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-quad.mesh";
int ser_ref_levels = 2;
int par_ref_levels = 0;
int order = 2;
int ode_solver_type = 3;
double t_final = 300.0;
double dt = 3;
double visc = 1e-2;
bool visualization = true;
int vis_steps = 1;
OptionsParser args(argc, argv);
args.AddOption(&mesh_file, "-m", "--mesh",
"Mesh file to use.");
args.AddOption(&ser_ref_levels, "-rs", "--refine-serial",
"Number of times to refine the mesh uniformly in serial.");
args.AddOption(&par_ref_levels, "-rp", "--refine-parallel",
"Number of times to refine the mesh uniformly in parallel.");
args.AddOption(&order, "-o", "--order",
"Order (degree) of the finite elements.");
args.AddOption(&ode_solver_type, "-s", "--ode-solver",
"ODE solver: 1 - Backward Euler, 2 - SDIRK2, 3 - SDIRK3,\n\t"
"\t 11 - Forward Euler, 12 - RK2, 13 - RK3 SSP, 14 - RK4.");
args.AddOption(&t_final, "-tf", "--t-final",
"Final time; start time is 0.");
args.AddOption(&dt, "-dt", "--time-step",
"Time step.");
args.AddOption(&visc, "-v", "--viscosity",
"Viscosity coefficient.");
args.AddOption(&visualization, "-vis", "--visualization", "-no-vis",
"--no-visualization",
"Enable or disable GLVis visualization.");
args.AddOption(&vis_steps, "-vs", "--visualization-steps",
"Visualize every n-th timestep.");
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 and hexahedral meshes
// with the same code.
Mesh *mesh;
ifstream imesh(mesh_file);
if (!imesh)
{
if (myid == 0)
cerr << "\nCan not open mesh file: " << mesh_file << '\n' << endl;
MPI_Finalize();
return 2;
}
mesh = new Mesh(imesh, 1, 1);
imesh.close();
int dim = mesh->Dimension();
// 4. Define the ODE solver used for time integration. Several implicit
// singly diagonal implicit Runge-Kutta (SDIRK) methods, as well as
// explicit Runge-Kutta methods are available.
ODESolver *ode_solver;
switch (ode_solver_type)
{
// Implicit L-stable methods
case 1: ode_solver = new BackwardEulerSolver; break;
case 2: ode_solver = new SDIRK23Solver(2); break;
case 3: ode_solver = new SDIRK33Solver; break;
// Explicit methods
case 11: ode_solver = new ForwardEulerSolver; break;
case 12: ode_solver = new RK2Solver(0.5); break; // midpoint method
case 13: ode_solver = new RK3SSPSolver; break;
case 14: ode_solver = new RK4Solver; break;
// Implicit A-stable methods (not L-stable)
case 22: ode_solver = new ImplicitMidpointSolver; break;
case 23: ode_solver = new SDIRK23Solver; break;
case 24: ode_solver = new SDIRK34Solver; break;
default:
if (myid == 0)
cout << "Unknown ODE solver type: " << ode_solver_type << '\n';
MPI_Finalize();
return 3;
}
// 5. Refine the mesh in serial to increase the resolution. In this example
// we do 'ser_ref_levels' of uniform refinement, where 'ser_ref_levels' is
// a command-line parameter.
for (int lev = 0; lev < ser_ref_levels; lev++)
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;
for (int lev = 0; lev < par_ref_levels; lev++)
pmesh->UniformRefinement();
// 7. Define the parallel vector finite element spaces representing the mesh
// deformation x_gf, the velocity v_gf, and the initial configuration,
// x_ref. Define also the elastic energy density, w_gf, which is in a
// discontinuous higher-order space. Since x and v are integrated in time
// as a system, we group them together in block vector vx, on the unique
// parallel degrees of freedom, with offsets given by array true_offset.
H1_FECollection fe_coll(order, dim);
ParFiniteElementSpace fespace(pmesh, &fe_coll, dim);
int glob_size = fespace.GlobalTrueVSize();
if (myid == 0)
cout << "Number of velocity/deformation unknowns: " << glob_size << endl;
int true_size = fespace.TrueVSize();
Array<int> true_offset(3);
true_offset[0] = 0;
true_offset[1] = true_size;
true_offset[2] = 2*true_size;
BlockVector vx(true_offset);
ParGridFunction v_gf(&fespace), x_gf(&fespace);
ParGridFunction x_ref(&fespace);
pmesh->GetNodes(x_ref);
L2_FECollection w_fec(order + 1, dim);
ParFiniteElementSpace w_fespace(pmesh, &w_fec);
ParGridFunction w_gf(&w_fespace);
// 8. Set the initial conditions for v_gf, x_gf and vx, and define the
// boundary conditions on a beam-like mesh (see description above).
VectorFunctionCoefficient velo(dim, InitialVelocity);
v_gf.ProjectCoefficient(velo);
VectorFunctionCoefficient deform(dim, InitialDeformation);
x_gf.ProjectCoefficient(deform);
v_gf.GetTrueDofs(vx.GetBlock(0));
x_gf.GetTrueDofs(vx.GetBlock(1));
Array<int> ess_bdr(fespace.GetMesh()->bdr_attributes.Max());
ess_bdr = 0;
ess_bdr[0] = 1; // boundary attribute 1 (index 0) is fixed
// 9. Initialize the hyperelastic operator, the GLVis visualization and print
// the initial energies.
HyperelasticOperator oper(fespace, ess_bdr, visc);
socketstream vis_v, vis_w;
if (visualization)
{
char vishost[] = "localhost";
int visport = 19916;
vis_v.open(vishost, visport);
vis_v.precision(8);
visualize(vis_v, pmesh, &x_gf, &v_gf, "Velocity", true);
// Make sure all ranks have sent their 'v' solution before initiating
// another set of GLVis connections (one from each rank):
MPI_Barrier(pmesh->GetComm());
vis_w.open(vishost, visport);
if (vis_w)
{
oper.GetElasticEnergyDensity(x_gf, w_gf);
vis_w.precision(8);
visualize(vis_w, pmesh, &x_gf, &w_gf, "Elastic energy density", true);
}
}
double ee0 = oper.ElasticEnergy(x_gf);
double ke0 = oper.KineticEnergy(v_gf);
if (myid == 0)
{
cout << "initial elastic energy (EE) = " << ee0 << endl;
cout << "initial kinetic energy (KE) = " << ke0 << endl;
cout << "initial total energy (TE) = " << (ee0 + ke0) << endl;
}
// 10. Perform time-integration (looping over the time iterations, ti, with a
// time-step dt).
ode_solver->Init(oper);
double t = 0.0;
bool last_step = false;
for (int ti = 1; !last_step; ti++)
{
if (t + dt >= t_final - dt/2)
last_step = true;
ode_solver->Step(vx, t, dt);
if (last_step || (ti % vis_steps) == 0)
{
v_gf.Distribute(vx.GetBlock(0));
x_gf.Distribute(vx.GetBlock(1));
double ee = oper.ElasticEnergy(x_gf);
double ke = oper.KineticEnergy(v_gf);
if (myid == 0)
cout << "step " << ti << ", t = " << t << ", EE = " << ee
<< ", KE = " << ke << ", ΔTE = " << (ee+ke)-(ee0+ke0) << endl;
if (visualization)
{
visualize(vis_v, pmesh, &x_gf, &v_gf);
if (vis_w)
{
oper.GetElasticEnergyDensity(x_gf, w_gf);
visualize(vis_w, pmesh, &x_gf, &w_gf);
}
}
}
}
// 11. Save the displaced mesh, the velocity and elastic energy.
{
GridFunction *nodes = &x_gf;
int owns_nodes = 0;
pmesh->SwapNodes(nodes, owns_nodes);
ostringstream mesh_name, velo_name, ee_name;
mesh_name << "deformed." << setfill('0') << setw(6) << myid;
velo_name << "velocity." << setfill('0') << setw(6) << myid;
ee_name << "elastic_energy." << setfill('0') << setw(6) << myid;
ofstream mesh_ofs(mesh_name.str().c_str());
mesh_ofs.precision(8);
pmesh->Print(mesh_ofs);
pmesh->SwapNodes(nodes, owns_nodes);
ofstream velo_ofs(velo_name.str().c_str());
velo_ofs.precision(8);
v_gf.Save(velo_ofs);
ofstream ee_ofs(ee_name.str().c_str());
ee_ofs.precision(8);
oper.GetElasticEnergyDensity(x_gf, w_gf);
w_gf.Save(ee_ofs);
}
// 10. Free the used memory.
delete ode_solver;
delete pmesh;
MPI_Finalize();
return 0;
}
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;
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(&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 && order > mesh->NURBSext->GetOrder())
{
mesh->DegreeElevate(order - mesh->NURBSext->GetOrder());
}
// 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->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();
}
