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// MFEM Example 12 - Parallel Version
//
// Compile with: make ex12p
//
// Sample runs:
// mpirun -np 4 ex12p -m ../data/beam-tri.mesh
// mpirun -np 4 ex12p -m ../data/beam-quad.mesh
// mpirun -np 4 ex12p -m ../data/beam-tet.mesh -n 10 -o 2 -elast
// mpirun -np 4 ex12p -m ../data/beam-hex.mesh -s 3876
// mpirun -np 4 ex12p -m ../data/beam-tri.mesh -o 2 -sys
// mpirun -np 4 ex12p -m ../data/beam-quad.mesh -s 4526 -n 6 -o 3 -elast
// mpirun -np 4 ex12p -m ../data/beam-quad-nurbs.mesh
// mpirun -np 4 ex12p -m ../data/beam-hex-nurbs.mesh
//
// Description: This example code solves the linear elasticity eigenvalue
// problem for a multi-material cantilever beam.
//
// Specifically, we compute a number of the lowest eigenmodes by
// approximating the weak form of -div(sigma(u)) = lambda u where
// sigma(u)=lambda*div(u)*I+mu*(grad*u+u*grad) is the stress
// tensor corresponding to displacement field u, and lambda and mu
// are the material Lame constants. The boundary conditions are
// u=0 on the fixed part of the boundary with attribute 1, and
// sigma(u).n=f on the remainder. The geometry of the domain is
// assumed to be as follows:
//
// +----------+----------+
// boundary --->| material | material |
// attribute 1 | 1 | 2 |
// (fixed) +----------+----------+
//
// The example highlights the use of the LOBPCG eigenvalue solver
// together with the BoomerAMG preconditioner in HYPRE. Reusing a
// single GLVis visualization window for multiple eigenfunctions
// is also illustrated.
//
// We recommend viewing examples 2 and 11 before viewing this
// example.
#include "mfem.hpp"
#include <fstream>
#include <iostream>
using namespace std;
using namespace mfem;
int main(int argc, char *argv[])
{
// 1. Initialize MPI.
int num_procs, myid;
MPI_Init(&argc, &argv);
MPI_Comm_size(MPI_COMM_WORLD, &num_procs);
MPI_Comm_rank(MPI_COMM_WORLD, &myid);
// 2. Parse command-line options.
const char *mesh_file = "../data/beam-tri.mesh";
int order = 1;
int nev = 5;
int seed = 75;
bool visualization = 1;
bool amg_elast = 0;
OptionsParser args(argc, argv);
args.AddOption(&mesh_file, "-m", "--mesh",
"Mesh file to use.");
args.AddOption(&order, "-o", "--order",
"Finite element order (polynomial degree).");
args.AddOption(&nev, "-n", "--num-eigs",
"Number of desired eigenmodes.");
args.AddOption(&seed, "-s", "--seed",
"Random seed used to initialize LOBPCG.");
args.AddOption(&amg_elast, "-elast", "--amg-for-elasticity", "-sys",
"--amg-for-systems",
"Use the special AMG elasticity solver (GM/LN approaches), "
"or standard AMG for systems (unknown approach).");
args.AddOption(&visualization, "-vis", "--visualization", "-no-vis",
"--no-visualization",
"Enable or disable GLVis visualization.");
args.Parse();
if (!args.Good())
{
if (myid == 0)
{
args.PrintUsage(cout);
}
MPI_Finalize();
return 1;
}
if (myid == 0)
{
args.PrintOptions(cout);
}
// 3. Read the (serial) mesh from the given mesh file on all processors. We
// can handle triangular, quadrilateral, tetrahedral, hexahedral, surface
// and volume meshes with the same code.
Mesh *mesh = new Mesh(mesh_file, 1, 1);
int dim = mesh->Dimension();
if (mesh->attributes.Max() < 2)
{
if (myid == 0)
cerr << "\nInput mesh should have at least two materials!"
<< " (See schematic in ex12p.cpp)\n"
<< endl;
MPI_Finalize();
return 3;
}
// 4. Select the order of the finite element discretization space. For NURBS
// meshes, we increase the order by degree elevation.
if (mesh->NURBSext)
{
mesh->DegreeElevate(order, order);
}
// 5. Refine the serial mesh on all processors to increase the resolution. In
// this example we do 'ref_levels' of uniform refinement. We choose
// 'ref_levels' to be the largest number that gives a final mesh with no
// more than 1,000 elements.
{
int ref_levels =
(int)floor(log(1000./mesh->GetNE())/log(2.)/dim);
for (int l = 0; l < ref_levels; l++)
{
mesh->UniformRefinement();
}
}
// 6. Define a parallel mesh by a partitioning of the serial mesh. Refine
// this mesh further in parallel to increase the resolution. Once the
// parallel mesh is defined, the serial mesh can be deleted.
ParMesh *pmesh = new ParMesh(MPI_COMM_WORLD, *mesh);
delete mesh;
{
int par_ref_levels = 1;
for (int l = 0; l < par_ref_levels; l++)
{
pmesh->UniformRefinement();
}
}
// 7. Define a parallel finite element space on the parallel mesh. Here we
// use vector finite elements, i.e. dim copies of a scalar finite element
// space. We use the ordering by vector dimension (the last argument of
// the FiniteElementSpace constructor) which is expected in the systems
// version of BoomerAMG preconditioner. For NURBS meshes, we use the
// (degree elevated) NURBS space associated with the mesh nodes.
FiniteElementCollection *fec;
ParFiniteElementSpace *fespace;
const bool use_nodal_fespace = pmesh->NURBSext && !amg_elast;
if (use_nodal_fespace)
{
fec = NULL;
fespace = (ParFiniteElementSpace *)pmesh->GetNodes()->FESpace();
}
else
{
fec = new H1_FECollection(order, dim);
fespace = new ParFiniteElementSpace(pmesh, fec, dim, Ordering::byVDIM);
}
HYPRE_Int size = fespace->GlobalTrueVSize();
if (myid == 0)
{
cout << "Number of unknowns: " << size << endl
<< "Assembling: " << flush;
}
// 8. Set up the parallel bilinear forms a(.,.) and m(.,.) on the finite
// element space corresponding to the linear elasticity integrator with
// piece-wise constants coefficient lambda and mu, a simple mass matrix
// needed on the right hand side of the generalized eigenvalue problem
// below. The boundary conditions are implemented by marking only boundary
// attribute 1 as essential. We use special values on the diagonal to
// shift the Dirichlet eigenvalues out of the computational range. After
// serial/parallel assembly we extract the corresponding parallel matrices
// A and M.
Vector lambda(pmesh->attributes.Max());
lambda = 1.0;
lambda(0) = lambda(1)*50;
PWConstCoefficient lambda_func(lambda);
Vector mu(pmesh->attributes.Max());
mu = 1.0;
mu(0) = mu(1)*50;
PWConstCoefficient mu_func(mu);
Array<int> ess_bdr(pmesh->bdr_attributes.Max());
ess_bdr = 0;
ess_bdr[0] = 1;
ParBilinearForm *a = new ParBilinearForm(fespace);
a->AddDomainIntegrator(new ElasticityIntegrator(lambda_func, mu_func));
if (myid == 0)
{
cout << "matrix ... " << flush;
}
a->Assemble();
a->EliminateEssentialBCDiag(ess_bdr, 1.0);
a->Finalize();
ParBilinearForm *m = new ParBilinearForm(fespace);
m->AddDomainIntegrator(new VectorMassIntegrator());
m->Assemble();
// shift the eigenvalue corresponding to eliminated dofs to a large value
m->EliminateEssentialBCDiag(ess_bdr, numeric_limits<double>::min());
m->Finalize();
if (myid == 0)
{
cout << "done." << endl;
}
HypreParMatrix *A = a->ParallelAssemble();
HypreParMatrix *M = m->ParallelAssemble();
delete a;
delete m;
// 9. Define and configure the LOBPCG eigensolver and the BoomerAMG
// preconditioner for A to be used within the solver. Set the matrices
// which define the generalized eigenproblem A x = lambda M x.
HypreBoomerAMG * amg = new HypreBoomerAMG(*A);
amg->SetPrintLevel(0);
if (amg_elast)
{
amg->SetElasticityOptions(fespace);
}
else
{
amg->SetSystemsOptions(dim);
}
HypreLOBPCG * lobpcg = new HypreLOBPCG(MPI_COMM_WORLD);
lobpcg->SetNumModes(nev);
lobpcg->SetRandomSeed(seed);
lobpcg->SetPreconditioner(*amg);
lobpcg->SetMaxIter(100);
lobpcg->SetTol(1e-8);
lobpcg->SetPrecondUsageMode(1);
lobpcg->SetPrintLevel(1);
lobpcg->SetMassMatrix(*M);
lobpcg->SetOperator(*A);
// 10. Compute the eigenmodes and extract the array of eigenvalues. Define a
// parallel grid function to represent each of the eigenmodes returned by
// the solver.
Array<double> eigenvalues;
lobpcg->Solve();
lobpcg->GetEigenvalues(eigenvalues);
ParGridFunction x(fespace);
// 11. For non-NURBS meshes, make the mesh curved based on the finite element
// space. This means that we define the mesh elements through a fespace
// based transformation of the reference element. This allows us to save
// the displaced mesh as a curved mesh when using high-order finite
// element displacement field. We assume that the initial mesh (read from
// the file) is not higher order curved mesh compared to the chosen FE
// space.
if (!use_nodal_fespace)
{
pmesh->SetNodalFESpace(fespace);
}
// 12. Save the refined mesh and the modes in parallel. This output can be
// viewed later using GLVis: "glvis -np <np> -m mesh -g mode".
{
ostringstream mesh_name, mode_name;
mesh_name << "mesh." << setfill('0') << setw(6) << myid;
ofstream mesh_ofs(mesh_name.str().c_str());
mesh_ofs.precision(8);
pmesh->Print(mesh_ofs);
for (int i=0; i<nev; i++)
{
// convert eigenvector from HypreParVector to ParGridFunction
x = lobpcg->GetEigenvector(i);
mode_name << "mode_" << setfill('0') << setw(2) << i << "."
<< setfill('0') << setw(6) << myid;
ofstream mode_ofs(mode_name.str().c_str());
mode_ofs.precision(8);
x.Save(mode_ofs);
mode_name.str("");
}
}
// 13. Send the above data by socket to a GLVis server. Use the "n" and "b"
// keys in GLVis to visualize the displacements.
if (visualization)
{
char vishost[] = "localhost";
int visport = 19916;
socketstream mode_sock(vishost, visport);
for (int i=0; i<nev; i++)
{
if ( myid == 0 )
{
cout << "Eigenmode " << i+1 << '/' << nev
<< ", Lambda = " << eigenvalues[i] << endl;
}
// convert eigenvector from HypreParVector to ParGridFunction
x = lobpcg->GetEigenvector(i);
mode_sock << "parallel " << num_procs << " " << myid << "\n"
<< "solution\n" << *pmesh << x << flush
<< "window_title 'Eigenmode " << i+1 << '/' << nev
<< ", Lambda = " << eigenvalues[i] << "'" << endl;
char c;
if (myid == 0)
{
cout << "press (q)uit or (c)ontinue --> " << flush;
cin >> c;
}
MPI_Bcast(&c, 1, MPI_CHAR, 0, MPI_COMM_WORLD);
if (c != 'c')
{
break;
}
}
mode_sock.close();
}
// 14. Free the used memory.
delete lobpcg;
delete amg;
delete M;
delete A;
if (fec)
{
delete fespace;
delete fec;
}
delete pmesh;
MPI_Finalize();
return 0;
}