522 lines
17 KiB
C++
522 lines
17 KiB
C++
// MFEM Example 1 - Parallel High-Performance Version
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//
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// Compile with: make ex1p
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//
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// Sample runs: mpirun -np 4 ex1p -m ../../data/fichera.mesh -perf -mf -pc lor
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// mpirun -np 4 ex1p -m ../../data/fichera.mesh -perf -asm -pc ho
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// mpirun -np 4 ex1p -m ../../data/fichera.mesh -perf -asm -pc ho -sc
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// mpirun -np 4 ex1p -m ../../data/fichera.mesh -std -asm -pc ho
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// mpirun -np 4 ex1p -m ../../data/fichera.mesh -std -asm -pc ho -sc
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// mpirun -np 4 ex1p -m ../../data/amr-hex.mesh -perf -asm -pc ho -sc
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// mpirun -np 4 ex1p -m ../../data/amr-hex.mesh -std -asm -pc ho -sc
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// mpirun -np 4 ex1p -m ../../data/ball-nurbs.mesh -perf -asm -pc ho -sc
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// mpirun -np 4 ex1p -m ../../data/ball-nurbs.mesh -std -asm -pc ho -sc
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// mpirun -np 4 ex1p -m ../../data/pipe-nurbs.mesh -perf -mf -pc lor
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// mpirun -np 4 ex1p -m ../../data/pipe-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 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-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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// Define template parameters for optimized build.
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const Geometry::Type geom = Geometry::CUBE; // mesh elements (default: hex)
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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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const int rdim = Geometry::Constants<geom>::Dimension;
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const int ir_order = 2*sol_p+rdim-1;
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// Static mesh type
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typedef H1_FiniteElement<geom,mesh_p> mesh_fe_t;
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typedef H1_FiniteElementSpace<mesh_fe_t> mesh_fes_t;
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typedef TMesh<mesh_fes_t> mesh_t;
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// Static solution finite element space type
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typedef H1_FiniteElement<geom,sol_p> sol_fe_t;
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typedef H1_FiniteElementSpace<sol_fe_t> sol_fes_t;
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// Static quadrature, coefficient and integrator types
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typedef TIntegrationRule<geom,ir_order> int_rule_t;
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typedef TConstantCoefficient<> coeff_t;
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typedef TIntegrator<coeff_t,TDiffusionKernel> integ_t;
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// Static bilinear form type, combining the above types
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typedef TBilinearForm<mesh_t,sol_fes_t,int_rule_t,integ_t> HPCBilinearForm;
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int main(int argc, char *argv[])
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{
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// 1. Initialize MPI.
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int num_procs, myid;
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MPI_Init(&argc, &argv);
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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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// 2. Parse command-line options.
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const char *mesh_file = "../../data/fichera.mesh";
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int ser_ref_levels = -1;
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int par_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 = "lor";
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bool perf = true;
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bool matrix_free = true;
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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(&ser_ref_levels, "-rs", "--refine-serial",
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"Number of times to refine the mesh uniformly in serial;"
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" -1 = auto: <= 10,000 elements.");
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args.AddOption(&par_ref_levels, "-rp", "--refine-parallel",
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"Number of times to refine the mesh uniformly in parallel.");
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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) AMG, "
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"ho - high-order (assembled) AMG, 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.Parse();
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if (!args.Good())
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{
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if (myid == 0)
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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 (static_cond && perf && matrix_free)
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{
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if (myid == 0)
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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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}
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MPI_Finalize();
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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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if (myid == 0)
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{
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args.PrintOptions(cout);
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}
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enum PCType { NONE, LOR, HO };
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PCType pc_choice;
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if (!strcmp(pc, "ho")) { pc_choice = HO; }
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else if (!strcmp(pc, "lor")) { pc_choice = LOR; }
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else if (!strcmp(pc, "none")) { pc_choice = 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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if (myid == 0)
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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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}
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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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if (myid == 0)
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{
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cout << "Using " << BasisType::Name(basis) << " basis ..." << endl;
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}
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// 3. Read the (serial) mesh from the given mesh file on all processors. We
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// can handle triangular, quadrilateral, tetrahedral, hexahedral, surface
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// and volume meshes with 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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// 4. Check if the optimized version matches the given mesh
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if (perf)
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{
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if (myid == 0)
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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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}
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if (!mesh_t::MatchesGeometry(*mesh))
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{
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if (myid == 0)
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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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}
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delete mesh;
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MPI_Finalize();
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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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if (myid == 0)
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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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}
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mesh->SetCurvature(mesh_p, false, -1, Ordering::byNODES);
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}
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}
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// 5. Refine the serial mesh on all processors to increase the resolution. In
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// this example we do 'ref_levels' of uniform refinement. We choose
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// 'ref_levels' to be the largest number that gives a final mesh with no
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// more than 10,000 elements, or as specified on the command line with the
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// option '--refine-serial'.
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{
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int ref_levels = (ser_ref_levels != -1) ? ser_ref_levels :
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(int)floor(log(10000./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 (!perf && mesh->NURBSext)
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{
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const int new_mesh_p = std::min(sol_p, mesh_p);
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if (myid == 0)
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{
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cout << "NURBS mesh: switching the mesh curvature to be "
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<< "min(sol_p, mesh_p) = " << new_mesh_p << " ..." << endl;
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}
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mesh->SetCurvature(new_mesh_p, false, -1, Ordering::byNODES);
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}
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// 6. Define a parallel mesh by a partitioning of the serial mesh. Refine
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// this mesh further in parallel to increase the resolution. Once the
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// parallel mesh is defined, the serial mesh can be deleted.
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ParMesh *pmesh = new ParMesh(MPI_COMM_WORLD, *mesh);
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delete mesh;
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{
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for (int l = 0; l < par_ref_levels; l++)
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{
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pmesh->UniformRefinement();
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}
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}
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if (pmesh->MeshGenerator() & 1) // simplex mesh
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{
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MFEM_VERIFY(pc_choice != LOR, "triangle and tet meshes do not support"
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" the LOR preconditioner yet");
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}
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// 7. Define a parallel finite element space on the parallel mesh. Here we
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// use continuous Lagrange finite elements of the specified order. If
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// order < 1, we 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 (pmesh->GetNodes())
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{
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fec = pmesh->GetNodes()->OwnFEC();
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if (myid == 0)
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{
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cout << "Using isoparametric FEs: " << fec->Name() << endl;
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}
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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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ParFiniteElementSpace *fespace = new ParFiniteElementSpace(pmesh, fec);
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HYPRE_Int size = fespace->GlobalTrueVSize();
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if (myid == 0)
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{
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cout << "Number of finite element unknowns: " << size << endl;
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}
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ParMesh *pmesh_lor = NULL;
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FiniteElementCollection *fec_lor = NULL;
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ParFiniteElementSpace *fespace_lor = NULL;
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if (pc_choice == 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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pmesh_lor = new ParMesh(pmesh, order, basis_lor);
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fec_lor = new H1_FECollection(1, dim);
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fespace_lor = new ParFiniteElementSpace(pmesh_lor, fec_lor);
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}
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// 8. 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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if (myid == 0)
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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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}
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delete fespace;
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delete fec;
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delete mesh;
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MPI_Finalize();
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return 5;
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}
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// 9. Determine the list of true (i.e. parallel conforming) essential
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// boundary dofs. In this example, the boundary conditions are defined
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// by marking all the boundary attributes from the mesh as essential
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// (Dirichlet) and converting them to a list of true dofs.
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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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fespace->GetEssentialTrueDofs(ess_bdr, ess_tdof_list);
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}
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// 10. Set up the parallel linear form b(.) which corresponds to the
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// right-hand side of the FEM linear system, which in this case is
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// (1,phi_i) where phi_i are the basis functions in fespace.
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ParLinearForm *b = new ParLinearForm(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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// 11. Define the solution vector x as a parallel finite element grid
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// function corresponding to fespace. Initialize x with initial guess of
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// zero, which satisfies the boundary conditions.
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ParGridFunction x(fespace);
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x = 0.0;
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// 12. Set up the parallel bilinear form a(.,.) on the finite element space
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// that will hold the matrix corresponding to the Laplacian operator.
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ParBilinearForm *a = new ParBilinearForm(fespace);
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ParBilinearForm *a_pc = NULL;
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if (pc_choice == LOR) { a_pc = new ParBilinearForm(fespace_lor); }
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if (pc_choice == HO) { a_pc = new ParBilinearForm(fespace); }
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// 13. Assemble the parallel bilinear form and the corresponding linear
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// system, applying any necessary transformations such as: parallel
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// assembly, eliminating boundary conditions, applying conforming
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// constraints for non-conforming AMR, 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 != LOR,
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"cannot use LOR preconditioner with static condensation");
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}
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if (myid == 0)
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{
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cout << "Assembling the matrix ..." << flush;
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}
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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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if (myid == 0)
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{
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cout << " done, " << tic_toc.RealTime() << "s." << endl;
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}
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// 14. Define and apply a parallel PCG solver for AX=B with the BoomerAMG
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// preconditioner from hypre.
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// Setup the operator matrix (if applicable)
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HypreParMatrix 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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HYPRE_Int glob_size = fespace->GlobalTrueVSize();
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if (myid == 0)
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{
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cout << "Size of linear system: " << glob_size << endl;
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}
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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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HYPRE_Int glob_size = A.GetGlobalNumRows();
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if (myid == 0)
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{
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cout << "Size of linear system: " << glob_size << endl;
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}
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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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if (myid == 0)
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{
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cout << "Assembling the preconditioning matrix ..." << flush;
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}
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tic_toc.Clear();
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tic_toc.Start();
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HypreParMatrix A_pc;
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if (pc_choice == 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 == 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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if (myid == 0)
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{
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cout << " done, " << tic_toc.RealTime() << "s." << endl;
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}
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// Solve with CG or PCG, depending if the matrix A_pc is available
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CGSolver *pcg;
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pcg = new CGSolver(MPI_COMM_WORLD);
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pcg->SetRelTol(1e-6);
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pcg->SetMaxIter(500);
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pcg->SetPrintLevel(1);
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HypreSolver *amg = NULL;
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pcg->SetOperator(*a_oper);
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if (pc_choice != NONE)
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{
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amg = new HypreBoomerAMG(A_pc);
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pcg->SetPreconditioner(*amg);
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}
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tic_toc.Clear();
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tic_toc.Start();
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pcg->Mult(B, X);
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tic_toc.Stop();
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delete amg;
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if (myid == 0)
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{
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// Note: In the pcg algorithm, the number of operator Mult() calls is
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// N_iter and the number of preconditioner Mult() calls is N_iter+1.
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cout << "Time per CG step: "
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<< tic_toc.RealTime() / pcg->GetNumIterations() << "s." << endl;
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}
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// 15. Recover the parallel grid function corresponding to X. This is the
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// local finite element solution on each processor.
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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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// 16. Save the refined mesh and the solution in parallel. This output can
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// be viewed later using GLVis: "glvis -np <np> -m mesh -g sol".
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{
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ostringstream mesh_name, sol_name;
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mesh_name << "mesh." << setfill('0') << setw(6) << myid;
|
|
sol_name << "sol." << setfill('0') << setw(6) << myid;
|
|
|
|
ofstream mesh_ofs(mesh_name.str().c_str());
|
|
mesh_ofs.precision(8);
|
|
pmesh->Print(mesh_ofs);
|
|
|
|
ofstream sol_ofs(sol_name.str().c_str());
|
|
sol_ofs.precision(8);
|
|
x.Save(sol_ofs);
|
|
}
|
|
|
|
// 17. Send the solution by socket to a GLVis server.
|
|
if (visualization)
|
|
{
|
|
char vishost[] = "localhost";
|
|
int visport = 19916;
|
|
socketstream sol_sock(vishost, visport);
|
|
sol_sock << "parallel " << num_procs << " " << myid << "\n";
|
|
sol_sock.precision(8);
|
|
sol_sock << "solution\n" << *pmesh << x << flush;
|
|
}
|
|
|
|
// 18. Free the used memory.
|
|
delete a;
|
|
delete a_hpc;
|
|
if (a_oper != &A) { delete a_oper; }
|
|
delete a_pc;
|
|
delete b;
|
|
delete fespace;
|
|
delete fespace_lor;
|
|
delete fec_lor;
|
|
delete pmesh_lor;
|
|
if (order > 0) { delete fec; }
|
|
delete pmesh;
|
|
delete pcg;
|
|
|
|
MPI_Finalize();
|
|
|
|
return 0;
|
|
}
|