Files
mfem/examples/ex41p.cpp
T
2025-12-11 10:43:08 -08:00

738 lines
22 KiB
C++

// MFEM Example 41 - Parallel Version
//
// Compile with: make ex41p
//
// Sample runs:
// mpirun -np 4 ex41p
// mpirun -np 4 ex41p -cg
// mpirun -np 4 ex41p -m ../data/periodic-hexagon.mesh -p 0 -dt 0.005 -tf 10
// mpirun -np 4 ex41p -m ../data/periodic-square.mesh -p 1 -dt 0.005 -tf 9
// mpirun -np 4 ex41p -m ../data/periodic-hexagon.mesh -p 1 -dt 0.005 -tf 9
// mpirun -np 4 ex41p -m ../data/star-q3.mesh -p 1 -rp 1 -dt 0.001 -tf 9
// mpirun -np 4 ex41p -m ../data/disc-nurbs.mesh -p 1 -rp 1 -dt 0.005 -tf 9
// mpirun -np 4 ex41p -m ../data/disc-nurbs.mesh -p 2 -rp 1 -dt 0.005 -tf 9
// mpirun -np 4 ex41p -m ../data/periodic-square.mesh -rp 2 -dt 0.0025 -tf 9 -vs 20
// mpirun -np 4 ex41p -m ../data/periodic-cube.mesh -p 0 -rs 2 -o 2 -dt 0.01 -tf 8
//
// Device sample runs:
//
// Description: This example code solves the time-dependent advection-diffusion
// equation du/dt + v.grad(u) - a div(grad(u)) = 0, where v is a
// given fluid velocity, a is the diffusion coefficient, and
// u0(x)=u(0,x) is a given initial condition.
//
// The example demonstrates the use of Discontinuous Galerkin (DG)
// bilinear forms in MFEM (face integrators), DG-LOR Preconditioning
// and the use of IMEX ODE time integrators.
//
// The Option to use Continuous Finite Elements is available too.
#include "mfem.hpp"
using namespace std;
using namespace mfem;
// Mesh bounding box
Vector bb_min, bb_max;
// Velocity coefficient
template<int problem=0>
void velocity_function(const Vector &x, Vector &v)
{
int dim = x.Size();
// map to the reference [-1,1] domain
Vector X(dim);
for (int i = 0; i < dim; i++)
{
real_t center = (bb_min[i] + bb_max[i]) * 0.5;
X(i) = 2 * (x(i) - center) / (bb_max[i] - bb_min[i]);
}
switch (problem)
{
case 0:
{
// Translations in 1D, 2D, and 3D
switch (dim)
{
case 1: v(0) = 1.0; break;
case 2: v(0) = sqrt(2./3.); v(1) = sqrt(1./3.); break;
case 3: v(0) = sqrt(3./6.); v(1) = sqrt(2./6.); v(2) = sqrt(1./6.);
break;
}
break;
}
case 1:
case 2:
{
// Clockwise rotation in 2D around the origin
const real_t w = M_PI/2;
switch (dim)
{
case 1: v(0) = 1.0; break;
case 2: v(0) = w*X(1); v(1) = -w*X(0); break;
case 3: v(0) = w*X(1); v(1) = -w*X(0); v(2) = 0.0; break;
}
break;
}
case 3:
{
// Clockwise twisting rotation in 2D around the origin
const real_t w = M_PI/2;
real_t d = max((X(0)+1.)*(1.-X(0)),0.) * max((X(1)+1.)*(1.-X(1)),0.);
d = d*d;
switch (dim)
{
case 1: v(0) = 1.0; break;
case 2: v(0) = d*w*X(1); v(1) = -d*w*X(0); break;
case 3: v(0) = d*w*X(1); v(1) = -d*w*X(0); v(2) = 0.0; break;
}
break;
}
}
}
// Initial condition
template<int problem=0>
real_t u0_function(const Vector &x)
{
int dim = x.Size();
// map to the reference [-1,1] domain
Vector X(dim);
for (int i = 0; i < dim; i++)
{
real_t center = (bb_min[i] + bb_max[i]) * 0.5;
X(i) = 2 * (x(i) - center) / (bb_max[i] - bb_min[i]);
}
switch (problem)
{
case 0:
case 1:
{
switch (dim)
{
case 1:
return exp(-40.*pow(X(0)-0.5,2));
case 2:
case 3:
{
real_t rx = 0.45, ry = 0.25, cx = 0., cy = -0.2, w = 10.;
if (dim == 3)
{
const real_t s = (1. + 0.25*cos(2*M_PI*X(2)));
rx *= s;
ry *= s;
}
return ( std::erfc(w*(X(0)-cx-rx))*std::erfc(-w*(X(0)-cx+rx)) *
std::erfc(w*(X(1)-cy-ry))*std::erfc(-w*(X(1)-cy+ry)) )/16;
}
}
}
case 2:
{
real_t x_ = X(0), y_ = X(1), rho, phi;
rho = std::hypot(x_, y_);
phi = atan2(y_, x_);
return pow(sin(M_PI*rho),2)*sin(3*phi);
}
case 3:
{
const real_t f = M_PI;
return sin(f*X(0))*sin(f*X(1));
}
}
return 0.0;
}
class Implicit_Solver : public Solver
{
private:
HypreParMatrix &M, &S;
HypreParMatrix *A;
CGSolver linear_solver;
real_t dt;
SparseMatrix M_diag;
public:
Implicit_Solver(HypreParMatrix &M_, HypreParMatrix &S_,
const FiniteElementSpace &fes)
: M(M_),
S(S_),
A(nullptr),
linear_solver(M.GetComm()),
dt(1.0)
{
linear_solver.iterative_mode = false;
linear_solver.SetRelTol(1e-9);
linear_solver.SetAbsTol(0.0);
linear_solver.SetMaxIter(100);
linear_solver.SetPrintLevel(0);
M.GetDiag(M_diag);
}
void SetTimeStep(real_t dt_)
{
real_t ddt = dt-dt_;
// syncronize ddt across all processes
MPI_Comm comm = M.GetComm();
int myrank;
MPI_Comm_rank(comm, &myrank);
MPI_Bcast(&ddt, 1, MPI_DOUBLE, 0, comm);
real_t epsilon;
epsilon = std::numeric_limits<real_t>::epsilon();
// allow for some tolerance in the time stepping process
epsilon*=10;
if (fabs(ddt) > epsilon)
{
if (0==myrank)
{
cout << "Updating Implicit_Solver time step from " << dt
<< " to " << dt_ << endl;
}
delete A;
dt = dt_;
// Form operator A = M + dt*S
A = Add(dt, S, 1.0, M);
linear_solver.SetOperator(*A);
}
}
void SetOperator(const Operator &op) override
{
linear_solver.SetOperator(op);
}
void Mult(const Vector &x, Vector &y) const override
{
linear_solver.Mult(x, y);
}
void SetPreconditioner(Solver &precond)
{
linear_solver.SetPreconditioner(precond);
}
~Implicit_Solver() override
{
delete A;
}
};
/** A time-dependent operator for the right-hand side of the ODE. The DG weak
form of the advection-diffusion equation is (M + dt S) du/dt = Su - K u + b
, where M and K are the mass and advection matrices, and b describes the
flow on the boundary. In the case of IMEX evolution, the diffusion term is
treated implicitly, and the advection term is treated explicitly. */
class IMEX_Evolution : public TimeDependentOperator
{
private:
OperatorHandle M, K, S, A;
const Vector &b;
Solver *M_prec;
CGSolver M_solver;
Implicit_Solver *implicit_solver;
LORSolver<HypreBoomerAMG>* lor_solver;
mutable Vector z;
mutable Vector w;
public:
IMEX_Evolution(ParBilinearForm &M_, ParBilinearForm &K_, ParBilinearForm &S_,
const Vector &b_, ParBilinearForm &A_);
virtual
~IMEX_Evolution()
{
delete implicit_solver;
delete lor_solver;
delete M_prec;
}
void Mult1(const Vector &x, Vector &y) const;
void ImplicitSolve2(const real_t dt, const Vector &x, Vector &k);
void Mult(const Vector &x, Vector &y) const override
{
if (TimeDependentOperator::EvalMode::ADDITIVE_TERM_1 == GetEvalMode())
{
Mult1(x,y);
}
else
{
mfem_error("TimeDependentOperator::Mult() is not overridden!");
}
}
void ImplicitSolve(const real_t dt, const Vector &x, Vector &k) override
{
if (TimeDependentOperator::EvalMode::ADDITIVE_TERM_2 == GetEvalMode())
{
ImplicitSolve2(dt,x,k);
}
else
{
mfem_error("TimeDependentOperator::ImplicitSolve() is not overridden!");
}
}
};
int main(int argc, char *argv[])
{
// 1. Initialize MPI and HYPRE.
Mpi::Init();
int num_procs = Mpi::WorldSize();
int myid = Mpi::WorldRank();
Hypre::Init();
// 2. Parse command-line options.
int problem = 0;
const char *mesh_file = "../data/periodic-square.mesh";
int ser_ref_levels = 2;
int par_ref_levels = 0;
int order = 3;
int ode_solver_type = 64; // 61 - Forward Backward Euler
// 62 - IMEXRK2(2,2,2)
// 63 - IMEXRK2(2,3,2)
// 64 - IMEXRK3(3,4,3)
real_t t_final = 10.0;
real_t dt = 0.01;
bool paraview = false;
bool cg = false;
int vis_steps = 50;
bool adios2 = false;
bool binary = false;
real_t diffusion_term = 0.01;
real_t kappa = -1.0;
real_t sigma = -1.0;
bool visualization = true;
bool visit = false;
int precision = 16;
cout.precision(precision);
OptionsParser args(argc, argv);
args.AddOption(&mesh_file, "-m", "--mesh",
"Mesh file to use.");
args.AddOption(&problem, "-p", "--problem",
"Problem setup to use. See options in velocity_function().");
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",
ODESolver::IMEXTypes.c_str());
args.AddOption(&t_final, "-tf", "--t-final",
"Final time; start time is 0.");
args.AddOption(&dt, "-dt", "--time-step",
"Time step.");
args.AddOption(&diffusion_term, "-dc", "--diffusion-coeff",
"Diffusion coefficient in the PDE.");
args.AddOption(&paraview, "-paraview", "--paraview-datafiles", "-no-paraview",
"--no-paraview-datafiles",
"Save data files for ParaView (paraview.org) visualization.");
args.AddOption(&visit, "-visit", "--visit-datafiles", "-no-visit",
"--no-visit-datafiles",
"Save data files for VisIt (visit.llnl.gov) visualization.");
args.AddOption(&adios2, "-adios2", "--adios2-streams", "-no-adios2",
"--no-adios2-streams",
"Save data using adios2 streams.");
args.AddOption(&binary, "-binary", "--binary-datafiles", "-ascii",
"--ascii-datafiles",
"Use binary (Sidre) or ascii format for VisIt data files.");
args.AddOption(&vis_steps, "-vs", "--visualization-steps",
"Visualize every n-th timestep.");
args.AddOption(&visualization, "-vis", "--visualization", "-no-vis",
"--no-visualization",
"Enable or disable GLVis visualization.");
args.AddOption(&cg, "-cg", "--continuous-galerkin", "-dg",
"--discontinuous-galerkin",
"Use Continuous-Galerkin Finite elements (Default is DG)");
args.Parse();
if (!args.Good())
{
if (Mpi::Root())
{
args.PrintUsage(cout);
}
return 1;
}
if (Mpi::Root())
{
args.PrintOptions(cout);
}
if (kappa < 0)
{
kappa = (order+1)*(order+1);
}
// 3. Read the mesh from the given mesh file. We can handle geometrically
// periodic meshes in this code.
Mesh *mesh = new Mesh(mesh_file);
const int dim = mesh->Dimension();
// 4. Define the IMEX (Split) ODE solver used for time integration. The IMEX
// solvers currently available are: 55 - Forward Backward Euler,
// 56 - IMEXRK2(2,2,2), 57 - IMEXRK2(2,3,2), and
unique_ptr<ODESolver> ode_solver = ODESolver::SelectIMEX(ode_solver_type);
// 5. Refine the mesh to increase the resolution. In this example we do
// 'ref_levels' of uniform refinement, where 'ref_levels' is a
// command-line parameter.
for (int lev = 0; lev < ser_ref_levels; lev++) { mesh->UniformRefinement(); }
if (mesh->NURBSext)
{
mesh->SetCurvature(max(order, 1));
}
mesh->GetBoundingBox(bb_min, bb_max, max(order, 1));
// 6. Define the 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 discontinuous DG finite element space of the given
// polynomial order on the refined mesh.
FiniteElementCollection *fec = NULL;
if (cg)
{
fec = new H1_FECollection(order, dim);
}
else
{
fec = new DG_FECollection(order, dim, BasisType::GaussLobatto);
}
ParFiniteElementSpace *fes = new ParFiniteElementSpace(pmesh, fec);
HYPRE_BigInt global_vSize = fes->GlobalTrueVSize();
if (Mpi::Root())
{
cout << "Number of unknowns: " << global_vSize << endl;
}
// 8. Set up and assemble the bilinear and linear forms corresponding to the
// DG discretization. The DGTraceIntegrator involves integrals over mesh
// interior faces.
std::unique_ptr<VectorFunctionCoefficient> velocity;
if (0==problem)
{
velocity.reset(new VectorFunctionCoefficient(dim, velocity_function<0>));
}
else if (1==problem)
{
velocity.reset(new VectorFunctionCoefficient(dim, velocity_function<1>));
}
else if (2==problem)
{
velocity.reset(new VectorFunctionCoefficient(dim, velocity_function<2>));
}
else if (3==problem)
{
velocity.reset(new VectorFunctionCoefficient(dim, velocity_function<3>));
}
ConstantCoefficient diff_coeff(diffusion_term);
ConstantCoefficient dt_diff_coeff(dt*diffusion_term);
ParBilinearForm *m = new ParBilinearForm(fes);
ParBilinearForm *k = new ParBilinearForm(fes);
ParBilinearForm *s = new ParBilinearForm(fes);
m->AddDomainIntegrator(new MassIntegrator());
constexpr real_t alpha = -1.0;
k->AddDomainIntegrator(new ConvectionIntegrator(*velocity, alpha));
s->AddDomainIntegrator(new DiffusionIntegrator(diff_coeff));
// For the preconditioner - create billinear form corresponding to
// operator (M + dt S)
ParBilinearForm *a = new ParBilinearForm(fes);
a->AddDomainIntegrator(new MassIntegrator);
a->AddDomainIntegrator(new DiffusionIntegrator(dt_diff_coeff));
if (!cg)
{
k->AddInteriorFaceIntegrator(new NonconservativeDGTraceIntegrator(*velocity,
alpha));
k->AddBdrFaceIntegrator(new NonconservativeDGTraceIntegrator(*velocity, alpha));
s->AddInteriorFaceIntegrator(new DGDiffusionIntegrator(diff_coeff, sigma,
kappa));
s->AddBdrFaceIntegrator(new DGDiffusionIntegrator(diff_coeff, sigma, kappa));
a->AddInteriorFaceIntegrator(new DGDiffusionIntegrator(dt_diff_coeff, sigma,
kappa));
a->AddBdrFaceIntegrator(new DGDiffusionIntegrator(dt_diff_coeff, sigma, kappa));
}
int skip_zeros = 0;
m->Assemble(skip_zeros);
k->Assemble(skip_zeros);
s->Assemble(skip_zeros);
a->Assemble();
m->Finalize(skip_zeros);
k->Finalize(skip_zeros);
s->Finalize(skip_zeros);
a->Finalize(skip_zeros);
HypreParVector b(fes);
b = 0.0;
// 9. Define the initial conditions. Set up visualization (if desired).
std::unique_ptr<FunctionCoefficient> u0;
if (0==problem)
{
u0.reset(new FunctionCoefficient(u0_function<0>));
}
else if (1==problem)
{
u0.reset(new FunctionCoefficient(u0_function<1>));
}
else if (2==problem)
{
u0.reset(new FunctionCoefficient(u0_function<2>));
}
else if (3==problem)
{
u0.reset(new FunctionCoefficient(u0_function<3>));
}
ParGridFunction *u = new ParGridFunction(fes);
u->ProjectCoefficient(*u0);
HypreParVector *U = u->GetTrueDofs();
DataCollection *dc = NULL;
if (visit)
{
if (binary)
{
#ifdef MFEM_USE_SIDRE
dc = new SidreDataCollection("Example41-Parallel", pmesh);
#else
MFEM_ABORT("Must build with MFEM_USE_SIDRE=YES for binary output.");
#endif
}
else
{
dc = new VisItDataCollection("Example41-Parallel", pmesh);
dc->SetPrecision(precision);
// To save the mesh using MFEM's parallel mesh format:
// dc->SetFormat(DataCollection::PARALLEL_FORMAT);
}
dc->RegisterField("solution", u);
dc->SetCycle(0);
dc->SetTime(0.0);
dc->Save();
}
ParaViewDataCollection *pd = NULL;
if (paraview)
{
pd = new ParaViewDataCollection("Example41P", pmesh);
pd->SetPrefixPath("ParaView");
pd->RegisterField("solution", u);
pd->SetLevelsOfDetail(order);
pd->SetDataFormat(VTKFormat::BINARY);
pd->SetHighOrderOutput(true);
pd->SetCycle(0);
pd->SetTime(0.0);
pd->Save();
}
socketstream sout;
if (visualization)
{
char vishost[] = "localhost";
int visport = 19916;
sout.open(vishost, visport);
if (!sout)
{
if (Mpi::Root())
{
cout << "Unable to connect to GLVis server at "
<< vishost << ':' << visport << endl;
}
visualization = false;
if (Mpi::Root())
{
cout << "GLVis visualization disabled.\n";
}
}
else
{
sout << "parallel " << num_procs << " " << myid << "\n";
sout.precision(precision);
sout << "solution\n" << *pmesh << *u;
sout << "pause\n";
sout << flush;
if (Mpi::Root())
{
cout << "GLVis visualization paused."
<< " Press space (in the GLVis window) to resume it.\n";
}
}
}
#ifdef MFEM_USE_ADIOS2
ADIOS2DataCollection *adios2_dc = NULL;
if (adios2)
{
std::string postfix(mesh_file);
postfix.erase(0, std::string("../data/").size() );
postfix += "_o" + std::to_string(order);
const std::string collection_name = "ex41-p-" + postfix + ".bp";
adios2_dc = new ADIOS2DataCollection(MPI_COMM_WORLD, collection_name, pmesh);
// output data substreams are half the number of mpi processes
adios2_dc->SetParameter("SubStreams", std::to_string(num_procs/2) );
// adios2_dc->SetLevelsOfDetail(2);
adios2_dc->RegisterField("solution", u);
adios2_dc->SetCycle(0);
adios2_dc->SetTime(0.0);
adios2_dc->Save();
}
#endif
// 10. Define the time-dependent evolution operator describing the
// ODE right-hand side, and perform time-integration (looping
// over the time iterations, ti, with a time-step dt).
IMEX_Evolution adv(*m, *k, *s, b, *a);
real_t t = 0.0;
adv.SetTime(t);
ode_solver->Init(adv);
bool done = false;
for (int ti = 0; !done; )
{
real_t dt_real = min(dt, t_final - t);
ode_solver->Step(*U, t, dt_real);
ti++;
done = (t >= t_final - 1e-8*dt);
if (done || ti % vis_steps == 0)
{
if (Mpi::Root())
{
cout << "time step: " << ti << ", time: " << t << endl;
}
*u = *U;
if (visualization)
{
sout << "parallel " << num_procs << " " << myid << "\n";
sout << "solution\n" << *pmesh << *u << flush;
}
if (paraview)
{
pd->SetCycle(ti);
pd->SetTime(t);
pd->Save();
}
#ifdef MFEM_USE_ADIOS2
// transient solutions can be visualized with ParaView
if (adios2)
{
adios2_dc->SetCycle(ti);
adios2_dc->SetTime(t);
adios2_dc->Save();
}
#endif
}
}
// 11. Free the used memory.
delete pd;
delete U;
delete u;
delete a;
delete s;
delete k;
delete m;
delete fes;
delete pmesh;
delete dc;
delete fec;
return 0;
}
// Implementation of class IMEX_Evolution
IMEX_Evolution::IMEX_Evolution(ParBilinearForm &M_, ParBilinearForm &K_,
ParBilinearForm &S_, const Vector &b_, ParBilinearForm &A_)
: TimeDependentOperator(M_.ParFESpace()->GetTrueVSize()), b(b_),
M_solver(M_.ParFESpace()->GetComm()), z(height), w(height)
{
if (M_.GetAssemblyLevel()==AssemblyLevel::LEGACY)
{
M.Reset(M_.ParallelAssemble(), true);
K.Reset(K_.ParallelAssemble(), true);
S.Reset(S_.ParallelAssemble(), true);
}
else
{
M.Reset(&M_, false);
K.Reset(&K_, false);
S.Reset(&S_, false);
}
M_solver.SetOperator(*M);
Array<int> ess_tdof_list;
if (M_.GetAssemblyLevel() == AssemblyLevel::LEGACY)
{
A.Reset(A_.ParallelAssemble(), true);
HypreParMatrix &M_mat = *M.As<HypreParMatrix>();
HypreParMatrix &S_mat = *S.As<HypreParMatrix>();
HypreSmoother *hypre_prec = new HypreSmoother(M_mat, HypreSmoother::Jacobi);
M_prec = hypre_prec;
implicit_solver = new Implicit_Solver(M_mat, S_mat, *M_.FESpace());
lor_solver = new LORSolver<HypreBoomerAMG>(A_, ess_tdof_list);
lor_solver->GetSolver().SetSystemsOptions(A_.ParFESpace()->GetVDim(), true);
implicit_solver -> SetPreconditioner(*lor_solver);
}
else
{
MFEM_ABORT("Implicit time integration is not supported with partial assembly");
}
M_solver.SetPreconditioner(*M_prec);
M_solver.iterative_mode = false;
M_solver.SetRelTol(1e-9);
M_solver.SetAbsTol(0.0);
M_solver.SetMaxIter(100);
M_solver.SetPrintLevel(0);
}
void IMEX_Evolution::Mult1(const Vector &x, Vector &y) const
{
// Perform the explicit step
// y = M^{-1} (K x + b)
K->Mult(x, z);
z += b;
M_solver.Mult(z, y);
}
void IMEX_Evolution::ImplicitSolve2(const real_t dt, const Vector &x, Vector &k)
{
// Perform the implicit step
// solve for k, k = -(M+dt S)^{-1} S x
MFEM_VERIFY(implicit_solver != NULL,
"Implicit time integration is not supported with partial assembly");
S->Mult(x, z);
z*= -1.0;
implicit_solver->SetTimeStep(dt);
implicit_solver->Mult(z, k);
}