307 lines
7.6 KiB
C++
307 lines
7.6 KiB
C++
//
|
|
// Compile with: make helmholtz
|
|
//
|
|
// Sample runs: helmholtz -m ../data/one-hex.mesh
|
|
// helmholtz -m ../data/fichera.mesh
|
|
// helmholtz -m ../data/fichera-mixed.mesh
|
|
//
|
|
// Description: This example code demonstrates the use of MFEM to define a
|
|
// simple finite element discretization of the Helmholtz problem
|
|
// -Delta p - omega^2 p = 1 with impedance boundary condition.
|
|
//
|
|
#include "mfem.hpp"
|
|
#include <fstream>
|
|
#include <iostream>
|
|
#include "complex_additive_schwarz.hpp"
|
|
#include "schwarz.hpp"
|
|
|
|
using namespace std;
|
|
using namespace mfem;
|
|
|
|
// Exact solution and r.h.s., see below for implementation.
|
|
double f_exact_Re(const Vector &x);
|
|
double f_exact_Im(const Vector &x);
|
|
|
|
int dim;
|
|
double omega;
|
|
int sol = 1;
|
|
bool pml = false;
|
|
double length = 1.0;
|
|
double pml_length = 0.25;
|
|
bool scatter = false;
|
|
|
|
#ifndef MFEM_USE_SUPERLU
|
|
#error This example requires that MFEM is built with MFEM_USE_PETSC=YES
|
|
#endif
|
|
|
|
int main(int argc, char *argv[])
|
|
{
|
|
|
|
// 2. Parse command-line options.
|
|
// geometry file
|
|
const char *mesh_file = "../../data/one-hex.mesh";
|
|
// finite element order of approximation
|
|
int order = 1;
|
|
// static condensation flag
|
|
bool static_cond = false;
|
|
bool visualization = 1;
|
|
// number of wavelengths
|
|
double k = 0.5;
|
|
// number of mg levels
|
|
int ref = 1;
|
|
// dimension
|
|
int nd = 2;
|
|
|
|
// optional command line inputs
|
|
OptionsParser args(argc, argv);
|
|
args.AddOption(&mesh_file, "-m", "--mesh",
|
|
"Mesh file to use.");
|
|
args.AddOption(&order, "-o", "--order",
|
|
"Finite element order (polynomial degree) or -1 for"
|
|
" isoparametric space.");
|
|
args.AddOption(&nd, "-nd", "--dim","Problem space dimension");
|
|
args.AddOption(&sol, "-sol", "--exact",
|
|
"Exact solution flag - 0:polynomial, 1: plane wave, -1: unknown exact");
|
|
args.AddOption(&k, "-k", "--wavelengths",
|
|
"Number of wavelengths.");
|
|
args.AddOption(&pml, "-pml", "--pml", "-no-pml",
|
|
"--no-pml", "Enable PML.");
|
|
args.AddOption(&pml_length, "-pml_length", "--pml_length",
|
|
"Length of the PML region in each direction");
|
|
args.AddOption(&length, "-length", "--length",
|
|
"length of the domainin in each direction.");
|
|
args.AddOption(&ref, "-ref", "--ref",
|
|
"Number of Refinements.");
|
|
args.AddOption(&static_cond, "-sc", "--static-condensation", "-no-sc",
|
|
"--no-static-condensation", "Enable static condensation.");
|
|
args.AddOption(&scatter, "-scat", "--scattering-prob", "-no-scat",
|
|
"--no-scattering", "Solve a scattering problem");
|
|
args.AddOption(&visualization, "-vis", "--visualization", "-no-vis",
|
|
"--no-visualization",
|
|
"Enable or disable GLVis visualization.");
|
|
args.Parse();
|
|
// check if the inputs are correct
|
|
if (!args.Good())
|
|
{
|
|
args.PrintUsage(cout);
|
|
return 1;
|
|
}
|
|
args.PrintOptions(cout);
|
|
// Angular frequency
|
|
omega = 2.0 * M_PI * k;
|
|
|
|
// 3. Read the mesh from the given mesh file.
|
|
Mesh *mesh;
|
|
|
|
if (nd == 2)
|
|
{
|
|
// mesh = new Mesh(mesh_file,1,1);
|
|
mesh = new Mesh(1, 1, Element::QUADRILATERAL, true, length, length, false);
|
|
}
|
|
else
|
|
{
|
|
mesh = new Mesh(1, 1, 1, Element::HEXAHEDRON, true, length, length, length,false);
|
|
}
|
|
|
|
// 3. Executing uniform h-refinement
|
|
for (int i = 0; i < ref; i++ )
|
|
{
|
|
mesh->UniformRefinement();
|
|
}
|
|
dim = mesh->Dimension();
|
|
|
|
|
|
// 6. Define a finite element space on the mesh.
|
|
FiniteElementCollection *fec = new H1_FECollection(order, dim);
|
|
FiniteElementSpace *fespace = new FiniteElementSpace(mesh, fec);
|
|
|
|
// 6. Set up the linear form (Real and Imaginary part)
|
|
FunctionCoefficient f_Re(f_exact_Re);
|
|
FunctionCoefficient f_Im(f_exact_Im);
|
|
|
|
// ParLinearForm *b_Re(new ParLinearForm);
|
|
ComplexLinearForm b(fespace, ComplexOperator::HERMITIAN);
|
|
b.AddDomainIntegrator(new DomainLFIntegrator(f_Re),
|
|
new DomainLFIntegrator(f_Im));
|
|
b.real().Vector::operator=(0.0);
|
|
b.imag().Vector::operator=(0.0);
|
|
b.Assemble();
|
|
|
|
// 7. Set up the bilinear form (Real and Imaginary part)
|
|
ConstantCoefficient one(1.0);
|
|
ConstantCoefficient sigma(-pow(omega, 2));
|
|
|
|
SesquilinearForm a(fespace,ComplexOperator::HERMITIAN);
|
|
ConstantCoefficient impedance(omega);
|
|
|
|
|
|
Array<int> bdr_attr(mesh->bdr_attributes.Max());
|
|
bdr_attr = 1;
|
|
RestrictedCoefficient imp_rest(impedance,bdr_attr);
|
|
a.AddDomainIntegrator(new DiffusionIntegrator(one),NULL);
|
|
a.AddDomainIntegrator(new MassIntegrator(sigma),NULL);
|
|
a.AddBoundaryIntegrator(NULL,new BoundaryMassIntegrator(imp_rest));
|
|
a.Assemble();
|
|
a.Finalize();
|
|
|
|
Array<int> ess_tdof_list;
|
|
Array<int> ess_bdr(mesh->bdr_attributes.Max());
|
|
ess_bdr = 0;
|
|
fespace->GetEssentialTrueDofs(ess_bdr, ess_tdof_list);
|
|
|
|
// Solution grid function
|
|
ComplexGridFunction p_gf(fespace);
|
|
|
|
OperatorHandle Ah;
|
|
Vector X, B;
|
|
|
|
a.FormLinearSystem(ess_tdof_list, p_gf, b, Ah, X, B);
|
|
|
|
ComplexSparseMatrix * AZ = Ah.As<ComplexSparseMatrix>();
|
|
SparseMatrix * A = AZ->GetSystemMatrix();
|
|
|
|
|
|
cout << "Size of fine grid system: "
|
|
<< A->Height() << " x " << A->Width() << endl;
|
|
|
|
|
|
|
|
|
|
ComplexAddSchwarz S(&a,ess_tdof_list, 1);
|
|
S.SetOperator(*A);
|
|
S.SetSmoothType(0);
|
|
S.SetLoadVector(B);
|
|
// S.SetNumSmoothSteps(7);
|
|
S.SetDumpingParam(1.0);
|
|
|
|
BlkSchwarzSmoother * BlkS = new BlkSchwarzSmoother(mesh,0,fespace,A);
|
|
|
|
X = 0.0;
|
|
GMRESSolver gmres;
|
|
gmres.SetPreconditioner(*BlkS);
|
|
gmres.SetOperator(*A);
|
|
gmres.SetRelTol(1e-4);
|
|
gmres.SetMaxIter(500);
|
|
gmres.SetPrintLevel(1);
|
|
gmres.Mult(B, X);
|
|
|
|
|
|
X = 0.0;
|
|
gmres.SetPreconditioner(S);
|
|
gmres.Mult(B, X);
|
|
|
|
KLUSolver klu(*A);
|
|
klu.Mult(B,X);
|
|
|
|
|
|
a.RecoverFEMSolution(X,B,p_gf);
|
|
|
|
|
|
if (visualization)
|
|
{
|
|
char vishost[] = "localhost";
|
|
int visport = 19916;
|
|
string keys;
|
|
if (dim ==2 )
|
|
{
|
|
keys = "keys mrRljc\n";
|
|
}
|
|
else
|
|
{
|
|
keys = "keys mc\n";
|
|
}
|
|
socketstream sol_sock_re(vishost, visport);
|
|
sol_sock_re.precision(8);
|
|
sol_sock_re << "solution\n" << *mesh << p_gf.real() <<
|
|
"window_title 'Numerical Pressure (real part): (KLU solver)' "
|
|
<< keys << flush;
|
|
}
|
|
|
|
delete fespace;
|
|
delete fec;
|
|
delete mesh;
|
|
return 0;
|
|
}
|
|
|
|
|
|
//calculate RHS from exact solution f = - \Delta u
|
|
double f_exact_Re(const Vector &x)
|
|
{
|
|
double f_re = 0.0;
|
|
double x0 = length/2.0;
|
|
double x1 = length/2.0;
|
|
double x2 = length/2.0;
|
|
x0 = 0.1;
|
|
x1 = 0.1;
|
|
double alpha,beta;
|
|
double n = 5.0 * omega/M_PI;
|
|
double coeff = pow(n,2)/M_PI;
|
|
beta = pow(x0-x(0),2) + pow(x1-x(1),2);
|
|
if (dim == 3) { beta += pow(x2-x(2),2); }
|
|
alpha = -pow(n,2) * beta;
|
|
f_re = coeff*exp(alpha);
|
|
|
|
// x0 = 0.9;
|
|
// x1 = 0.9;
|
|
// n = 5.0 * omega/M_PI;
|
|
// coeff = pow(n,2)/M_PI;
|
|
// beta = pow(x0-x(0),2) + pow(x1-x(1),2);
|
|
// if (dim == 3) { beta += pow(x2-x(2),2); }
|
|
// alpha = -pow(n,2) * beta;
|
|
// f_re += coeff*exp(alpha);
|
|
|
|
// x0 = 0.9;
|
|
// x1 = 0.1;
|
|
// n = 5.0 * omega/M_PI;
|
|
// coeff = pow(n,2)/M_PI;
|
|
// beta = pow(x0-x(0),2) + pow(x1-x(1),2);
|
|
// if (dim == 3) { beta += pow(x2-x(2),2); }
|
|
// alpha = -pow(n,2) * beta;
|
|
// f_re += coeff*exp(alpha);
|
|
|
|
// x0 = 0.1;
|
|
// x1 = 0.9;
|
|
// n = 5.0 * omega/M_PI;
|
|
// coeff = pow(n,2)/M_PI;
|
|
// beta = pow(x0-x(0),2) + pow(x1-x(1),2);
|
|
// if (dim == 3) { beta += pow(x2-x(2),2); }
|
|
// alpha = -pow(n,2) * beta;
|
|
// f_re += coeff*exp(alpha);
|
|
|
|
return f_re;
|
|
}
|
|
double f_exact_Im(const Vector &x)
|
|
{
|
|
double f_im;
|
|
f_im = 0.0;
|
|
return f_im;
|
|
}
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|