375 lines
13 KiB
C++
375 lines
13 KiB
C++
// MFEM Example 28 - Parallel Version
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//
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// Compile with: make ex28p
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//
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// Sample runs: ex28p
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// ex28p --visit-datafiles
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// ex28p --order 4
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// ex28p --penalty 1e+5
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//
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// mpirun -np 4 ex28p
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// mpirun -np 4 ex28p --penalty 1e+5
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//
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// Description: Demonstrates a sliding boundary condition in an elasticity
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// problem. A trapezoid, roughly as pictured below, is pushed
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// from the right into a rigid notch. Normal displacement is
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// restricted, but tangential movement is allowed, so the
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// trapezoid compresses into the notch.
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//
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// /-------+
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// normal constrained --->/ | <--- boundary force (2)
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// boundary (4) /---------+
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// ^
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// |
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// normal constrained boundary (1)
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//
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// This example demonstrates the use of the ConstrainedSolver
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// framework.
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//
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// We recommend viewing Example 2 before viewing this example.
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#include "mfem.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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// Return a mesh with a single element with vertices (0, 0), (1, 0), (1, 1),
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// (offset, 1) to demonstrate boundary conditions on a surface that is not
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// axis-aligned.
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Mesh * build_trapezoid_mesh(double offset)
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{
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MFEM_VERIFY(offset < 0.9, "offset is too large!");
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const int dimension = 2;
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const int nvt = 4; // vertices
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const int nbe = 4; // num boundary elements
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Mesh * mesh = new Mesh(dimension, nvt, 1, nbe);
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// vertices
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double vc[dimension];
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vc[0] = 0.0; vc[1] = 0.0;
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mesh->AddVertex(vc);
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vc[0] = 1.0; vc[1] = 0.0;
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mesh->AddVertex(vc);
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vc[0] = offset; vc[1] = 1.0;
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mesh->AddVertex(vc);
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vc[0] = 1.0; vc[1] = 1.0;
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mesh->AddVertex(vc);
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// element
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Array<int> vert(4);
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vert[0] = 0; vert[1] = 1; vert[2] = 3; vert[3] = 2;
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mesh->AddQuad(vert, 1);
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// boundary
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Array<int> sv(2);
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sv[0] = 0; sv[1] = 1;
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mesh->AddBdrSegment(sv, 1);
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sv[0] = 1; sv[1] = 3;
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mesh->AddBdrSegment(sv, 2);
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sv[0] = 2; sv[1] = 3;
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mesh->AddBdrSegment(sv, 3);
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sv[0] = 0; sv[1] = 2;
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mesh->AddBdrSegment(sv, 4);
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mesh->FinalizeQuadMesh(1, 0, true);
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return mesh;
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}
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int main(int argc, char *argv[])
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{
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#ifdef HYPRE_USING_GPU
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cout << "\nAs of mfem-4.3 and hypre-2.22.0 (July 2021) this example\n"
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<< "is NOT supported with the GPU version of hypre.\n\n";
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return 242;
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#endif
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// 1. Initialize MPI and HYPRE.
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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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Hypre::Init();
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// 2. Parse command-line options.
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int order = 1;
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bool visualization = 1;
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bool reorder_space = false;
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double offset = 0.3;
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bool visit = false;
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double penalty = 0.0;
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OptionsParser args(argc, argv);
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args.AddOption(&order, "-o", "--order",
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"Finite element order (polynomial degree).");
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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(&reorder_space, "-nodes", "--by-nodes", "-vdim", "--by-vdim",
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"Use byNODES ordering of vector space instead of byVDIM");
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args.AddOption(&offset, "--offset", "--offset",
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"How much to offset the trapezoid.");
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args.AddOption(&visit, "-visit", "--visit-datafiles", "-no-visit",
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"--no-visit-datafiles",
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"Save data files for VisIt (visit.llnl.gov) visualization.");
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args.AddOption(&penalty, "-p", "--penalty",
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"Penalty parameter; 0 means use elimination solver.");
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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 (myid == 0)
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{
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args.PrintOptions(cout);
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}
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// 3. Build a trapezoidal mesh with a single quadrilateral element, where
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// 'offset' determines how far off it is from a rectangle.
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Mesh *mesh = build_trapezoid_mesh(offset);
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int dim = mesh->Dimension();
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// 4. 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 1,000 elements.
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{
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int ref_levels =
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(int)floor(log(1000./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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// 5. 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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int par_ref_levels = 1;
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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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// 6. Define a parallel finite element space on the parallel mesh. Here we
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// use vector finite elements, i.e. dim copies of a scalar finite element
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// space. We use the ordering by vector dimension (the last argument of
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// the FiniteElementSpace constructor) which is expected in the systems
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// version of BoomerAMG preconditioner. For NURBS meshes, we use the
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// (degree elevated) NURBS space associated with the mesh nodes.
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FiniteElementCollection *fec;
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ParFiniteElementSpace *fespace;
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const bool use_nodal_fespace = pmesh->NURBSext;
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if (use_nodal_fespace)
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{
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fec = NULL;
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fespace = (ParFiniteElementSpace *)pmesh->GetNodes()->FESpace();
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}
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else
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{
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fec = new H1_FECollection(order, dim);
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if (reorder_space)
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{
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fespace = new ParFiniteElementSpace(pmesh, fec, dim, Ordering::byNODES);
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}
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else
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{
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fespace = new ParFiniteElementSpace(pmesh, fec, dim, Ordering::byVDIM);
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}
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}
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HYPRE_BigInt 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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<< "Assembling matrix and r.h.s... " << flush;
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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, there are no essential boundary
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// conditions in the usual sense, but we leave the machinery here for
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// users to modify if they wish.
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Array<int> ess_tdof_list, ess_bdr(pmesh->bdr_attributes.Max());
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ess_bdr = 0;
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fespace->GetEssentialTrueDofs(ess_bdr, ess_tdof_list);
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// 8. Set up the parallel linear form b(.) which corresponds to the
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// right-hand side of the FEM linear system. In this case, b_i equals the
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// boundary integral of f*phi_i where f represents a "pull down" force on
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// the Neumann part of the boundary and phi_i are the basis functions in
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// the finite element fespace. The force is defined by the object f, which
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// is a vector of Coefficient objects. The fact that f is non-zero on
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// boundary attribute 2 is indicated by the use of piece-wise constants
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// coefficient for its last component.
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VectorArrayCoefficient f(dim);
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for (int i = 0; i < dim-1; i++)
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{
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f.Set(i, new ConstantCoefficient(0.0));
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}
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// 9. Put a leftward force on the right side of the trapezoid
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{
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Vector push_force(pmesh->bdr_attributes.Max());
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push_force = 0.0;
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push_force(1) = -5.0e-2; // index 1 attribute 2
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f.Set(0, new PWConstCoefficient(push_force));
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}
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ParLinearForm *b = new ParLinearForm(fespace);
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b->AddBoundaryIntegrator(new VectorBoundaryLFIntegrator(f));
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b->Assemble();
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// 10. 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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// 11. Set up the parallel bilinear form a(.,.) on the finite element space
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// corresponding to the linear elasticity integrator with piece-wise
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// constants coefficient lambda and mu. We use constant coefficients,
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// but see ex2 for how to set up piecewise constant coefficients based
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// on attribute.
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Vector lambda(pmesh->attributes.Max());
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lambda = 1.0;
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PWConstCoefficient lambda_func(lambda);
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Vector mu(pmesh->attributes.Max());
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mu = 1.0;
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PWConstCoefficient mu_func(mu);
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ParBilinearForm *a = new ParBilinearForm(fespace);
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a->AddDomainIntegrator(new ElasticityIntegrator(lambda_func, mu_func));
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// 12. 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, etc.
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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 << "done." << endl;
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cout << "Size of linear system: " << A.GetGlobalNumRows() << endl;
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}
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// 13. Set up constraint matrix to constrain normal displacement (but
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// allow tangential displacement) on specified boundaries.
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Array<int> constraint_atts(2);
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constraint_atts[0] = 1; // attribute 1 bottom
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constraint_atts[1] = 4; // attribute 4 left side
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Array<int> constraint_rowstarts;
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SparseMatrix* local_constraints =
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ParBuildNormalConstraints(*fespace, constraint_atts,
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constraint_rowstarts);
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// 14. Define and apply a parallel PCG solver for the constrained system
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// where the normal boundary constraints have been separately eliminated
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// from the system.
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ConstrainedSolver * solver;
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if (penalty == 0.0)
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{
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solver = new EliminationCGSolver(A, *local_constraints,
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constraint_rowstarts, dim,
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reorder_space);
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}
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else
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{
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solver = new PenaltyPCGSolver(A, *local_constraints, penalty,
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dim, reorder_space);
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}
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solver->SetRelTol(1e-8);
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solver->SetMaxIter(500);
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solver->SetPrintLevel(1);
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solver->Mult(B, X);
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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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a->RecoverFEMSolution(X, *b, x);
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// 16. For non-NURBS meshes, make the mesh curved based on the finite element
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// space. This means that we define the mesh elements through a fespace
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// based transformation of the reference element. This allows us to save
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// the displaced mesh as a curved mesh when using high-order finite
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// element displacement field. We assume that the initial mesh (read from
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// the file) is not higher order curved mesh compared to the chosen FE
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// space.
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if (!use_nodal_fespace)
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{
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pmesh->SetNodalFESpace(fespace);
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}
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GridFunction *nodes = pmesh->GetNodes();
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*nodes += x;
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// 17. Save the refined mesh and the solution in VisIt format.
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if (visit)
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{
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VisItDataCollection visit_dc(MPI_COMM_WORLD, "ex28p", pmesh);
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visit_dc.SetLevelsOfDetail(4);
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visit_dc.RegisterField("displacement", &x);
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visit_dc.Save();
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}
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// 18. Save in parallel the displaced mesh and the inverted solution (which
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// gives the backward displacements to the original grid). This output
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// can be viewed later using GLVis: "glvis -np <np> -m mesh -g sol".
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{
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x *= -1; // sign convention for GLVis displacements
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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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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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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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// 19. Send the above data by socket to a GLVis server. Use the "n" and "b"
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// keys in GLVis to visualize the displacements.
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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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// 20. Free the used memory.
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delete local_constraints;
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delete solver;
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delete a;
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delete b;
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if (fec)
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{
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delete fespace;
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delete fec;
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}
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delete pmesh;
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// HYPRE_Finalize();
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MPI_Finalize();
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return 0;
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}
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