int main (int argc, char** args) {
// init Petsc-MPI communicator
FemusInit mpinit (argc, args, MPI_COMM_WORLD);
// define multilevel mesh
MultiLevelMesh mlMsh;
// read coarse level mesh and generate finers level meshes
double scalingFactor = 1.;
//mlMsh.ReadCoarseMesh("./input/cube_hex.neu","seventh",scalingFactor);
//mlMsh.ReadCoarseMesh("./input/square_quad.neu", "seventh", scalingFactor);
mlMsh.ReadCoarseMesh ("./input/quadAMR.neu", "seventh", scalingFactor);
/* "seventh" is the order of accuracy that is used in the gauss integration scheme
probably in the furure it is not going to be an argument of this function */
unsigned dim = mlMsh.GetDimension();
// unsigned numberOfUniformLevels = 3;
// unsigned numberOfSelectiveLevels = 0;
// mlMsh.RefineMesh(numberOfUniformLevels , numberOfUniformLevels + numberOfSelectiveLevels, NULL);
unsigned numberOfUniformLevels = 4;
unsigned numberOfSelectiveLevels = 3;
mlMsh.RefineMesh (numberOfUniformLevels + numberOfSelectiveLevels, numberOfUniformLevels , SetRefinementFlag);
// erase all the coarse mesh levels
//mlMsh.EraseCoarseLevels(numberOfUniformLevels - 3);
// print mesh info
mlMsh.PrintInfo();
MultiLevelSolution mlSol (&mlMsh);
// add variables to mlSol
mlSol.AddSolution ("U", LAGRANGE, SERENDIPITY);
mlSol.AddSolution ("V", LAGRANGE, SECOND);
mlSol.Initialize ("All");
// attach the boundary condition function and generate boundary data
mlSol.AttachSetBoundaryConditionFunction (SetBoundaryCondition);
mlSol.GenerateBdc ("All");
// define the multilevel problem attach the mlSol object to it
MultiLevelProblem mlProb (&mlSol);
// add system Poisson in mlProb as a Linear Implicit System
NonLinearImplicitSystem& system = mlProb.add_system < NonLinearImplicitSystem > ("Poisson");
// add solution "u" to system
system.AddSolutionToSystemPDE ("U");
system.AddSolutionToSystemPDE ("V");
//system.SetLinearEquationSolverType(FEMuS_DEFAULT);
system.SetLinearEquationSolverType (FEMuS_ASM); // Additive Swartz Method
// attach the assembling function to system
system.SetAssembleFunction (AssemblePoisson_AD);
system.SetMaxNumberOfNonLinearIterations(10);
system.SetMaxNumberOfLinearIterations(3);
system.SetAbsoluteLinearConvergenceTolerance(1.e-12);
system.SetNonLinearConvergenceTolerance(1.e-8);
system.SetMgType(F_CYCLE); // Q1 What's F cycle
system.SetNumberPreSmoothingStep (0);
system.SetNumberPostSmoothingStep (2);
// initilaize and solve the system
system.init();
system.SetSolverFineGrids (GMRES);
system.SetPreconditionerFineGrids (ILU_PRECOND);
system.SetTolerances (1.e-3, 1.e-20, 1.e+50, 5);
system.SetNumberOfSchurVariables (1);
system.SetElementBlockNumber (4);
//system.SetDirichletBCsHandling(ELIMINATION);
//system.solve();
system.MGsolve();
// print solutions
std::vector < std::string > variablesToBePrinted;
variablesToBePrinted.push_back ("All");
VTKWriter vtkIO (&mlSol);
vtkIO.Write (DEFAULT_OUTPUTDIR, "biquadratic", variablesToBePrinted);
GMVWriter gmvIO (&mlSol);
variablesToBePrinted.push_back ("all");
gmvIO.SetDebugOutput (true);
gmvIO.Write (DEFAULT_OUTPUTDIR, "biquadratic", variablesToBePrinted);
return 0;
}
int main (int argc, char** args) {
// init Petsc-MPI communicator
FemusInit mpinit (argc, args, MPI_COMM_WORLD);
// define multilevel mesh
MultiLevelMesh mlMsh;
// read coarse level mesh and generate finers level meshes
double scalingFactor = 1.;
//mlMsh.ReadCoarseMesh("./input/cube_hex.neu","seventh",scalingFactor);
//mlMsh.ReadCoarseMesh("./input/square_quad.neu", "seventh", scalingFactor);
mlMsh.ReadCoarseMesh ("./input/quadAMR.neu", "seventh", scalingFactor);
/* "seventh" is the order of accuracy that is used in the gauss integration scheme
probably in the furure it is not going to be an argument of this function */
unsigned dim = mlMsh.GetDimension();
unsigned maxNumberOfMeshes = 5;
vector < vector < double > > l2Norm;
l2Norm.resize (maxNumberOfMeshes);
vector < vector < double > > semiNorm;
semiNorm.resize (maxNumberOfMeshes);
// unsigned numberOfUniformLevels = 3;
// unsigned numberOfSelectiveLevels = 0;
// mlMsh.RefineMesh(numberOfUniformLevels , numberOfUniformLevels + numberOfSelectiveLevels, NULL);
for (unsigned i = 1; i < maxNumberOfMeshes; i++) {
unsigned numberOfUniformLevels = i + 3;
unsigned numberOfSelectiveLevels = 0;
//mlMsh.RefineMesh (numberOfUniformLevels + numberOfSelectiveLevels, numberOfUniformLevels , SetRefinementFlag);
mlMsh.RefineMesh (numberOfUniformLevels + numberOfSelectiveLevels, numberOfUniformLevels , NULL);
// erase all the coarse mesh levels
//mlMsh.EraseCoarseLevels(numberOfUniformLevels - 3);
// print mesh info
mlMsh.PrintInfo();
FEOrder feOrder[3] = {FIRST, SERENDIPITY, SECOND};
l2Norm[i].resize (3);
semiNorm[i].resize (3);
for (unsigned j = 0; j < 3; j++) {
MultiLevelSolution mlSol (&mlMsh);
// add variables to mlSol
mlSol.AddSolution("Flag", DISCONTINOUS_POLYNOMIAL, ZERO);
mlSol.AddSolution ("U", LAGRANGE, feOrder[j]);
mlSol.Initialize ("All");
// attach the boundary condition function and generate boundary data
mlSol.AttachSetBoundaryConditionFunction (SetBoundaryCondition);
mlSol.GenerateBdc ("All");
// define the multilevel problem attach the mlSol object to it
MultiLevelProblem mlProb (&mlSol);
// add system Poisson in mlProb as a Linear Implicit System
NonLinearImplicitSystem& system = mlProb.add_system < NonLinearImplicitSystem > ("Poisson");
// add solution "u" to system
system.AddSolutionToSystemPDE ("U");
//system.SetMgSmoother(GMRES_SMOOTHER);
system.SetMgSmoother (ASM_SMOOTHER); // Additive Swartz Method
// attach the assembling function to system
system.SetAssembleFunction (AssemblePoisson_AD);
system.SetMaxNumberOfNonLinearIterations (10);
system.SetMaxNumberOfLinearIterations (3);
system.SetAbsoluteLinearConvergenceTolerance (1.e-12);
system.SetNonLinearConvergenceTolerance (1.e-8);
system.SetMgType (F_CYCLE);
system.SetNumberPreSmoothingStep (0);
system.SetNumberPostSmoothingStep (2);
// initilaize and solve the system
system.init();
system.SetSolverFineGrids (GMRES);
system.SetPreconditionerFineGrids (ILU_PRECOND);
system.SetTolerances (1.e-3, 1.e-20, 1.e+50, 5);
system.SetNumberOfSchurVariables (1);
system.SetElementBlockNumber (4);
//system.SetDirichletBCsHandling(ELIMINATION);
//system.solve();
system.MGsolve();
std::pair< double , double > norm = GetErrorNorm (&mlSol);
l2Norm[i][j] = norm.first;
semiNorm[i][j] = norm.second;
// print solutions
std::vector < std::string > variablesToBePrinted;
variablesToBePrinted.push_back ("All");
VTKWriter vtkIO (&mlSol);
vtkIO.SetDebugOutput (true);
vtkIO.Write (DEFAULT_OUTPUTDIR, "biquadratic", variablesToBePrinted, i);
// GMVWriter gmvIO (&mlSol);
// variablesToBePrinted.push_back ("all");
// gmvIO.SetDebugOutput (true);
// gmvIO.Write (DEFAULT_OUTPUTDIR, "biquadratic", variablesToBePrinted, i);
}
}
// print the seminorm of the error and the order of convergence between different levels
std::cout << std::endl;
std::cout << std::endl;
std::cout << "l2 ERROR and ORDER OF CONVERGENCE:\n\n";
std::cout << "LEVEL\tFIRST\t\t\tSERENDIPITY\t\tSECOND\n";
for (unsigned i = 1; i < maxNumberOfMeshes; i++) {
std::cout << i + 1 << "\t";
std::cout.precision (14);
for (unsigned j = 0; j < 3; j++) {
std::cout << l2Norm[i][j] << "\t";
}
std::cout << std::endl;
}
std::cout << std::endl;
std::cout << std::endl;
std::cout << "SEMINORM ERROR and ORDER OF CONVERGENCE:\n\n";
std::cout << "LEVEL\tFIRST\t\t\tSERENDIPITY\t\tSECOND\n";
for (unsigned i = 1; i < maxNumberOfMeshes; i++) {
std::cout << i + 1 << "\t";
std::cout.precision (14);
for (unsigned j = 0; j < 3; j++) {
std::cout << semiNorm[i][j] << "\t";
}
std::cout << std::endl;
}
return 0;
}
