void NumProcEnergyCalc :: Do(LocalHeap & lh)
{
double result = 0;
double potential = 0;
double conversion = 1.602176565e-19 * 6.02214129e23 * 0.5 / 1000.0;
const BilinearFormIntegrator & bfi = (bfa) ? *bfa->GetIntegrator(0) : *gfu->GetFESpace().GetIntegrator();
const BilinearFormIntegrator & bfi2 = (bfa) ? *bfa->GetIntegrator(0) : *gfu->GetFESpace().GetIntegrator();
cout.precision(dbl::digits10);
for(unsigned int kk=0; kk<molecule.size(); kk++)
{
Atom currentAtom = molecule.at(kk);
point(0) = currentAtom.x;
point(1) = currentAtom.y;
point(2) = currentAtom.z;
FlatVector<double> pflux(bfi.DimFlux(), lh);
CalcPointFlux (ma, *gfu, point, domains,
pflux, bfi, applyd, lh, component);
result = pflux(0);
if (showsteps)
cout << "(" << pflux(0)*conversion;
CalcPointFlux (ma, *gfu0, point, domains,
pflux, bfi2, applyd, lh, component);
result -= pflux(0);
if (showsteps)
cout << " - " << pflux(0)*conversion << ")*" << currentAtom.charge << " = " << currentAtom.charge * result*conversion << endl;
potential += currentAtom.charge * result;
}
double energy;
energy = (1.602176565e-19 * 6.02214129e23 * 0.5 * potential)/1000;
if (MyMPI_GetNTasks() == 1 || MyMPI_GetId() != 0){
ofstream resultFile;
resultFile.open("result.out");
resultFile << "The energy difference is " << energy << " [kJ/mol].\n";
resultFile.close();
cout << "The energy difference is " << setprecision(12) << energy << " [kJ/mol].\n";
}
pde.GetVariable(variablename,true) = result;
}
/*virtual*/ Operand* InnerProductScalar::Simplify( const SimplificationContext& simplificationContext )
{
if( exponent == 0 )
{
NumericScalar* numericScalar = new NumericScalar();
numericScalar->SetReal( 1.0 );
return numericScalar;
}
BilinearForm* bilinearForm = BilinearForm::Get();
if( !bilinearForm )
return 0;
double result;
if( !bilinearForm->Evaluate( nameA, nameB, result ) )
return 0;
NumericScalar* numericScalar = new NumericScalar();
numericScalar->SetReal( result );
return numericScalar;
}
void UpdateProblem(Mesh &mesh, FiniteElementSpace &fespace,
GridFunction &x, BilinearForm &a, LinearForm &b)
{
// Update the space: recalculate the number of DOFs and construct a matrix
// that will adjust any GridFunctions to the new mesh state.
fespace.Update();
// Interpolate the solution on the new mesh by applying the transformation
// matrix computed in the finite element space. Multiple GridFunctions could
// be updated here.
x.Update();
// Free any transformation matrices to save memory.
fespace.UpdatesFinished();
// Inform the linear and bilinear forms that the space has changed.
a.Update();
b.Update();
}
int main (int argc, char *argv[])
{
Mesh *mesh;
SightInit(argc, argv, "ex1", "dbg.MFEM.ex2");
if (argc == 1)
{
cout << "\nUsage: ex2 <mesh_file>\n" << endl;
return 1;
}
// 1. Read the mesh from the given mesh file. We can handle triangular,
// quadrilateral, tetrahedral or hexahedral elements with the same code.
ifstream imesh(argv[1]);
if (!imesh)
{
cerr << "\nCan not open mesh file: " << argv[1] << '\n' << endl;
return 2;
}
mesh = new Mesh(imesh, 1, 1);
imesh.close();
if (mesh->attributes.Max() < 2 || mesh->bdr_attributes.Max() < 2)
{
cerr << "\nInput mesh should have at least two materials and "
<< "two boundary attributes! (See schematic in ex2.cpp)\n"
<< endl;
return 3;
}
int dim = mesh->Dimension();
// 2. Select the order of the finite element discretization space. For NURBS
// meshes, we increase the order by degree elevation.
int p;
if(argc==3) p = atoi(argv[2]);
else {
cout << "Enter finite element space order --> " << flush;
cin >> p;
}
if (mesh->NURBSext && p > mesh->NURBSext->GetOrder())
mesh->DegreeElevate(p - mesh->NURBSext->GetOrder());
// 3. Refine the mesh 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 5,000
// elements.
{
int ref_levels =
(int)floor(log(5000./mesh->GetNE())/log(2.)/dim);
for (int l = 0; l < ref_levels; l++)
mesh->UniformRefinement();
}
// 4. Define a finite element space on the mesh. Here we use vector finite
// elements, i.e. dim copies of a scalar finite element space. The vector
// dimension is specified by the last argument of the FiniteElementSpace
// constructor. For NURBS meshes, we use the (degree elevated) NURBS space
// associated with the mesh nodes.
FiniteElementCollection *fec;
FiniteElementSpace *fespace;
if (mesh->NURBSext)
{
fec = NULL;
fespace = mesh->GetNodes()->FESpace();
}
else
{
fec = new H1_FECollection(p, dim);
fespace = new FiniteElementSpace(mesh, fec, dim);
}
dbg << "Number of unknowns: " << fespace->GetVSize() << endl
<< "Assembling: " << flush;
// 5. Set up the linear form b(.) which corresponds to the right-hand side of
// the FEM linear system. In this case, b_i equals the boundary integral
// of f*phi_i where f represents a "pull down" force on the Neumann part
// of the boundary and phi_i are the basis functions in the finite element
// fespace. The force is defined by the VectorArrayCoefficient object f,
// which is a vector of Coefficient objects. The fact that f is non-zero
// on boundary attribute 2 is indicated by the use of piece-wise constants
// coefficient for its last component.
VectorArrayCoefficient f(dim);
for (int i = 0; i < dim-1; i++)
f.Set(i, new ConstantCoefficient(0.0));
{
Vector pull_force(mesh->bdr_attributes.Max());
pull_force = 0.0;
pull_force(1) = -1.0e-2;
f.Set(dim-1, new PWConstCoefficient(pull_force));
}
LinearForm *b = new LinearForm(fespace);
b->AddBoundaryIntegrator(new VectorBoundaryLFIntegrator(f));
dbg << "r.h.s. ... " << flush;
b->Assemble();
// 6. Define the solution vector x as a finite element grid function
// corresponding to fespace. Initialize x with initial guess of zero,
// which satisfies the boundary conditions.
GridFunction x(fespace);
x = 0.0;
// 7. Set up the bilinear form a(.,.) on the finite element space
// corresponding to the linear elasticity integrator with piece-wise
// constants coefficient lambda and mu. The boundary conditions are
// implemented by marking only boundary attribute 1 as essential. After
// assembly and finalizing we extract the corresponding sparse matrix A.
Vector lambda(mesh->attributes.Max());
lambda = 1.0;
lambda(0) = lambda(1)*50;
PWConstCoefficient lambda_func(lambda);
Vector mu(mesh->attributes.Max());
mu = 1.0;
mu(0) = mu(1)*50;
PWConstCoefficient mu_func(mu);
BilinearForm *a = new BilinearForm(fespace);
a->AddDomainIntegrator(new ElasticityIntegrator(lambda_func,mu_func));
dbg << "matrix ... " << flush;
a->Assemble();
Array<int> ess_bdr(mesh->bdr_attributes.Max());
ess_bdr = 0;
ess_bdr[0] = 1;
a->EliminateEssentialBC(ess_bdr, x, *b);
a->Finalize();
dbg << "done." << endl;
const SparseMatrix &A = a->SpMat();
// 8. Define a simple symmetric Gauss-Seidel preconditioner and use it to
// solve the system Ax=b with PCG.
GSSmoother M(A);
PCG(A, M, *b, x, 1, 500, 1e-8, 0.0);
// 9. 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 (!mesh->NURBSext)
mesh->SetNodalFESpace(fespace);
// 10. Save the displaced mesh and the inverted solution (which gives the
// backward displacements to the original grid). This output can be
// viewed later using GLVis: "glvis -m displaced.mesh -g sol.gf".
{
GridFunction *nodes = mesh->GetNodes();
*nodes += x;
x *= -1;
ofstream mesh_ofs("displaced.mesh");
mesh_ofs.precision(8);
mesh->Print(mesh_ofs);
ofstream sol_ofs("sol.gf");
sol_ofs.precision(8);
x.Save(sol_ofs);
}
// 11. (Optional) Send the above data by socket to a GLVis server. Use the
// "n" and "b" keys in GLVis to visualize the displacements.
/*char vishost[] = "localhost";
int visport = 19916;
osockstream sol_sock(visport, vishost);
sol_sock << "solution\n";
sol_sock.precision(8);
mesh->Print(sol_sock);
x.Save(sol_sock);
sol_sock.send();*/
#if defined(VNC_ENABLED)
mfem::emitMesh(mesh, &x);
#endif
// 12. Free the used memory.
delete a;
delete b;
if (fec)
{
delete fespace;
delete fec;
}
delete mesh;
return 0;
}
int main (int argc, char *argv[])
{
SightInit(argc, argv, "ex3", "dbg.MFEM.ex3");
Mesh *mesh;
if (argc == 1)
{
cerr << "\nUsage: ex3 <mesh_file>\n" << endl;
return 1;
}
// 1. Read the mesh from the given mesh file. In this 3D example, we can
// handle tetrahedral or hexahedral meshes with the same code.
ifstream imesh(argv[1]);
if (!imesh)
{
cerr << "\nCan not open mesh file: " << argv[1] << '\n' << endl;
return 2;
}
mesh = new Mesh(imesh, 1, 1);
imesh.close();
if (mesh -> Dimension() != 3)
{
cerr << "\nThis example requires a 3D mesh\n" << endl;
return 3;
}
// 2. Refine the mesh 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 50,000
// elements.
{
int ref_levels =
(int)floor(log(50000./mesh->GetNE())/log(2.)/mesh->Dimension());
for (int l = 0; l < ref_levels; l++)
mesh->UniformRefinement();
}
// 3. Define a finite element space on the mesh. Here we use the lowest order
// Nedelec finite elements, but we can easily swich to higher-order spaces
// by changing the value of p.
int p = 1;
FiniteElementCollection *fec = new ND_FECollection(p, mesh -> Dimension());
FiniteElementSpace *fespace = new FiniteElementSpace(mesh, fec);
dbg << "Number of unknowns: " << fespace->GetVSize() << endl;
// 4. Set up the linear form b(.) which corresponds to the right-hand side
// of the FEM linear system, which in this case is (f,phi_i) where f is
// given by the function f_exact and phi_i are the basis functions in the
// finite element fespace.
VectorFunctionCoefficient f(3, f_exact);
LinearForm *b = new LinearForm(fespace);
b->AddDomainIntegrator(new VectorFEDomainLFIntegrator(f));
b->Assemble();
// 5. Define the solution vector x as a finite element grid function
// corresponding to fespace. Initialize x by projecting the exact
// solution. Note that only values from the boundary edges will be used
// when eliminating the non-homogenious boundary condition to modify the
// r.h.s. vector b.
GridFunction x(fespace);
VectorFunctionCoefficient E(3, E_exact);
x.ProjectCoefficient(E);
// 6. Set up the bilinear form corresponding to the EM diffusion operator
// curl muinv curl + sigma I, by adding the curl-curl and the mass domain
// integrators and finally imposing the non-homogeneous Dirichlet boundary
// conditions. The boundary conditions are implemented by marking all the
// boundary attributes from the mesh as essential (Dirichlet). After
// assembly and finalizing we extract the corresponding sparse matrix A.
Coefficient *muinv = new ConstantCoefficient(1.0);
Coefficient *sigma = new ConstantCoefficient(1.0);
BilinearForm *a = new BilinearForm(fespace);
a->AddDomainIntegrator(new CurlCurlIntegrator(*muinv));
a->AddDomainIntegrator(new VectorFEMassIntegrator(*sigma));
a->Assemble();
Array<int> ess_bdr(mesh->bdr_attributes.Max());
ess_bdr = 1;
a->EliminateEssentialBC(ess_bdr, x, *b);
a->Finalize();
const SparseMatrix &A = a->SpMat();
// 7. Define a simple symmetric Gauss-Seidel preconditioner and use it to
// solve the system Ax=b with PCG.
GSSmoother M(A);
x = 0.0;
PCG(A, M, *b, x, 1, 500, 1e-12, 0.0);
// 8. Compute and print the L^2 norm of the error.
dbg << "\n|| E_h - E ||_{L^2} = " << x.ComputeL2Error(E) << '\n' << endl;
// 9. Save the refined mesh and the solution. This output can be viewed
// later using GLVis: "glvis -m refined.mesh -g sol.gf".
{
ofstream mesh_ofs("refined.mesh");
mesh_ofs.precision(8);
mesh->Print(mesh_ofs);
ofstream sol_ofs("sol.gf");
sol_ofs.precision(8);
x.Save(sol_ofs);
}
// 10. (Optional) Send the solution by socket to a GLVis server.
/*char vishost[] = "localhost";
int visport = 19916;
osockstream sol_sock(visport, vishost);
sol_sock << "solution\n";
sol_sock.precision(8);
mesh->Print(sol_sock);
x.Save(sol_sock);
sol_sock.send();*/
#if defined(VNC_ENABLED)
mfem::emitMesh(mesh, &x);
#endif
// 11. Free the used memory.
delete a;
delete sigma;
delete muinv;
delete b;
delete fespace;
delete fec;
delete mesh;
return 0;
}
int main(int argc, char *argv[])
{
// 1. Parse command-line options.
const char *mesh_file = "../data/beam-tri.mesh";
int order = 1;
bool static_cond = false;
bool visualization = 1;
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(&static_cond, "-sc", "--static-condensation", "-no-sc",
"--no-static-condensation", "Enable static condensation.");
args.AddOption(&visualization, "-vis", "--visualization", "-no-vis",
"--no-visualization",
"Enable or disable GLVis visualization.");
args.Parse();
if (!args.Good())
{
args.PrintUsage(cout);
return 1;
}
args.PrintOptions(cout);
// 2. Read the mesh from the given mesh file. We can handle triangular,
// quadrilateral, tetrahedral or hexahedral elements with the same code.
Mesh *mesh = new Mesh(mesh_file, 1, 1);
int dim = mesh->Dimension();
if (mesh->attributes.Max() < 2 || mesh->bdr_attributes.Max() < 2)
{
cerr << "\nInput mesh should have at least two materials and "
<< "two boundary attributes! (See schematic in ex2.cpp)\n"
<< endl;
return 3;
}
// 3. 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);
}
// 4. Refine the mesh 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 5,000
// elements.
{
int ref_levels =
(int)floor(log(5000./mesh->GetNE())/log(2.)/dim);
for (int l = 0; l < ref_levels; l++)
{
mesh->UniformRefinement();
}
}
// 5. Define a finite element space on the mesh. Here we use vector finite
// elements, i.e. dim copies of a scalar finite element space. The vector
// dimension is specified by the last argument of the FiniteElementSpace
// constructor. For NURBS meshes, we use the (degree elevated) NURBS space
// associated with the mesh nodes.
FiniteElementCollection *fec;
FiniteElementSpace *fespace;
if (mesh->NURBSext)
{
fec = NULL;
fespace = mesh->GetNodes()->FESpace();
}
else
{
fec = new H1_FECollection(order, dim);
fespace = new FiniteElementSpace(mesh, fec, dim);
}
cout << "Number of finite element unknowns: " << fespace->GetTrueVSize()
<< endl << "Assembling: " << flush;
// 6. Determine the list of true (i.e. conforming) essential boundary dofs.
// In this example, the boundary conditions are defined by marking only
// boundary attribute 1 from the mesh as essential and converting it to a
// list of true dofs.
Array<int> ess_tdof_list, ess_bdr(mesh->bdr_attributes.Max());
ess_bdr = 0;
ess_bdr[0] = 1;
fespace->GetEssentialTrueDofs(ess_bdr, ess_tdof_list);
// 7. Set up the linear form b(.) which corresponds to the right-hand side of
// the FEM linear system. In this case, b_i equals the boundary integral
// of f*phi_i where f represents a "pull down" force on the Neumann part
// of the boundary and phi_i are the basis functions in the finite element
// fespace. The force is defined by the VectorArrayCoefficient object f,
// which is a vector of Coefficient objects. The fact that f is non-zero
// on boundary attribute 2 is indicated by the use of piece-wise constants
// coefficient for its last component.
VectorArrayCoefficient f(dim);
for (int i = 0; i < dim-1; i++)
{
f.Set(i, new ConstantCoefficient(0.0));
}
{
Vector pull_force(mesh->bdr_attributes.Max());
pull_force = 0.0;
pull_force(1) = -1.0e-2;
f.Set(dim-1, new PWConstCoefficient(pull_force));
}
LinearForm *b = new LinearForm(fespace);
b->AddBoundaryIntegrator(new VectorBoundaryLFIntegrator(f));
cout << "r.h.s. ... " << flush;
b->Assemble();
// 8. Define the solution vector x as a finite element grid function
// corresponding to fespace. Initialize x with initial guess of zero,
// which satisfies the boundary conditions.
GridFunction x(fespace);
x = 0.0;
// 9. Set up the bilinear form a(.,.) on the finite element space
// corresponding to the linear elasticity integrator with piece-wise
// constants coefficient lambda and mu.
Vector lambda(mesh->attributes.Max());
lambda = 1.0;
lambda(0) = lambda(1)*50;
PWConstCoefficient lambda_func(lambda);
Vector mu(mesh->attributes.Max());
mu = 1.0;
mu(0) = mu(1)*50;
PWConstCoefficient mu_func(mu);
BilinearForm *a = new BilinearForm(fespace);
a->AddDomainIntegrator(new ElasticityIntegrator(lambda_func,mu_func));
// 10. Assemble the bilinear form and the corresponding linear system,
// applying any necessary transformations such as: eliminating boundary
// conditions, applying conforming constraints for non-conforming AMR,
// static condensation, etc.
cout << "matrix ... " << flush;
if (static_cond) { a->EnableStaticCondensation(); }
a->Assemble();
SparseMatrix A;
Vector B, X;
a->FormLinearSystem(ess_tdof_list, x, *b, A, X, B);
cout << "done." << endl;
cout << "Size of linear system: " << A.Height() << endl;
#ifndef MFEM_USE_SUITESPARSE
// 11. Define a simple symmetric Gauss-Seidel preconditioner and use it to
// solve the system Ax=b with PCG.
GSSmoother M(A);
PCG(A, M, B, X, 1, 500, 1e-8, 0.0);
#else
// 11. If MFEM was compiled with SuiteSparse, use UMFPACK to solve the system.
UMFPackSolver umf_solver;
umf_solver.Control[UMFPACK_ORDERING] = UMFPACK_ORDERING_METIS;
umf_solver.SetOperator(A);
umf_solver.Mult(B, X);
#endif
// 12. Recover the solution as a finite element grid function.
a->RecoverFEMSolution(X, *b, x);
// 13. 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 (!mesh->NURBSext)
{
mesh->SetNodalFESpace(fespace);
}
// 14. Save the displaced mesh and the inverted solution (which gives the
// backward displacements to the original grid). This output can be
// viewed later using GLVis: "glvis -m displaced.mesh -g sol.gf".
{
GridFunction *nodes = mesh->GetNodes();
*nodes += x;
x *= -1;
ofstream mesh_ofs("displaced.mesh");
mesh_ofs.precision(8);
mesh->Print(mesh_ofs);
ofstream sol_ofs("sol.gf");
sol_ofs.precision(8);
x.Save(sol_ofs);
}
// 15. 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 sol_sock(vishost, visport);
sol_sock.precision(8);
sol_sock << "solution\n" << *mesh << x << flush;
}
// 16. Free the used memory.
delete a;
delete b;
if (fec)
{
delete fespace;
delete fec;
}
delete mesh;
return 0;
}
int main(int argc, char *argv[])
{
// 1. Parse command-line options.
int elem_type = 1;
int ref_levels = 2;
int amr = 0;
int order = 2;
bool always_snap = false;
bool visualization = 1;
OptionsParser args(argc, argv);
args.AddOption(&elem_type, "-e", "--elem",
"Type of elements to use: 0 - triangles, 1 - quads.");
args.AddOption(&order, "-o", "--order",
"Finite element order (polynomial degree).");
args.AddOption(&ref_levels, "-r", "--refine",
"Number of times to refine the mesh uniformly.");
args.AddOption(&amr, "-amr", "--refine-locally",
"Additional local (non-conforming) refinement:"
" 1 = refine around north pole, 2 = refine randomly.");
args.AddOption(&visualization, "-vis", "--visualization", "-no-vis",
"--no-visualization",
"Enable or disable GLVis visualization.");
args.AddOption(&always_snap, "-snap", "--always-snap", "-no-snap",
"--snap-at-the-end",
"If true, snap nodes to the sphere initially and after each refinement "
"otherwise, snap only after the last refinement");
args.Parse();
if (!args.Good())
{
args.PrintUsage(cout);
return 1;
}
args.PrintOptions(cout);
// 2. Generate an initial high-order (surface) mesh on the unit sphere. The
// Mesh object represents a 2D mesh in 3 spatial dimensions. We first add
// the elements and the vertices of the mesh, and then make it high-order
// by specifying a finite element space for its nodes.
int Nvert = 8, Nelem = 6;
if (elem_type == 0)
{
Nvert = 6;
Nelem = 8;
}
Mesh *mesh = new Mesh(2, Nvert, Nelem, 0, 3);
if (elem_type == 0) // inscribed octahedron
{
const double tri_v[6][3] =
{
{ 1, 0, 0}, { 0, 1, 0}, {-1, 0, 0},
{ 0, -1, 0}, { 0, 0, 1}, { 0, 0, -1}
};
const int tri_e[8][3] =
{
{0, 1, 4}, {1, 2, 4}, {2, 3, 4}, {3, 0, 4},
{1, 0, 5}, {2, 1, 5}, {3, 2, 5}, {0, 3, 5}
};
for (int j = 0; j < Nvert; j++)
{
mesh->AddVertex(tri_v[j]);
}
for (int j = 0; j < Nelem; j++)
{
int attribute = j + 1;
mesh->AddTriangle(tri_e[j], attribute);
}
mesh->FinalizeTriMesh(1, 1, true);
}
else // inscribed cube
{
const double quad_v[8][3] =
{
{-1, -1, -1}, {+1, -1, -1}, {+1, +1, -1}, {-1, +1, -1},
{-1, -1, +1}, {+1, -1, +1}, {+1, +1, +1}, {-1, +1, +1}
};
const int quad_e[6][4] =
{
{3, 2, 1, 0}, {0, 1, 5, 4}, {1, 2, 6, 5},
{2, 3, 7, 6}, {3, 0, 4, 7}, {4, 5, 6, 7}
};
for (int j = 0; j < Nvert; j++)
{
mesh->AddVertex(quad_v[j]);
}
for (int j = 0; j < Nelem; j++)
{
int attribute = j + 1;
mesh->AddQuad(quad_e[j], attribute);
}
mesh->FinalizeQuadMesh(1, 1, true);
}
// Set the space for the high-order mesh nodes.
H1_FECollection fec(order, mesh->Dimension());
FiniteElementSpace nodal_fes(mesh, &fec, mesh->SpaceDimension());
mesh->SetNodalFESpace(&nodal_fes);
// 3. Refine the mesh while snapping nodes to the sphere.
for (int l = 0; l <= ref_levels; l++)
{
if (l > 0) // for l == 0 just perform snapping
{
mesh->UniformRefinement();
}
// Snap the nodes of the refined mesh back to sphere surface.
if (always_snap || l == ref_levels)
{
SnapNodes(*mesh);
}
}
if (amr == 1)
{
for (int l = 0; l < 5; l++)
{
mesh->RefineAtVertex(Vertex(0, 0, 1));
}
SnapNodes(*mesh);
}
else if (amr == 2)
{
for (int l = 0; l < 4; l++)
{
mesh->RandomRefinement(0.5); // 50% probability
}
SnapNodes(*mesh);
}
// 4. Define a finite element space on the mesh. Here we use isoparametric
// finite elements -- the same as the mesh nodes.
FiniteElementSpace *fespace = new FiniteElementSpace(mesh, &fec);
cout << "Number of unknowns: " << fespace->GetTrueVSize() << endl;
// 5. Set up the linear form b(.) which corresponds to the right-hand side of
// the FEM linear system, which in this case is (1,phi_i) where phi_i are
// the basis functions in the finite element fespace.
LinearForm *b = new LinearForm(fespace);
ConstantCoefficient one(1.0);
FunctionCoefficient rhs_coef (analytic_rhs);
FunctionCoefficient sol_coef (analytic_solution);
b->AddDomainIntegrator(new DomainLFIntegrator(rhs_coef));
b->Assemble();
// 6. Define the solution vector x as a finite element grid function
// corresponding to fespace. Initialize x with initial guess of zero.
GridFunction x(fespace);
x = 0.0;
// 7. Set up the bilinear form a(.,.) on the finite element space
// corresponding to the Laplacian operator -Delta, by adding the Diffusion
// and Mass domain integrators.
BilinearForm *a = new BilinearForm(fespace);
a->AddDomainIntegrator(new DiffusionIntegrator(one));
a->AddDomainIntegrator(new MassIntegrator(one));
// 8. Assemble the linear system, apply conforming constraints, etc.
a->Assemble();
SparseMatrix A;
Vector B, X;
Array<int> empty_tdof_list;
a->FormLinearSystem(empty_tdof_list, x, *b, A, X, B);
#ifndef MFEM_USE_SUITESPARSE
// 9. Define a simple symmetric Gauss-Seidel preconditioner and use it to
// solve the system AX=B with PCG.
GSSmoother M(A);
PCG(A, M, B, X, 1, 200, 1e-12, 0.0);
#else
// 9. If MFEM was compiled with SuiteSparse, use UMFPACK to solve the system.
UMFPackSolver umf_solver;
umf_solver.Control[UMFPACK_ORDERING] = UMFPACK_ORDERING_METIS;
umf_solver.SetOperator(A);
umf_solver.Mult(B, X);
#endif
// 10. Recover the solution as a finite element grid function.
a->RecoverFEMSolution(X, *b, x);
// 11. Compute and print the L^2 norm of the error.
cout<<"\nL2 norm of error: " << x.ComputeL2Error(sol_coef) << endl;
// 12. Save the refined mesh and the solution. This output can be viewed
// later using GLVis: "glvis -m sphere_refined.mesh -g sol.gf".
{
ofstream mesh_ofs("sphere_refined.mesh");
mesh_ofs.precision(8);
mesh->Print(mesh_ofs);
ofstream sol_ofs("sol.gf");
sol_ofs.precision(8);
x.Save(sol_ofs);
}
// 13. Send the solution by socket to a GLVis server.
if (visualization)
{
char vishost[] = "localhost";
int visport = 19916;
socketstream sol_sock(vishost, visport);
sol_sock.precision(8);
sol_sock << "solution\n" << *mesh << x << flush;
}
// 14. Free the used memory.
delete a;
delete b;
delete fespace;
delete mesh;
return 0;
}
int main(int argc, char *argv[])
{
// 1. Parse command-line options.
const char *mesh_file = "../../data/fichera.mesh";
int order = sol_p;
bool static_cond = false;
bool visualization = 1;
bool perf = true;
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(&perf, "-perf", "--hpc-version", "-std", "--standard-version",
"Enable high-performance, tensor-based, assembly.");
args.AddOption(&static_cond, "-sc", "--static-condensation", "-no-sc",
"--no-static-condensation", "Enable static condensation.");
args.AddOption(&visualization, "-vis", "--visualization", "-no-vis",
"--no-visualization",
"Enable or disable GLVis visualization.");
args.Parse();
if (!args.Good())
{
args.PrintUsage(cout);
return 1;
}
args.PrintOptions(cout);
// 2. Read the mesh from the given mesh file. 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();
// 3. Check if the optimized version matches the given mesh
if (perf)
{
cout << "High-performance version using integration rule with "
<< int_rule_t::qpts << " points ..." << endl;
if (!mesh_t::MatchesGeometry(*mesh))
{
cout << "The given mesh does not match the optimized 'geom' parameter.\n"
<< "Recompile with suitable 'geom' value." << endl;
delete mesh;
return 3;
}
else if (!mesh_t::MatchesNodes(*mesh))
{
cout << "Switching the mesh curvature to match the "
<< "optimized value (order " << mesh_p << ") ..." << endl;
mesh->SetCurvature(mesh_p, false, -1, Ordering::byNODES);
}
}
// 4. Refine the mesh 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 50,000
// elements.
{
int ref_levels =
(int)floor(log(50000./mesh->GetNE())/log(2.)/dim);
for (int l = 0; l < ref_levels; l++)
{
mesh->UniformRefinement();
}
}
// 5. Define a finite element space on the mesh. Here we use continuous
// Lagrange finite elements of the specified order. If order < 1, we
// instead use an isoparametric/isogeometric space.
FiniteElementCollection *fec;
if (order > 0)
{
fec = new H1_FECollection(order, dim);
}
else if (mesh->GetNodes())
{
fec = mesh->GetNodes()->OwnFEC();
cout << "Using isoparametric FEs: " << fec->Name() << endl;
}
else
{
fec = new H1_FECollection(order = 1, dim);
}
FiniteElementSpace *fespace = new FiniteElementSpace(mesh, fec);
cout << "Number of finite element unknowns: "
<< fespace->GetTrueVSize() << endl;
// 6. Check if the optimized version matches the given space
if (perf && !sol_fes_t::Matches(*fespace))
{
cout << "The given order does not match the optimized parameter.\n"
<< "Recompile with suitable 'sol_p' value." << endl;
delete fespace;
delete fec;
delete mesh;
return 4;
}
// 7. Determine the list of true (i.e. conforming) essential boundary dofs.
// In this example, the boundary conditions are defined by marking all
// the boundary attributes from the mesh as essential (Dirichlet) and
// converting them to a list of true dofs.
Array<int> ess_tdof_list;
if (mesh->bdr_attributes.Size())
{
Array<int> ess_bdr(mesh->bdr_attributes.Max());
ess_bdr = 1;
fespace->GetEssentialTrueDofs(ess_bdr, ess_tdof_list);
}
// 8. Set up the linear form b(.) which corresponds to the right-hand side of
// the FEM linear system, which in this case is (1,phi_i) where phi_i are
// the basis functions in the finite element fespace.
LinearForm *b = new LinearForm(fespace);
ConstantCoefficient one(1.0);
b->AddDomainIntegrator(new DomainLFIntegrator(one));
b->Assemble();
// 9. Define the solution vector x as a finite element grid function
// corresponding to fespace. Initialize x with initial guess of zero,
// which satisfies the boundary conditions.
GridFunction x(fespace);
x = 0.0;
// 10. Set up the bilinear form a(.,.) on the finite element space that will
// hold the matrix corresponding to the Laplacian operator -Delta.
BilinearForm *a = new BilinearForm(fespace);
// 11. Assemble the bilinear form and the corresponding linear system,
// applying any necessary transformations such as: eliminating boundary
// conditions, applying conforming constraints for non-conforming AMR,
// static condensation, etc.
if (static_cond) { a->EnableStaticCondensation(); }
cout << "Assembling the matrix ..." << flush;
tic_toc.Clear();
tic_toc.Start();
// Pre-allocate sparsity assuming dense element matrices
a->UsePrecomputedSparsity();
if (!perf)
{
// Standard assembly using a diffusion domain integrator
a->AddDomainIntegrator(new DiffusionIntegrator(one));
a->Assemble();
}
else
{
// High-performance assembly using the templated operator type
oper_t a_oper(integ_t(coeff_t(1.0)), *fespace);
a_oper.AssembleBilinearForm(*a);
}
tic_toc.Stop();
cout << " done, " << tic_toc.RealTime() << "s." << endl;
SparseMatrix A;
Vector B, X;
a->FormLinearSystem(ess_tdof_list, x, *b, A, X, B);
cout << "Size of linear system: " << A.Height() << endl;
#ifndef MFEM_USE_SUITESPARSE
// 12. Define a simple symmetric Gauss-Seidel preconditioner and use it to
// solve the system A X = B with PCG.
GSSmoother M(A);
PCG(A, M, B, X, 1, 500, 1e-12, 0.0);
#else
// 12. If MFEM was compiled with SuiteSparse, use UMFPACK to solve the system.
UMFPackSolver umf_solver;
umf_solver.Control[UMFPACK_ORDERING] = UMFPACK_ORDERING_METIS;
umf_solver.SetOperator(A);
umf_solver.Mult(B, X);
#endif
// 13. Recover the solution as a finite element grid function.
a->RecoverFEMSolution(X, *b, x);
// 14. Save the refined mesh and the solution. This output can be viewed later
// using GLVis: "glvis -m refined.mesh -g sol.gf".
ofstream mesh_ofs("refined.mesh");
mesh_ofs.precision(8);
mesh->Print(mesh_ofs);
ofstream sol_ofs("sol.gf");
sol_ofs.precision(8);
x.Save(sol_ofs);
// 15. Send the solution by socket to a GLVis server.
if (visualization)
{
char vishost[] = "localhost";
int visport = 19916;
socketstream sol_sock(vishost, visport);
sol_sock.precision(8);
sol_sock << "solution\n" << *mesh << x << flush;
}
// 16. Free the used memory.
delete a;
delete b;
delete fespace;
if (order > 0) { delete fec; }
delete mesh;
return 0;
}
