int main(int argc, char** argv)
{
// Initialize libMesh.
LibMeshInit init (argc, argv);
// Skip adaptive examples on a non-adaptive libMesh build
#ifndef LIBMESH_ENABLE_AMR
libmesh_example_assert(false, "--enable-amr");
#else
// Parse the input file
GetPot input_file("adaptivity_ex3.in");
// Read in parameters from the input file
const unsigned int max_r_steps = input_file("max_r_steps", 3);
const unsigned int max_r_level = input_file("max_r_level", 3);
const Real refine_percentage = input_file("refine_percentage", 0.5);
const Real coarsen_percentage = input_file("coarsen_percentage", 0.5);
const unsigned int uniform_refine = input_file("uniform_refine",0);
const std::string refine_type = input_file("refinement_type", "h");
const std::string approx_type = input_file("approx_type", "LAGRANGE");
const unsigned int approx_order = input_file("approx_order", 1);
const std::string element_type = input_file("element_type", "tensor");
const int extra_error_quadrature = input_file("extra_error_quadrature", 0);
const int max_linear_iterations = input_file("max_linear_iterations", 5000);
const bool output_intermediate = input_file("output_intermediate", false);
dim = input_file("dimension", 2);
const std::string indicator_type = input_file("indicator_type", "kelly");
singularity = input_file("singularity", true);
// Skip higher-dimensional examples on a lower-dimensional libMesh build
libmesh_example_assert(dim <= LIBMESH_DIM, "2D/3D support");
// Output file for plotting the error as a function of
// the number of degrees of freedom.
std::string approx_name = "";
if (element_type == "tensor")
approx_name += "bi";
if (approx_order == 1)
approx_name += "linear";
else if (approx_order == 2)
approx_name += "quadratic";
else if (approx_order == 3)
approx_name += "cubic";
else if (approx_order == 4)
approx_name += "quartic";
std::string output_file = approx_name;
output_file += "_";
output_file += refine_type;
if (uniform_refine == 0)
output_file += "_adaptive.m";
else
output_file += "_uniform.m";
std::ofstream out (output_file.c_str());
out << "% dofs L2-error H1-error" << std::endl;
out << "e = [" << std::endl;
// Create a mesh.
Mesh mesh;
// Read in the mesh
if (dim == 1)
MeshTools::Generation::build_line(mesh,1,-1.,0.);
else if (dim == 2)
mesh.read("lshaped.xda");
else
mesh.read("lshaped3D.xda");
// Use triangles if the config file says so
if (element_type == "simplex")
MeshTools::Modification::all_tri(mesh);
// We used first order elements to describe the geometry,
// but we may need second order elements to hold the degrees
// of freedom
if (approx_order > 1 || refine_type != "h")
mesh.all_second_order();
// Mesh Refinement object
MeshRefinement mesh_refinement(mesh);
mesh_refinement.refine_fraction() = refine_percentage;
mesh_refinement.coarsen_fraction() = coarsen_percentage;
mesh_refinement.max_h_level() = max_r_level;
// Create an equation systems object.
EquationSystems equation_systems (mesh);
// Declare the system and its variables.
// Creates a system named "Laplace"
LinearImplicitSystem& system =
equation_systems.add_system<LinearImplicitSystem> ("Laplace");
// Adds the variable "u" to "Laplace", using
// the finite element type and order specified
// in the config file
system.add_variable("u", static_cast<Order>(approx_order),
Utility::string_to_enum<FEFamily>(approx_type));
// Give the system a pointer to the matrix assembly
// function.
system.attach_assemble_function (assemble_laplace);
// Initialize the data structures for the equation system.
equation_systems.init();
// Set linear solver max iterations
equation_systems.parameters.set<unsigned int>("linear solver maximum iterations")
= max_linear_iterations;
// Linear solver tolerance.
equation_systems.parameters.set<Real>("linear solver tolerance") =
std::pow(TOLERANCE, 2.5);
// Prints information about the system to the screen.
equation_systems.print_info();
// Construct ExactSolution object and attach solution functions
ExactSolution exact_sol(equation_systems);
exact_sol.attach_exact_value(exact_solution);
exact_sol.attach_exact_deriv(exact_derivative);
// Use higher quadrature order for more accurate error results
exact_sol.extra_quadrature_order(extra_error_quadrature);
// A refinement loop.
for (unsigned int r_step=0; r_step<max_r_steps; r_step++)
{
std::cout << "Beginning Solve " << r_step << std::endl;
// Solve the system "Laplace", just like example 2.
system.solve();
std::cout << "System has: " << equation_systems.n_active_dofs()
<< " degrees of freedom."
<< std::endl;
std::cout << "Linear solver converged at step: "
<< system.n_linear_iterations()
<< ", final residual: "
<< system.final_linear_residual()
<< std::endl;
#ifdef LIBMESH_HAVE_EXODUS_API
// After solving the system write the solution
// to a ExodusII-formatted plot file.
if (output_intermediate)
{
OStringStream outfile;
outfile << "lshaped_" << r_step << ".e";
ExodusII_IO (mesh).write_equation_systems (outfile.str(),
equation_systems);
}
#endif // #ifdef LIBMESH_HAVE_EXODUS_API
// Compute the error.
exact_sol.compute_error("Laplace", "u");
// Print out the error values
std::cout << "L2-Error is: "
<< exact_sol.l2_error("Laplace", "u")
<< std::endl;
std::cout << "H1-Error is: "
<< exact_sol.h1_error("Laplace", "u")
<< std::endl;
// Print to output file
out << equation_systems.n_active_dofs() << " "
<< exact_sol.l2_error("Laplace", "u") << " "
<< exact_sol.h1_error("Laplace", "u") << std::endl;
// Possibly refine the mesh
if (r_step+1 != max_r_steps)
{
std::cout << " Refining the mesh..." << std::endl;
if (uniform_refine == 0)
{
// The \p ErrorVector is a particular \p StatisticsVector
// for computing error information on a finite element mesh.
ErrorVector error;
if (indicator_type == "exact")
{
// The \p ErrorEstimator class interrogates a
// finite element solution and assigns to each
// element a positive error value.
// This value is used for deciding which elements to
// refine and which to coarsen.
// For these simple test problems, we can use
// numerical quadrature of the exact error between
// the approximate and analytic solutions.
// However, for real problems, we would need an error
// indicator which only relies on the approximate
// solution.
ExactErrorEstimator error_estimator;
error_estimator.attach_exact_value(exact_solution);
error_estimator.attach_exact_deriv(exact_derivative);
// We optimize in H1 norm, the default
// error_estimator.error_norm = H1;
// Compute the error for each active element using
// the provided indicator. Note in general you
// will need to provide an error estimator
// specifically designed for your application.
error_estimator.estimate_error (system, error);
}
else if (indicator_type == "patch")
{
// The patch recovery estimator should give a
// good estimate of the solution interpolation
// error.
PatchRecoveryErrorEstimator error_estimator;
error_estimator.estimate_error (system, error);
}
else if (indicator_type == "uniform")
{
// Error indication based on uniform refinement
// is reliable, but very expensive.
UniformRefinementEstimator error_estimator;
error_estimator.estimate_error (system, error);
}
else
{
libmesh_assert_equal_to (indicator_type, "kelly");
// The Kelly error estimator is based on
// an error bound for the Poisson problem
// on linear elements, but is useful for
// driving adaptive refinement in many problems
KellyErrorEstimator error_estimator;
error_estimator.estimate_error (system, error);
}
// Write out the error distribution
OStringStream ss;
ss << r_step;
#ifdef LIBMESH_HAVE_EXODUS_API
std::string error_output = "error_"+ss.str()+".e";
#else
std::string error_output = "error_"+ss.str()+".gmv";
#endif
error.plot_error( error_output, mesh );
// This takes the error in \p error and decides which elements
// will be coarsened or refined. Any element within 20% of the
// maximum error on any element will be refined, and any
// element within 10% of the minimum error on any element might
// be coarsened. Note that the elements flagged for refinement
// will be refined, but those flagged for coarsening _might_ be
// coarsened.
mesh_refinement.flag_elements_by_error_fraction (error);
// If we are doing adaptive p refinement, we want
// elements flagged for that instead.
if (refine_type == "p")
mesh_refinement.switch_h_to_p_refinement();
// If we are doing "matched hp" refinement, we
// flag elements for both h and p
if (refine_type == "matchedhp")
mesh_refinement.add_p_to_h_refinement();
// If we are doing hp refinement, we
// try switching some elements from h to p
if (refine_type == "hp")
{
HPCoarsenTest hpselector;
hpselector.select_refinement(system);
}
// If we are doing "singular hp" refinement, we
// try switching most elements from h to p
if (refine_type == "singularhp")
{
// This only differs from p refinement for
// the singular problem
libmesh_assert (singularity);
HPSingularity hpselector;
// Our only singular point is at the origin
hpselector.singular_points.push_back(Point());
hpselector.select_refinement(system);
}
// This call actually refines and coarsens the flagged
// elements.
mesh_refinement.refine_and_coarsen_elements();
}
else if (uniform_refine == 1)
{
if (refine_type == "h" || refine_type == "hp" ||
refine_type == "matchedhp")
mesh_refinement.uniformly_refine(1);
if (refine_type == "p" || refine_type == "hp" ||
refine_type == "matchedhp")
mesh_refinement.uniformly_p_refine(1);
}
// This call reinitializes the \p EquationSystems object for
// the newly refined mesh. One of the steps in the
// reinitialization is projecting the \p solution,
// \p old_solution, etc... vectors from the old mesh to
// the current one.
equation_systems.reinit ();
}
}
#ifdef LIBMESH_HAVE_EXODUS_API
// Write out the solution
// After solving the system write the solution
// to a ExodusII-formatted plot file.
ExodusII_IO (mesh).write_equation_systems ("lshaped.e",
equation_systems);
#endif // #ifdef LIBMESH_HAVE_EXODUS_API
// Close up the output file.
out << "];" << std::endl;
out << "hold on" << std::endl;
out << "plot(e(:,1), e(:,2), 'bo-');" << std::endl;
out << "plot(e(:,1), e(:,3), 'ro-');" << std::endl;
// out << "set(gca,'XScale', 'Log');" << std::endl;
// out << "set(gca,'YScale', 'Log');" << std::endl;
out << "xlabel('dofs');" << std::endl;
out << "title('" << approx_name << " elements');" << std::endl;
out << "legend('L2-error', 'H1-error');" << std::endl;
// out << "disp('L2-error linear fit');" << std::endl;
// out << "polyfit(log10(e(:,1)), log10(e(:,2)), 1)" << std::endl;
// out << "disp('H1-error linear fit');" << std::endl;
// out << "polyfit(log10(e(:,1)), log10(e(:,3)), 1)" << std::endl;
#endif // #ifndef LIBMESH_ENABLE_AMR
// All done.
return 0;
}
int main(int argc, char** argv){
//initialize libMesh
LibMeshInit init(argc, argv);
//parameters
GetPot infile("fem_system_params.in");
const bool transient = infile("transient", true);
const Real deltat = infile("deltat", 0.005);
unsigned int n_timesteps = infile("n_timesteps", 20);
const int nx = infile("nx",100);
const int ny = infile("ny",100);
const int nz = infile("nz",100);
//const unsigned int dim = 3;
const unsigned int max_r_steps = infile("max_r_steps", 3);
const unsigned int max_r_level = infile("max_r_level", 3);
const Real refine_percentage = infile("refine_percentage", 0.1);
const Real coarsen_percentage = infile("coarsen_percentage", 0.0);
const std::string indicator_type = infile("indicator_type", "kelly");
const bool write_error = infile("write_error",false);
const bool flag_by_elem_frac = infile("flag_by_elem_frac",true);
#ifdef LIBMESH_HAVE_EXODUS_API
const unsigned int write_interval = infile("write_interval", 5);
#endif
// Create a mesh, with dimension to be overridden later, distributed
// across the default MPI communicator.
Mesh mesh(init.comm());
//create mesh
unsigned int dim;
if(nz == 0){ //to check if oscillations happen in 2D as well...
dim = 2;
MeshTools::Generation::build_square(mesh, nx, ny, 497150.0, 501750.0, 537350.0, 540650.0, QUAD9);
}else{
dim = 3;
MeshTools::Generation::build_cube(mesh,
nx, ny, nz,
497150.0, 501750.0,
537350.0, 540650.0,
0.0, 100.0,
HEX27);
}
// Print information about the mesh to the screen.
mesh.print_info();
// Create an equation systems object.
EquationSystems equation_systems (mesh);
//name system
ContamTransSysInv & system =
equation_systems.add_system<ContamTransSysInv>("ContamTransInv");
//solve as steady or transient
if(transient){
//system.time_solver = AutoPtr<TimeSolver>(new EulerSolver(system)); //backward Euler
system.time_solver = AutoPtr<TimeSolver>(new SteadySolver(system));
std::cout << "\n\nAaahhh transience not yet available!\n" << std::endl;
n_timesteps = 1;
}
else{
system.time_solver = AutoPtr<TimeSolver>(new SteadySolver(system));
libmesh_assert_equal_to (n_timesteps, 1); //this doesn't seem to work?
}
// Initialize the system
equation_systems.init ();
//initial conditions
read_initial_parameters();
system.project_solution(initial_value, initial_grad,
equation_systems.parameters);
finish_initialization();
// Set the time stepping options...
system.deltat = deltat;
//...and the nonlinear solver options...
NewtonSolver *solver = new NewtonSolver(system);
system.time_solver->diff_solver() = AutoPtr<DiffSolver>(solver);
solver->quiet = infile("solver_quiet", true);
solver->verbose = !solver->quiet;
solver->max_nonlinear_iterations =
infile("max_nonlinear_iterations", 15);
solver->relative_step_tolerance =
infile("relative_step_tolerance", 1.e-3);
solver->relative_residual_tolerance =
infile("relative_residual_tolerance", 0.0);
solver->absolute_residual_tolerance =
infile("absolute_residual_tolerance", 0.0);
// And the linear solver options
solver->max_linear_iterations = infile("max_linear_iterations", 10000);
solver->initial_linear_tolerance = infile("initial_linear_tolerance",1.e-13);
solver->minimum_linear_tolerance = infile("minimum_linear_tolerance",1.e-13);
solver->linear_tolerance_multiplier = infile("linear_tolerance_multiplier",1.e-3);
// Mesh Refinement object - to test effect of constant refined mesh (not refined at every timestep)
MeshRefinement mesh_refinement(mesh);
mesh_refinement.refine_fraction() = refine_percentage;
mesh_refinement.coarsen_fraction() = coarsen_percentage;
mesh_refinement.max_h_level() = max_r_level;
// Print information about the system to the screen.
equation_systems.print_info();
ExodusII_IO exodusIO = ExodusII_IO(mesh); //for writing multiple timesteps to one file
for (unsigned int r_step=0; r_step<max_r_steps; r_step++)
{
std::cout << "\nBeginning Solve " << r_step+1 << std::endl;
for (unsigned int t_step=0; t_step != n_timesteps; ++t_step)
{
std::cout << "\n\nSolving time step " << t_step << ", time = "
<< system.time << std::endl;
system.solve();
system.postprocess();
// Advance to the next timestep in a transient problem
system.time_solver->advance_timestep();
} //end stepping through time loop
std::cout << "\n Refining the mesh..." << std::endl;
// The \p ErrorVector is a particular \p StatisticsVector
// for computing error information on a finite element mesh.
ErrorVector error;
if (indicator_type == "patch")
{
// The patch recovery estimator should give a
// good estimate of the solution interpolation
// error.
PatchRecoveryErrorEstimator error_estimator;
error_estimator.set_patch_reuse(false); //anisotropy trips up reuse
error_estimator.estimate_error (system, error);
}
else if (indicator_type == "kelly")
{
// The Kelly error estimator is based on
// an error bound for the Poisson problem
// on linear elements, but is useful for
// driving adaptive refinement in many problems
KellyErrorEstimator error_estimator;
error_estimator.estimate_error (system, error);
}
// Write out the error distribution
if(write_error){
std::ostringstream ss;
ss << r_step;
#ifdef LIBMESH_HAVE_EXODUS_API
std::string error_output = "error_"+ss.str()+".e";
#else
std::string error_output = "error_"+ss.str()+".gmv";
#endif
error.plot_error( error_output, mesh );
}
// This takes the error in \p error and decides which elements
// will be coarsened or refined.
if(flag_by_elem_frac)
mesh_refinement.flag_elements_by_elem_fraction(error);
else
mesh_refinement.flag_elements_by_error_fraction (error);
// This call actually refines and coarsens the flagged
// elements.
mesh_refinement.refine_and_coarsen_elements();
// This call reinitializes the \p EquationSystems object for
// the newly refined mesh. One of the steps in the
// reinitialization is projecting the \p solution,
// \p old_solution, etc... vectors from the old mesh to
// the current one.
equation_systems.reinit ();
std::cout << "System has: " << equation_systems.n_active_dofs()
<< " degrees of freedom."
<< std::endl;
} //end refinement loop
//use that final refinement
for (unsigned int t_step=0; t_step != n_timesteps; ++t_step)
{
std::cout << "\n\nSolving time step " << t_step << ", time = "
<< system.time << std::endl;
system.solve();
system.postprocess();
Number QoI_computed = system.get_QoI_value("computed", 0);
std::cout<< "Computed QoI is " << std::setprecision(17) << QoI_computed << std::endl;
// Advance to the next timestep in a transient problem
system.time_solver->advance_timestep();
} //end stepping through time loop
#ifdef LIBMESH_HAVE_EXODUS_API
for (unsigned int t_step=0; t_step != n_timesteps; ++t_step)
{
// Write out this timestep if we're requested to
if ((t_step+1)%write_interval == 0)
{
std::ostringstream ex_file_name;
std::ostringstream tplot_file_name;
// We write the file in the ExodusII format.
//ex_file_name << "out_"
// << std::setw(3)
// << std::setfill('0')
// << std::right
// << t_step+1
// << ".e";
tplot_file_name << "out_"
<< std::setw(3)
<< std::setfill('0')
<< std::right
<< t_step+1
<< ".plt";
//ExodusII_IO(mesh).write_timestep(ex_file_name.str(),
// equation_systems,
// 1, /* This number indicates how many time steps
// are being written to the file */
// system.time);
exodusIO.write_timestep("output.exo", equation_systems, t_step+1, system.time); //outputs all timesteps in one file
TecplotIO(mesh).write_equation_systems(tplot_file_name.str(), equation_systems);
}
}
#endif // #ifdef LIBMESH_HAVE_EXODUS_API
// All done.
return 0;
} //end main