413 lines
12 KiB
C++
413 lines
12 KiB
C++
// MFEM Example 1 - Parallel 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/square-disc.mesh
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// mpirun -np 4 ex1p -m ../data/star.mesh
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// mpirun -np 4 ex1p -m ../data/escher.mesh
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// mpirun -np 4 ex1p -m ../data/fichera.mesh
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// mpirun -np 4 ex1p -m ../data/square-disc-p2.vtk -o 2
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// mpirun -np 4 ex1p -m ../data/square-disc-p3.mesh -o 3
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// mpirun -np 4 ex1p -m ../data/square-disc-nurbs.mesh -o -1
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// mpirun -np 4 ex1p -m ../data/disc-nurbs.mesh -o -1
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// mpirun -np 4 ex1p -m ../data/pipe-nurbs.mesh -o -1
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// mpirun -np 4 ex1p -m ../data/ball-nurbs.mesh -o 2
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// mpirun -np 4 ex1p -m ../data/star-surf.mesh
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// mpirun -np 4 ex1p -m ../data/square-disc-surf.mesh
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// mpirun -np 4 ex1p -m ../data/inline-segment.mesh
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// mpirun -np 4 ex1p -m ../data/amr-quad.mesh
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// mpirun -np 4 ex1p -m ../data/amr-hex.mesh
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// mpirun -np 4 ex1p -m ../data/mobius-strip.mesh
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// mpirun -np 4 ex1p -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 "./spe10_coeff.cpp"
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int* LoadIterations(int NRows, int NCol)
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{
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ifstream in("iter_grad.txt");
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//initialize
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int *iters = new int[NCol*NRows];
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for (int col = 0; col < NCol; col++)
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{
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for (int row = 0; row < NRows; row++)
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{
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iters[row*NCol+col] = -1;
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}
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}
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if (!in)
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{
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cout << "Cannot open file.\n";
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return iters;
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}
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for (int row = 0; row < NRows; row++)
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for (int col = 0; col < NCol; col++)
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{
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if (in.eof())
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{
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in.close();
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return iters;
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}
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in >> iters[row*NCol+col];
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}
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in.close();
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return iters;
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}
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void putIterationsInArray(int iter, int row, int col, int NCol, int* iters)
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{
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iters[row*NCol+col] = iter;
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}
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void WriteIterations(int *iters, int NRows, int NCol)
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{
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ofstream out;
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out.open("iter_grad.txt",fstream::out);
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if (!out)
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{
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cout << "Cannot open file.\n";
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delete[] iters;
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return;
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}
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for (int row = 0; row < NRows; row++)
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{
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for (int col = 0; col < NCol; col++)
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{
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out << iters[row*NCol+col] << "\t";
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}
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out << endl;
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}
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out.close();
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delete[] iters;
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}
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using namespace std;
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using namespace mfem;
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double kappa = 1.0;
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double u_exact(const Vector &x)
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{
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int dim = x.Size();
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if (dim==4)
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{
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return cos(M_PI*x(0))*cos(M_PI*x(1))*cos(M_PI*x(2))*cos(M_PI*x(3));
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}
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else { return 0.0; }
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}
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double f_exact(const Vector &x)
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{
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int dim = x.Size();
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if (dim==4)
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{
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return (kappa + 4.0 * M_PI*M_PI) * cos(M_PI*x(0))*cos(M_PI*x(1))*cos(M_PI*x(
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2))*cos(M_PI*x(3));
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}
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else { return 0.0; }
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}
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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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bool verbose = (myid==0);
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// 2. Parse command-line options.
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const char *mesh_file = "../data/cube4d_96.MFEM";
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int order = 1;
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bool static_cond = false;
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bool visualization = 1;
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int sequ_ref_levels = 0;
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int par_ref_levels = 0;
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double tol = 1e-6;
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bool set_bc = true;
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bool standardCG = true;
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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(&sequ_ref_levels, "-sr", "--seqrefinement",
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"Number of sequential refinement steps.");
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args.AddOption(&par_ref_levels, "-pr", "--parrefinement",
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"Number of parallel refinement steps.");
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args.AddOption(&order, "-o", "--order",
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"Polynomial order of the finite element space.");
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args.AddOption(&tol, "-tol", "--tol",
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"A parameter.");
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args.AddOption(&set_bc, "-bc", "--impose-bc", "-no-bc", "--dont-impose-bc",
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"Impose or not essential boundary conditions.");
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args.AddOption(&standardCG, "-sCG", "--stdCG", "-rCG", "--resCG",
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"Switch between standard PCG or recompute residuals in every step and use the residuals itself for the stopping criteria.");
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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 (verbose) { args.PrintOptions(cout); }
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Mesh *mesh;
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ifstream imesh(mesh_file);
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if (!imesh)
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{
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cerr << "\nCan not open mesh file: " << mesh_file << '\n' << endl;
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return 2;
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}
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mesh = new Mesh(imesh, 1, 1);
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imesh.close();
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int dim = mesh->Dimension();
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int sdim = mesh->SpaceDimension();
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// if(dim !=4 || sdim != 4)
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// {
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// MPI_Finalize();
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// return 0;
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// }
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for (int i=0; i<sequ_ref_levels; i++) { mesh->UniformRefinement(); }
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if (verbose) { mesh->PrintCharacteristics(); }
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if (verbose) { cout << "now we partition the mesh..." << endl << endl; }
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ParMesh *pmesh = new ParMesh(MPI_COMM_WORLD, *mesh);
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delete mesh;
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for (int i=0; i<par_ref_levels; i++) { pmesh->UniformRefinement(); }
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pmesh->PrintInfo(std::cout);
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if (verbose) { cout << endl; }
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// 6. 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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if (dim==4)
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{
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if (order==1) { fec = new LinearFECollection; }
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else { fec = new QuadraticFECollection; }
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}
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else { fec = new H1_FECollection(order, dim); }
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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);
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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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// 7. 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 = set_bc ? 1 : 0;
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fespace->GetEssentialTrueDofs(ess_bdr, ess_tdof_list);
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}
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FunctionCoefficient uExact(u_exact);
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ParGridFunction x(fespace);
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int NExpo =8;
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for (int expo=-NExpo; expo<=NExpo; expo++)
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{
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double weight = pow(10.0,expo);
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kappa = weight;
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x.ProjectCoefficient(uExact);
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ParLinearForm *b = new ParLinearForm(fespace);
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FunctionCoefficient ffunc(f_exact);
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b->AddDomainIntegrator(new DomainLFIntegrator(ffunc));
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b->Assemble();
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x = 0.0;
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// 10. Set up the parallel 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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// std::string permFile = "spe_perm.dat";
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// InversePermeabilityFunction::ReadPermeabilityFile(permFile, MPI_COMM_WORLD);
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// FunctionCoefficient *cspe10 = new FunctionCoefficient(InversePermeabilityFunction::Norm2Permeability);
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Coefficient *beta = new ConstantCoefficient(weight);
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ParBilinearForm *a = new ParBilinearForm(fespace);
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a->AddDomainIntegrator(new DiffusionIntegrator);
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a->AddDomainIntegrator(new MassIntegrator(*beta));
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// 11. 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) { a->EnableStaticCondensation(); }
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a->Assemble();
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HypreParMatrix A;
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Vector B, X;
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a->FormLinearSystem(ess_tdof_list, x, *b, A, X, B);
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if (myid == 0)
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{
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cout << "Size of linear system: " << A.GetGlobalNumRows() << endl;
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}
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// 12. Define and apply a parallel PCG solver for AX=B with the BoomerAMG
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// preconditioner from hypre.
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HypreSolver *amg = new HypreBoomerAMG(A);
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int iter = -1;
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if (standardCG)
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{
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IterativeSolver *pcg = new CGSolver(MPI_COMM_WORLD);
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pcg->SetOperator(A);
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pcg->SetRelTol(tol);
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pcg->SetMaxIter(5000);
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pcg->SetPrintLevel(1);
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pcg->SetPreconditioner(*amg);
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pcg->Mult(B, X);
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iter = pcg->GetNumIterations();
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delete pcg;
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}
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else
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{
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HyprePCG *pcg = new HyprePCG(A);
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pcg->SetTol(tol);
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pcg->SetMaxIter(5000);
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pcg->SetResidualConvergenceOptions(1,tol);
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pcg->SetPrintLevel(2);
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pcg->SetPreconditioner(*amg);
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pcg->Mult(B, X);
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pcg->GetNumIterations(iter);
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delete pcg;
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}
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if (myid==0)
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{
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cout << "Weigth: " << weight << " " << iter << endl;
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int *iters = LoadIterations(10, 2*NExpo+1);
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putIterationsInArray(iter, sequ_ref_levels+par_ref_levels, expo+NExpo,
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2*NExpo+1, iters);
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WriteIterations(iters, 10, 2*NExpo+1);
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}
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// 13. 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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a->RecoverFEMSolution(X, *b, x);
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{
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double err = x.ComputeL2Error(uExact);
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if (myid == 0)
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{
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cout << "\n|| u - u_h ||_{L^2} = " << err << '\n' << endl;
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}
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}
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// 14. 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;
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// sol_name << "sol." << setfill('0') << setw(6) << myid;
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//
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// ofstream mesh_ofs(mesh_name.str().c_str());
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// mesh_ofs.precision(8);
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// pmesh->Print(mesh_ofs);
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//
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// ofstream sol_ofs(sol_name.str().c_str());
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// sol_ofs.precision(8);
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// x.Save(sol_ofs);
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// }
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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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// int visport = 19916;
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// socketstream sol_sock(vishost, visport);
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// sol_sock << "parallel " << num_procs << " " << myid << "\n";
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// sol_sock.precision(8);
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// sol_sock << "solution\n" << *pmesh << x << flush;
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// }
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delete amg;
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delete a;
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delete beta;
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delete b;
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}
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// 16. Free the used memory.
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delete fespace;
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if (order > 0) { delete fec; }
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delete pmesh;
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MPI_Finalize();
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return 0;
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}
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