundary conditions, static condensation, and the
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// optional connection to the GLVis tool for visualization.
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#include "mfem-performance.hpp"
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#include <fstream>
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#include <iostream>
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using namespace std;
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using namespace mfem;
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enum class PCType { NONE, LOR, HO };
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// Define template parameters for optimized build.
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template <int dim> struct geom_t { };
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template <>
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struct geom_t<2> { static const Geometry::Type value = Geometry::SQUARE; };
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template <>
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struct geom_t<3> { static const Geometry::Type value = Geometry::CUBE; };
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const int mesh_p = 3; // mesh curvature (default: 3)
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const int sol_p = 3; // solution order (default: 3)
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template <int dim>
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struct ex1_t
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{
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static const Geometry::Type geom = geom_t<dim>::value;
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static const int rdim = Geometry::Constants<geom>::Dimension;
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static const int ir_order = 2*sol_p+rdim-1;
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// Static mesh type
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using mesh_fe_t = H1_FiniteElement<geom,mesh_p>;
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using mesh_fes_t = H1_FiniteElementSpace<mesh_fe_t>;
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using mesh_t = TMesh<mesh_fes_t>;
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// Static solution finite element space type
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using sol_fe_t = H1_FiniteElement<geom,sol_p>;
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using sol_fes_t = H1_FiniteElementSpace<sol_fe_t>;
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// Static quadrature, coefficient and integrator types
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using int_rule_t = TIntegrationRule<geom,ir_order>;
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using coeff_t = TConstantCoefficient<>;
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using integ_t = TIntegrator<coeff_t,TDiffusionKernel>;
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using HPCBilinearForm = TBilinearForm<mesh_t,sol_fes_t,int_rule_t,integ_t>;
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static int run(Mesh *mesh, int ref_levels, int order, int basis,
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bool static_cond, PCType pc_choice, bool perf,
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bool matrix_free, bool visualization, int visport = 19916);
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};
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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/fichera.mesh";
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int ref_levels = -1;
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int order = sol_p;
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const char *basis_type = "G"; // Gauss-Lobatto
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bool static_cond = false;
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const char *pc = "none";
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bool perf = true;
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bool matrix_free = true;
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int visport = 19916;
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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(&ref_levels, "-r", "--refine",
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"Number of times to refine the mesh uniformly;"
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" -1 = auto: <= 50,000 elements.");
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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(&basis_type, "-b", "--basis-type",
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"Basis: G - Gauss-Lobatto, P - Positive, U - Uniform");
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args.AddOption(&perf, "-perf", "--hpc-version", "-std", "--standard-version",
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"Enable high-performance, tensor-based, assembly/evaluation.");
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args.AddOption(&matrix_free, "-mf", "--matrix-free", "-asm", "--assembly",
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"Use matrix-free evaluation or efficient matrix assembly in "
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"the high-performance version.");
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args.AddOption(&pc, "-pc", "--preconditioner",
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"Preconditioner: lor - low-order-refined (matrix-free) GS, "
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"ho - high-order (assembled) GS, none.");
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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(&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(&visport, "-p", "--send-port", "Socket for GLVis.");
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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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if (static_cond && perf && matrix_free)
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{
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cout << "\nStatic condensation can not be used with matrix-free"
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" evaluation!\n" << endl;
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return 2;
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}
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MFEM_VERIFY(perf || !matrix_free,
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"--standard-version is not compatible with --matrix-free");
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args.PrintOptions(cout);
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PCType pc_choice;
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if (!strcmp(pc, "ho")) { pc_choice = PCType::HO; }
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else if (!strcmp(pc, "lor")) { pc_choice = PCType::LOR; }
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else if (!strcmp(pc, "none")) { pc_choice = PCType::NONE; }
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else
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{
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mfem_error("Invalid Preconditioner specified");
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return 3;
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}
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cout << "\nMFEM SIMD width: " << MFEM_SIMD_BYTES/sizeof(double)
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<< " doubles\n" << endl;
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// See class BasisType in fem/fe_coll.hpp for available basis types
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int basis = BasisType::GetType(basis_type[0]);
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cout << "Using " << BasisType::Name(basis) << " basis ..." << endl;
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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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if (dim == 2)
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{
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return ex1_t<2>::run(mesh, ref_levels, order, basis, static_cond,
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pc_choice, perf, matrix_free, visualization, visport);
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}
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else if (dim == 3)
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{
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return ex1_t<3>::run(mesh, ref_levels, order, basis, static_cond,
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pc_choice, perf, matrix_free, visualization, visport);
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}
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else
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{
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MFEM_ABORT("Dimension must be 2 or 3.")
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}
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return 0;
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}
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template <int dim>
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int ex1_t<dim>::run(Mesh *mesh, int ref_levels, int order, int basis,
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bool static_cond, PCType pc_choice, bool perf,
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bool matrix_free, bool visualization, int visport)
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{
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// 3. Check if the optimized version matches the given mesh
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if (perf)
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{
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cout << "High-performance version using integration rule with "
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<< int_rule_t::qpts << " points ..." << endl;
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if (!mesh_t::MatchesGeometry(*mesh))
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{
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cout << "The given mesh does not match the optimized 'geom' parameter.\n"
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<< "Recompile with suitable 'geom' value." << endl;
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delete mesh;
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return 4;
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}
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else if (!mesh_t::MatchesNodes(*mesh))
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{
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cout << "Switching the mesh curvature to match the "
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<< "optimized value (order " << mesh_p << ") ..." << endl;
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mesh->SetCurvature(mesh_p, false, -1, Ordering::byNODES);
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}
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}
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// 4. Refine the mesh to increase the resolution. In this example we do
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// 'ref_levels' of uniform refinement. We choose 'ref_levels' to be the
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// largest number that gives a final mesh with no more than 50,000
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// elements, or as specified on the command line with the option
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// '--refine'.
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{
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ref_levels = (ref_levels != -1) ? 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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if (mesh->MeshGenerator() & 1) // simplex mesh
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{
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MFEM_VERIFY(pc_choice != PCType::LOR, "triangle and tet meshes do not "
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" support the LOR preconditioner yet");
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}
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// 5. Define a finite element space on the mesh. Here we use continuous
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// Lagrange finite elements of the specified order. If order < 1, we
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// instead use an isoparametric/isogeometric space.
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FiniteElementCollection *fec;
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if (order > 0)
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{
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fec = new H1_FECollection(order, dim, basis);
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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, basis);
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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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// Create the LOR mesh and finite element space. In the settings of this
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// example, we can transfer between HO and LOR with the identity operator.
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Mesh mesh_lor;
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FiniteElementCollection *fec_lor = NULL;
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FiniteElementSpace *fespace_lor = NULL;
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if (pc_choice == PCType::LOR)
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{
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int basis_lor = basis;
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if (basis == BasisType::Positive) { basis_lor=BasisType::ClosedUniform; }
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mesh_lor = Mesh::MakeRefined(*mesh, order, basis_lor);
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fec_lor = new H1_FECollection(1, dim);
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fespace_lor = new FiniteElementSpace(&mesh_lor, fec_lor);
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}
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// 6. Check if the optimized version matches the given space
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if (perf && !sol_fes_t::Matches(*fespace))
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{
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cout << "The given order does not match the optimized parameter.\n"
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<< "Recompile with suitable 'sol_p' value." << endl;
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delete fespace;
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delete fec;
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delete mesh;
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return 5;
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}
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// 7. 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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// 8. 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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// 9. 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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// 10. Set up the bilinear form a(.,.) on the finite element space that will
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// hold the matrix corresponding to the Laplacian operator -Delta.
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// Optionally setup a form to be assembled for preconditioning (a_pc).
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BilinearForm *a = new BilinearForm(fespace);
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BilinearForm *a_pc = NULL;
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if (pc_choice == PCType::LOR) { a_pc = new BilinearForm(fespace_lor); }
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if (pc_choice == PCType::HO) { a_pc = new BilinearForm(fespace); }
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// 11. 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)
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{
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a->EnableStaticCondensation();
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MFEM_VERIFY(pc_choice != PCType::LOR,
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"cannot use LOR preconditioner with static condensation");
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}
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cout << "Assembling the bilinear form ..." << flush;
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tic_toc.Clear();
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tic_toc.Start();
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// Pre-allocate sparsity assuming dense element matrices
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a->UsePrecomputedSparsity();
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HPCBilinearForm *a_hpc = NULL;
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Operator *a_oper = NULL;
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if (!perf)
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{
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// Standard assembly using a diffusion domain integrator
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a->AddDomainIntegrator(new DiffusionIntegrator(one));
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a->Assemble();
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}
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else
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{
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// High-performance assembly/evaluation using the templated operator type
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a_hpc = new HPCBilinearForm(integ_t(coeff_t(1.0)), *fespace);
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if (matrix_free)
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{
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a_hpc->Assemble(); // partial assembly
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}
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else
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{
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a_hpc->AssembleBilinearForm(*a); // full matrix assembly
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}
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}
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tic_toc.Stop();
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cout << " done, " << tic_toc.RealTime() << "s." << endl;
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// 12. Solve the system A X = B with CG. In the standard case, use a simple
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// symmetric Gauss-Seidel preconditioner.
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// Setup the operator matrix (if applicable)
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SparseMatrix A;
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Vector B, X;
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if (perf && matrix_free)
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{
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a_hpc->FormLinearSystem(ess_tdof_list, x, *b, a_oper, X, B);
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cout << "Size of linear system: " << a_hpc->Height() << endl;
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}
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else
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{
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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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a_oper = &A;
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}
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// Setup the matrix used for preconditioning
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cout << "Assembling the preconditioning matrix ..." << flush;
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tic_toc.Clear();
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tic_toc.Start();
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SparseMatrix A_pc;
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if (pc_choice == PCType::LOR)
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{
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// TODO: assemble the LOR matrix using the performance code
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a_pc->AddDomainIntegrator(new DiffusionIntegrator(one));
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a_pc->UsePrecomputedSparsity();
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a_pc->Assemble();
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a_pc->FormSystemMatrix(ess_tdof_list, A_pc);
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}
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else if (pc_choice == PCType::HO)
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{
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if (!matrix_free)
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{
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A_pc.MakeRef(A); // matrix already assembled, reuse it
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}
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else
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{
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a_pc->UsePrecomputedSparsity();
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a_hpc->AssembleBilinearForm(*a_pc);
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a_pc->FormSystemMatrix(ess_tdof_list, A_pc);
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}
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}
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tic_toc.Stop();
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cout << " done, " << tic_toc.RealTime() << "s." << endl;
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// Solve with CG or PCG, depending if the matrix A_pc is available
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if (pc_choice != PCType::NONE)
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{
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GSSmoother M(A_pc);
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PCG(*a_oper, M, B, X, 1, 500, 1e-12, 0.0);
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}
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else
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{
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CG(*a_oper, B, X, 1, 500, 1e-12, 0.0);
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}
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// 13. Recover the solution as a finite element grid function.
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if (perf && matrix_free)
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{
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a_hpc->RecoverFEMSolution(X, *b, x);
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}
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else
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{
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a->RecoverFEMSolution(X, *b, x);
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}
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// 14. 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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// 15. 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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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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// 16. Free the used memory.
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delete a;
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delete a_hpc;
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if (a_oper != &A) { delete a_oper; }
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delete a_pc;
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delete b;
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delete fespace;
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delete fespace_lor;
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delete fec_lor;
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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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