main(int argc, char* argv[]){
static vec u(M+1), utp1(M+1), utp2(M+1);
static vec sol(M+1);
int k,n;
std::string op=argv[1];
init(u,sol);
val dx=1.0/M, tn, dt=T/N, dx2=dx*dx, up, un;
val r=NU*dt/dx2; // r = nu*dt/dx^2
for(n=1;n<=N;n++){
utp2=u; // u^n-1
tn=n*dt;
u(0)=0.0; // a(tn)
for(k=1;k<M;k++){
up=u(k-1);
un=u(k+1);
if(n==1) u(k)=exact_sol(k*dx,tn);
else u(k)=utp1(k)+2*r*(un-2*u(k)+up); // u_k = 2*r*(u_k+1 - 2*u_k + u_k-1)
sol(k)=exact_sol(k*dx,tn);
}
utp1=utp2;
u(M)= 0.0; // b(tn)
output(tn, dx, u, sol, op);
}
return 0;
}
// Exact solution.
scalar3 exact(double x, double y, double z, scalar3 &dx, scalar3 &dy, scalar3 &dz)
{
scalar3 ex(0.0, 0.0, 0.0);
exact_sol(x, y, z, ex[0], ex[1], dx[1], dy[0]);
return ex;
}
int run( char* argv[], GRINS::Runner & grins )
{
grins.init();
grins.run();
GRINS::Simulation & sim = grins.get_simulation();
// Get equation systems to create ExactSolution object
std::shared_ptr<libMesh::EquationSystems>
es = sim.get_equation_system();
//es->write("foobar.xdr");
// Create Exact solution object and attach exact solution quantities
libMesh::ExactSolution exact_sol(*es);
libMesh::EquationSystems es_ref( es->get_mesh() );
// Filename of file where comparison solution is stashed
std::string solution_file = std::string(argv[2]);
es_ref.read( solution_file );
exact_sol.attach_reference_solution( &es_ref );
// Compute error and get it in various norms
exact_sol.compute_error("StretchedElasticSheet", "u");
exact_sol.compute_error("StretchedElasticSheet", "v");
exact_sol.compute_error("StretchedElasticSheet", "w");
double u_l2error = exact_sol.l2_error("StretchedElasticSheet", "u");
double u_h1error = exact_sol.h1_error("StretchedElasticSheet", "u");
double v_l2error = exact_sol.l2_error("StretchedElasticSheet", "v");
double v_h1error = exact_sol.h1_error("StretchedElasticSheet", "v");
double w_l2error = exact_sol.l2_error("StretchedElasticSheet", "w");
double w_h1error = exact_sol.h1_error("StretchedElasticSheet", "w");
int return_flag = 0;
double tol = 5.0e-8;
if( u_l2error > tol || u_h1error > tol ||
v_l2error > tol || v_h1error > tol ||
w_l2error > tol || w_h1error > tol )
{
return_flag = 1;
std::cout << "Tolerance exceeded for thermally driven flow test." << std::endl
<< "tolerance = " << tol << std::endl
<< "u l2 error = " << u_l2error << std::endl
<< "u h1 error = " << u_h1error << std::endl
<< "v l2 error = " << v_l2error << std::endl
<< "v h1 error = " << v_h1error << std::endl
<< "w l2 error = " << w_l2error << std::endl
<< "w h1 error = " << w_h1error << std::endl;
}
return return_flag;
}
// Exact solution.
scalar3 &exact(double x, double y, double z, scalar3 &dx, scalar3 &dy, scalar3 &dz)
{
static scalar3 ex;
ex[0] = ex[1] = ex[2] = 0;
exact_sol(x, y, z, ex[0], ex[1], dx[1], dy[0]);
return ex;
}
void init(vec &u, vec &sol){
int k;
val dx=1.0/M, xk;
for(k=0;k<=M;k++){
xk=k*dx;
u(k)=f(xk);
sol(k)=exact_sol(xk,0);
}
}
scalar2 exact(double x, double y, scalar2& dx, scalar2& dy)
{
static scalar2 ex(0.0, 0.0);
exact_sol(x,y, ex[0], ex[1], dx[1], dy[0]);
dx[0] = 0.0; // not important
dy[1] = 0.0; // not important
return ex;
}
int main(int argc, char* argv[])
{
#ifdef GRINS_USE_GRVY_TIMERS
GRVY::GRVY_Timer_Class grvy_timer;
grvy_timer.Init("GRINS Timer");
#endif
// Check command line count.
if( argc < 2 )
{
// TODO: Need more consistent error handling.
std::cerr << "Error: Must specify libMesh input file." << std::endl;
exit(1); // TODO: something more sophisticated for parallel runs?
}
// libMesh input file should be first argument
std::string libMesh_input_filename = argv[1];
// Create our GetPot object.
GetPot libMesh_inputfile( libMesh_input_filename );
#ifdef GRINS_USE_GRVY_TIMERS
grvy_timer.BeginTimer("Initialize Solver");
#endif
// Initialize libMesh library.
libMesh::LibMeshInit libmesh_init(argc, argv);
GRINS::SimulationBuilder sim_builder;
GRINS::SharedPtr<GRINS::BoundaryConditionsFactory> bc_factory( new ParabolicBCFactory );
sim_builder.attach_bc_factory(bc_factory);
GRINS::Simulation grins( libMesh_inputfile,
sim_builder,
libmesh_init.comm() );
#ifdef GRINS_USE_GRVY_TIMERS
grvy_timer.EndTimer("Initialize Solver");
// Attach GRVY timer to solver
grins.attach_grvy_timer( &grvy_timer );
#endif
// Solve
grins.run();
// Get equation systems to create ExactSolution object
GRINS::SharedPtr<libMesh::EquationSystems> es = grins.get_equation_system();
// Create Exact solution object and attach exact solution quantities
libMesh::ExactSolution exact_sol(*es);
exact_sol.attach_exact_value(&exact_solution);
exact_sol.attach_exact_deriv(&exact_derivative);
// Compute error and get it in various norms
exact_sol.compute_error("GRINS", "u");
double l2error = exact_sol.l2_error("GRINS", "u");
double h1error = exact_sol.h1_error("GRINS", "u");
int return_flag = 0;
const double tol = 1.0e-8;
if( l2error > tol || h1error > tol )
{
return_flag = 1;
std::cout << "Tolerance exceeded for velocity in Poiseuille test." << std::endl
<< "l2 error = " << l2error << std::endl
<< "h1 error = " << h1error << std::endl;
}
// Compute error and get it in various norms
exact_sol.compute_error("GRINS", "p");
l2error = exact_sol.l2_error("GRINS", "p");
h1error = exact_sol.h1_error("GRINS", "p");
if( l2error > tol || h1error > tol )
{
return_flag = 1;
std::cout << "Tolerance exceeded for pressure in Poiseuille test." << std::endl
<< "l2 error = " << l2error << std::endl
<< "h1 error = " << h1error << std::endl;
}
return return_flag;
}
int main(int argc, char* argv[])
{
#ifdef GRINS_USE_GRVY_TIMERS
GRVY::GRVY_Timer_Class grvy_timer;
grvy_timer.Init("GRINS Timer");
#endif
// Check command line count.
if( argc < 3 )
{
// TODO: Need more consistent error handling.
std::cerr << "Error: Must specify libMesh input file and solution file." << std::endl;
exit(1); // TODO: something more sophisticated for parallel runs?
}
// libMesh input file should be first argument
std::string libMesh_input_filename = argv[1];
// Create our GetPot object.
GetPot libMesh_inputfile( libMesh_input_filename );
#ifdef GRINS_USE_GRVY_TIMERS
grvy_timer.BeginTimer("Initialize Solver");
#endif
// Initialize libMesh library.
libMesh::LibMeshInit libmesh_init(argc, argv);
GRINS::SimulationBuilder sim_builder;
sim_builder.attach_bc_factory( GRINS::SharedPtr<GRINS::BoundaryConditionsFactory>( new GRINS::ThermallyDrivenFlowTestBCFactory( libMesh_inputfile ) ) );
GRINS::Simulation grins( libMesh_inputfile,
sim_builder,
libmesh_init.comm() );
#ifdef GRINS_USE_GRVY_TIMERS
grvy_timer.EndTimer("Initialize Solver");
// Attach GRVY timer to solver
grins.attach_grvy_timer( &grvy_timer );
#endif
// Do solve here
grins.run();
// Get equation systems to create ExactSolution object
GRINS::SharedPtr<libMesh::EquationSystems> es = grins.get_equation_system();
//es->write("foobar.xdr");
// Create Exact solution object and attach exact solution quantities
libMesh::ExactSolution exact_sol(*es);
libMesh::EquationSystems es_ref( es->get_mesh() );
// Filename of file where comparison solution is stashed
std::string solution_file = std::string(argv[2]);
es_ref.read( solution_file );
exact_sol.attach_reference_solution( &es_ref );
// Compute error and get it in various norms
exact_sol.compute_error("GRINS", "u");
exact_sol.compute_error("GRINS", "v");
if( (es->get_mesh()).mesh_dimension() == 3 )
exact_sol.compute_error("GRINS", "w");
exact_sol.compute_error("GRINS", "p");
exact_sol.compute_error("GRINS", "T");
double u_l2error = exact_sol.l2_error("GRINS", "u");
double u_h1error = exact_sol.h1_error("GRINS", "u");
double v_l2error = exact_sol.l2_error("GRINS", "v");
double v_h1error = exact_sol.h1_error("GRINS", "v");
double p_l2error = exact_sol.l2_error("GRINS", "p");
double p_h1error = exact_sol.h1_error("GRINS", "p");
double T_l2error = exact_sol.l2_error("GRINS", "T");
double T_h1error = exact_sol.h1_error("GRINS", "T");
double w_l2error = 0.0,
w_h1error = 0.0;
if( (es->get_mesh()).mesh_dimension() == 3 )
{
w_l2error = exact_sol.l2_error("GRINS", "w");
w_h1error = exact_sol.h1_error("GRINS", "w");
}
int return_flag = 0;
// This is the tolerance of the iterative linear solver so
// it's unreasonable to expect anything better than this.
double tol = 8.0e-9;
if( u_l2error > tol || u_h1error > tol ||
v_l2error > tol || v_h1error > tol ||
w_l2error > tol || w_h1error > tol ||
p_l2error > tol || p_h1error > tol ||
T_l2error > tol || T_h1error > tol )
{
return_flag = 1;
std::cout << "Tolerance exceeded for thermally driven flow test." << std::endl
<< "tolerance = " << tol << std::endl
<< "u l2 error = " << u_l2error << std::endl
<< "u h1 error = " << u_h1error << std::endl
<< "v l2 error = " << v_l2error << std::endl
<< "v h1 error = " << v_h1error << std::endl
<< "w l2 error = " << w_l2error << std::endl
<< "w h1 error = " << w_h1error << std::endl
<< "p l2 error = " << p_l2error << std::endl
<< "p h1 error = " << p_h1error << std::endl
<< "T l2 error = " << T_l2error << std::endl
<< "T h1 error = " << T_h1error << std::endl;
}
return return_flag;
}
int run( int argc, char* argv[], const GetPot& input )
{
// Initialize libMesh library.
libMesh::LibMeshInit libmesh_init(argc, argv);
GRINS::SimulationBuilder sim_builder;
std::tr1::shared_ptr<GRINS::BoundaryConditionsFactory> bc_factory( new NitridationCalibration::BoundaryConditionsFactory(input) );
sim_builder.attach_bc_factory( bc_factory );
std::tr1::shared_ptr<GRINS::QoIFactory> qoi_factory( new NitridationCalibration::QoIFactory );
sim_builder.attach_qoi_factory( qoi_factory );
GRINS::Simulation grins( input,
sim_builder,
libmesh_init.comm());
//FIXME: We need to move this to within the Simulation object somehow...
std::string restart_file = input( "restart-options/restart_file", "none" );
std::tr1::shared_ptr<NitridationCalibration::TubeTempBC> wall_temp;
std::string system_name = input( "screen-options/system_name", "GRINS" );
if( restart_file == "none" )
{
// Asssign initial temperature value
std::tr1::shared_ptr<libMesh::EquationSystems> es = grins.get_equation_system();
const libMesh::System& system = es->get_system(system_name);
libMesh::Parameters ¶ms = es->parameters;
libMesh::Real& w_N2 = params.set<libMesh::Real>( "w_N2" );
w_N2 = input( "Physics/ReactingLowMachNavierStokes/bound_species_1", 0.0, 0 );
libMesh::Real& w_N = params.set<libMesh::Real>( "w_N" );
w_N = input( "Physics/ReactingLowMachNavierStokes/bound_species_1", 0.0, 1 );
wall_temp.reset( new NitridationCalibration::TubeTempBC( input ) );
std::tr1::shared_ptr<NitridationCalibration::TubeTempBC>& dummy = params.set<std::tr1::shared_ptr<NitridationCalibration::TubeTempBC> >( "wall_temp" );
dummy = wall_temp;
system.project_solution( initial_values, NULL, params );
}
grins.run();
// Get equation systems to create ExactSolution object
std::tr1::shared_ptr<libMesh::EquationSystems> es = grins.get_equation_system();
//es->write("foobar.xdr");
// Create Exact solution object and attach exact solution quantities
libMesh::ExactSolution exact_sol(*es);
libMesh::EquationSystems es_ref( es->get_mesh() );
// Filename of file where comparison solution is stashed
std::string solution_file = std::string(argv[2]);
es_ref.read( solution_file );
exact_sol.attach_reference_solution( &es_ref );
// Compute error and get it in various norms
exact_sol.compute_error(system_name, "u");
exact_sol.compute_error(system_name, "v");
if( (es->get_mesh()).mesh_dimension() == 3 )
exact_sol.compute_error(system_name, "w");
exact_sol.compute_error(system_name, "p");
exact_sol.compute_error(system_name, "T");
exact_sol.compute_error(system_name, "w_N2");
exact_sol.compute_error(system_name, "w_N");
exact_sol.compute_error(system_name, "w_CN");
double u_l2error = exact_sol.l2_error(system_name, "u");
double u_h1error = exact_sol.h1_error(system_name, "u");
double v_l2error = exact_sol.l2_error(system_name, "v");
double v_h1error = exact_sol.h1_error(system_name, "v");
double p_l2error = exact_sol.l2_error(system_name, "p");
double p_h1error = exact_sol.h1_error(system_name, "p");
double T_l2error = exact_sol.l2_error(system_name, "T");
double T_h1error = exact_sol.h1_error(system_name, "T");
double wN_l2error = exact_sol.l2_error(system_name, "w_N");
double wN_h1error = exact_sol.h1_error(system_name, "w_N");
double wN2_l2error = exact_sol.l2_error(system_name, "w_N2");
double wN2_h1error = exact_sol.h1_error(system_name, "w_N2");
double wCN_l2error = exact_sol.l2_error(system_name, "w_CN");
double wCN_h1error = exact_sol.h1_error(system_name, "w_CN");
double w_l2error = 0.0,
w_h1error = 0.0;
if( (es->get_mesh()).mesh_dimension() == 3 )
{
w_l2error = exact_sol.l2_error(system_name, "w");
w_h1error = exact_sol.h1_error(system_name, "w");
}
int return_flag = 0;
// This is the tolerance of the iterative linear solver so
// it's unreasonable to expect anything better than this.
double tol = 5.0e-10;
if( u_l2error > tol || u_h1error > tol ||
v_l2error > tol || v_h1error > tol ||
w_l2error > tol || w_h1error > tol ||
p_l2error > tol || p_h1error > tol ||
T_l2error > tol || T_h1error > tol ||
wN_l2error > tol || wN_h1error > tol ||
wN2_l2error > tol || wN2_h1error > tol ||
wCN_l2error > tol || wCN_h1error > tol )
{
return_flag = 1;
std::cout << "Tolerance exceeded for solution fields." << std::endl
<< "tolerance = " << tol << std::endl
<< "u l2 error = " << u_l2error << std::endl
<< "u h1 error = " << u_h1error << std::endl
<< "v l2 error = " << v_l2error << std::endl
<< "v h1 error = " << v_h1error << std::endl
<< "w l2 error = " << w_l2error << std::endl
<< "w h1 error = " << w_h1error << std::endl
<< "p l2 error = " << p_l2error << std::endl
<< "p h1 error = " << p_h1error << std::endl
<< "T l2 error = " << T_l2error << std::endl
<< "T h1 error = " << T_h1error << std::endl
<< "w_N l2 error = " << wN_l2error << std::endl
<< "w_N h1 error = " << wN_h1error << std::endl
<< "w_N2 l2 error = " << wN2_l2error << std::endl
<< "w_N2 h1 error = " << wN2_h1error << std::endl
<< "w_CN l2 error = " << wCN_l2error << std::endl
<< "w_CN h1 error = " << wCN_h1error << std::endl;
}
// Now test QoI Values
const libMesh::Real mass_loss_reg = atof(argv[3]);
const libMesh::Real avg_N_reg = atof(argv[4]);
/* The value we compute is negative by convention, but the data are given
as positive by convention, so convert to data convention. */
const libMesh::Real mass_loss_comp = std::fabs(grins.get_qoi_value(0));
const libMesh::Real avg_N_comp = grins.get_qoi_value(1);
const double qoi_tol = 1.0e-9;
const double mass_loss_error = std::fabs( (mass_loss_comp - mass_loss_reg)/mass_loss_reg );
const double avg_N_error = std::fabs( (avg_N_comp - avg_N_reg)/avg_N_reg );
if( mass_loss_error > qoi_tol ||
avg_N_error > qoi_tol )
{
return_flag = 1;
std::cout << "Tolerance exceeded for qoi values." << std::endl
<< "tolerance = " << qoi_tol << std::endl
<< "mass loss = " << mass_loss_comp << std::endl
<< "avg N = " << avg_N_comp << std::endl
<< "mass loss error = " << mass_loss_error << std::endl
<< "avg N error = " << avg_N_error << std::endl;
}
return return_flag;
}
int main(int argc, char **args)
{
// Time measurement.
TimePeriod cpu_time;
cpu_time.tick();
// Load the mesh.
Mesh mesh;
H3DReader mloader;
mloader.load("lshape_hex.mesh3d", &mesh);
// Perform initial mesh refinement.
for (int i=0; i < INIT_REF_NUM; i++) mesh.refine_all_elements(H3D_H3D_H3D_REFT_HEX_XYZ);
// Create an Hcurl space with default shapeset.
HcurlSpace space(&mesh, bc_types, essential_bc_values, Ord3(P_INIT_X, P_INIT_Y, P_INIT_Z));
// Initialize weak formulation.
WeakForm wf;
wf.add_matrix_form(biform<double, scalar>, biform<Ord, Ord>, HERMES_SYM);
wf.add_matrix_form_surf(biform_surf, biform_surf_ord);
wf.add_vector_form_surf(liform_surf, liform_surf_ord);
// Set exact solution.
ExactSolution exact_sol(&mesh, exact);
// DOF and CPU convergence graphs.
SimpleGraph graph_dof_est, graph_cpu_est, graph_dof_exact, graph_cpu_exact;
// Adaptivity loop.
int as = 1;
bool done = false;
do
{
info("---- Adaptivity step %d:", as);
// Construct globally refined reference mesh and setup reference space.
Space* ref_space = construct_refined_space(&space, 1);
// Initialize discrete problem.
bool is_linear = true;
DiscreteProblem dp(&wf, ref_space, is_linear);
// Set up the solver, matrix, and rhs according to the solver selection.
SparseMatrix* matrix = create_matrix(matrix_solver);
Vector* rhs = create_vector(matrix_solver);
Solver* solver = create_linear_solver(matrix_solver, matrix, rhs);
// Initialize the preconditioner in the case of SOLVER_AZTECOO.
if (matrix_solver == SOLVER_AZTECOO)
{
((AztecOOSolver*) solver)->set_solver(iterative_method);
((AztecOOSolver*) solver)->set_precond(preconditioner);
// Using default iteration parameters (see solver/aztecoo.h).
}
// Assemble the reference problem.
info("Assembling on reference mesh (ndof: %d).", Space::get_num_dofs(ref_space));
dp.assemble(matrix, rhs);
// Time measurement.
cpu_time.tick();
// Solve the linear system on reference mesh. If successful, obtain the solution.
info("Solving on reference mesh.");
Solution ref_sln(ref_space->get_mesh());
if(solver->solve()) Solution::vector_to_solution(solver->get_solution(), ref_space, &ref_sln);
else error ("Matrix solver failed.\n");
// Time measurement.
cpu_time.tick();
// Project the reference solution on the coarse mesh.
Solution sln(space.get_mesh());
info("Projecting reference solution on coarse mesh.");
OGProjection::project_global(&space, &ref_sln, &sln, matrix_solver, HERMES_HCURL_NORM);
// Time measurement.
cpu_time.tick();
// Output solution and mesh with polynomial orders.
if (solution_output)
{
out_fn_vtk(&sln, "sln", as);
out_orders_vtk(&space, "order", as);
}
// Skip the visualization time.
cpu_time.tick(HERMES_SKIP);
// Calculate element errors and total error estimate.
info("Calculating error estimate and exact error.");
Adapt *adaptivity = new Adapt(&space, HERMES_HCURL_NORM);
bool solutions_for_adapt = true;
double err_est_rel = adaptivity->calc_err_est(&sln, &ref_sln, solutions_for_adapt) * 100;
// Calculate exact error.
solutions_for_adapt = false;
double err_exact_rel = adaptivity->calc_err_exact(&sln, &exact_sol, solutions_for_adapt) * 100;
// Report results.
info("ndof_coarse: %d, ndof_fine: %d.", Space::get_num_dofs(&space), Space::get_num_dofs(ref_space));
info("err_est_rel: %g%%, err_exact_rel: %g%%.", err_est_rel, err_exact_rel);
// Add entry to DOF and CPU convergence graphs.
graph_dof_est.add_values(Space::get_num_dofs(&space), err_est_rel);
graph_dof_est.save("conv_dof_est.dat");
graph_cpu_est.add_values(cpu_time.accumulated(), err_est_rel);
graph_cpu_est.save("conv_cpu_est.dat");
graph_dof_exact.add_values(Space::get_num_dofs(&space), err_exact_rel);
graph_dof_exact.save("conv_dof_exact.dat");
graph_cpu_exact.add_values(cpu_time.accumulated(), err_exact_rel);
graph_cpu_exact.save("conv_cpu_exact.dat");
// If err_est_rel is too large, adapt the mesh.
if (err_est_rel < ERR_STOP) done = true;
else
{
info("Adapting coarse mesh.");
adaptivity->adapt(THRESHOLD);
}
if (Space::get_num_dofs(&space) >= NDOF_STOP) done = true;
// Clean up.
delete ref_space->get_mesh();
delete ref_space;
delete matrix;
delete rhs;
delete solver;
delete adaptivity;
// Increase the counter of performed adaptivity steps.
as++;
} while (!done);
return 0;
}
int run( int argc, char* argv[], const GetPot& input, GetPot& command_line )
{
// Initialize libMesh library.
libMesh::LibMeshInit libmesh_init(argc, argv);
GRINS::SimulationBuilder sim_builder;
GRINS::Simulation grins( input,
sim_builder,
libmesh_init.comm() );
//FIXME: We need to move this to within the Simulation object somehow...
std::string restart_file = input( "restart-options/restart_file", "none" );
if( restart_file == "none" )
{
// Asssign initial temperature value
std::string system_name = input( "screen-options/system_name", "GRINS" );
std::tr1::shared_ptr<libMesh::EquationSystems> es = grins.get_equation_system();
const libMesh::System& system = es->get_system(system_name);
libMesh::Parameters ¶ms = es->parameters;
libMesh::Real& w_N2 = params.set<libMesh::Real>( "w_N2" );
w_N2 = input( "Physics/ReactingLowMachNavierStokes/bound_species_0", 0.0, 0.0 );
libMesh::Real& w_N = params.set<libMesh::Real>( "w_N" );
w_N = input( "Physics/ReactingLowMachNavierStokes/bound_species_0", 0.0, 1.0 );
system.project_solution( initial_values, NULL, params );
}
grins.run();
// Get equation systems to create ExactSolution object
std::tr1::shared_ptr<libMesh::EquationSystems> es = grins.get_equation_system();
// Create Exact solution object and attach exact solution quantities
libMesh::ExactSolution exact_sol(*es);
libMesh::EquationSystems es_ref( es->get_mesh() );
// Filename of file where comparison solution is stashed
std::string solution_file = command_line("soln-data", "DIE!");
es_ref.read( solution_file );
exact_sol.attach_reference_solution( &es_ref );
// Now grab the variables for which we want to compare
unsigned int n_vars = command_line.vector_variable_size("vars");
std::vector<std::string> vars(n_vars);
for( unsigned int v = 0; v < n_vars; v++ )
{
vars[v] = command_line("vars", "DIE!", v);
}
// Now grab the norms to compute for each variable error
unsigned int n_norms = command_line.vector_variable_size("norms");
std::vector<std::string> norms(n_norms);
for( unsigned int n = 0; n < n_norms; n++ )
{
norms[n] = command_line("norms", "DIE!", n);
if( norms[n] != std::string("L2") &&
norms[n] != std::string("H1") )
{
std::cerr << "ERROR: Invalid norm input " << norms[n] << std::endl
<< " Valid values are: L2" << std::endl
<< " H1" << std::endl;
}
}
const std::string& system_name = grins.get_multiphysics_system_name();
// Now compute error for each variable
for( unsigned int v = 0; v < n_vars; v++ )
{
exact_sol.compute_error(system_name, vars[v]);
}
int return_flag = 0;
double tol = command_line("tol", 1.0e-10);
// Now test error for each variable, for each norm
for( unsigned int v = 0; v < n_vars; v++ )
{
for( unsigned int n = 0; n < n_norms; n++ )
{
test_error_norm( exact_sol, system_name, vars[v], norms[n], tol, return_flag );
}
}
return return_flag;
}
int main(int argc, char* argv[])
{
// Check command line count.
if( argc < 4 )
{
// TODO: Need more consistent error handling.
std::cerr << "Error: Must specify libMesh input file, regression file, and regression tolerance." << std::endl;
exit(1); // TODO: something more sophisticated for parallel runs?
}
// libMesh input file should be first argument
std::string libMesh_input_filename = argv[1];
// Create our GetPot object.
GetPot libMesh_inputfile( libMesh_input_filename );
// Initialize libMesh library.
LibMeshInit libmesh_init(argc, argv);
GRINS::SimulationBuilder sim_builder;
GRINS::Simulation grins( libMesh_inputfile,
sim_builder,
libmesh_init.comm() );
grins.run();
// Get equation systems to create ExactSolution object
std::tr1::shared_ptr<EquationSystems> es = grins.get_equation_system();
//es->write("foobar.xdr");
// Create Exact solution object and attach exact solution quantities
ExactSolution exact_sol(*es);
EquationSystems es_ref( es->get_mesh() );
// Filename of file where comparison solution is stashed
std::string solution_file = std::string(argv[2]);
es_ref.read( solution_file );
exact_sol.attach_reference_solution( &es_ref );
std::string system_name = libMesh_inputfile( "screen-options/system_name", "GRINS" );
// Compute error and get it in various norms
exact_sol.compute_error(system_name, "u");
exact_sol.compute_error(system_name, "v");
exact_sol.compute_error(system_name, "p");
double u_l2error = exact_sol.l2_error(system_name, "u");
double u_h1error = exact_sol.h1_error(system_name, "u");
double v_l2error = exact_sol.l2_error(system_name, "v");
double v_h1error = exact_sol.h1_error(system_name, "v");
double p_l2error = exact_sol.l2_error(system_name, "p");
double p_h1error = exact_sol.h1_error(system_name, "p");
int return_flag = 0;
// This is the tolerance of the iterative linear solver so
// it's unreasonable to expect anything better than this.
double tol = atof(argv[3]);
if( u_l2error > tol || u_h1error > tol ||
v_l2error > tol || v_h1error > tol ||
p_l2error > tol || p_h1error > tol )
{
return_flag = 1;
std::cout << "Tolerance exceeded for thermally driven flow test." << std::endl
<< "tolerance = " << tol << std::endl
<< "u l2 error = " << u_l2error << std::endl
<< "u h1 error = " << u_h1error << std::endl
<< "v l2 error = " << v_l2error << std::endl
<< "v h1 error = " << v_h1error << std::endl
<< "p l2 error = " << p_l2error << std::endl
<< "p h1 error = " << p_h1error << std::endl;
}
return return_flag;
}
// exact solution
scalar2& exact(double x, double y, scalar2& dx, scalar2& dy)
{
static scalar2 ex;
exact_sol(x,y, ex[0], ex[1], dx[1], dy[0]);
return ex;
}
int main()
{
// Time measurement.
TimePeriod cpu_time;
cpu_time.tick();
// Create coarse mesh, set Dirichlet BC, enumerate basis functions.
Space* space = new Space(A, B, NELEM, DIR_BC_LEFT, DIR_BC_RIGHT, P_INIT, NEQ);
// Enumerate basis functions, info for user.
int ndof = Space::get_num_dofs(space);
info("ndof: %d", ndof);
// Initialize the weak formulation.
WeakForm wf;
wf.add_matrix_form(jacobian);
wf.add_vector_form(residual);
// Initialize the FE problem.
bool is_linear = false;
DiscreteProblem *dp_coarse = new DiscreteProblem(&wf, space, is_linear);
if(JFNK == 0)
{
// Newton's loop on coarse mesh.
// Fill vector coeff_vec using dof and coeffs arrays in elements.
double *coeff_vec_coarse = new double[Space::get_num_dofs(space)];
get_coeff_vector(space, coeff_vec_coarse);
// Set up the solver, matrix, and rhs according to the solver selection.
SparseMatrix* matrix_coarse = create_matrix(matrix_solver);
Vector* rhs_coarse = create_vector(matrix_solver);
Solver* solver_coarse = create_linear_solver(matrix_solver, matrix_coarse, rhs_coarse);
int it = 1;
while (1)
{
// Obtain the number of degrees of freedom.
int ndof_coarse = Space::get_num_dofs(space);
// Assemble the Jacobian matrix and residual vector.
dp_coarse->assemble(coeff_vec_coarse, matrix_coarse, rhs_coarse);
// Calculate the l2-norm of residual vector.
double res_l2_norm = get_l2_norm(rhs_coarse);
// Info for user.
info("---- Newton iter %d, ndof %d, res. l2 norm %g", it, Space::get_num_dofs(space), res_l2_norm);
// If l2 norm of the residual vector is within tolerance, then quit.
// NOTE: at least one full iteration forced
// here because sometimes the initial
// residual on fine mesh is too small.
if(res_l2_norm < NEWTON_TOL_COARSE && it > 1) break;
// Multiply the residual vector with -1 since the matrix
// equation reads J(Y^n) \deltaY^{n+1} = -F(Y^n).
for(int i = 0; i < ndof_coarse; i++) rhs_coarse->set(i, -rhs_coarse->get(i));
// Solve the linear system.
if(!solver_coarse->solve())
error ("Matrix solver failed.\n");
// Add \deltaY^{n+1} to Y^n.
for (int i = 0; i < ndof_coarse; i++) coeff_vec_coarse[i] += solver_coarse->get_solution()[i];
// If the maximum number of iteration has been reached, then quit.
if (it >= NEWTON_MAX_ITER) error ("Newton method did not converge.");
// Copy coefficients from vector y to elements.
set_coeff_vector(coeff_vec_coarse, space);
it++;
}
// Cleanup.
delete matrix_coarse;
delete rhs_coarse;
delete solver_coarse;
delete [] coeff_vec_coarse;
}
else
jfnk_cg(dp_coarse, space, MATRIX_SOLVER_TOL, MATRIX_SOLVER_MAXITER,
JFNK_EPSILON, NEWTON_TOL_COARSE, NEWTON_MAX_ITER, matrix_solver);
// Cleanup.
delete dp_coarse;
// DOF and CPU convergence graphs.
SimpleGraph graph_dof_est, graph_cpu_est;
SimpleGraph graph_dof_exact, graph_cpu_exact;
// Adaptivity loop:
int as = 1;
double ftr_errors[MAX_ELEM_NUM]; // This array decides what
// elements will be refined.
bool done = false;
do
{
info("---- Adaptivity step %d:", as);
// Construct globally refined reference mesh and setup reference space.
Space* ref_space = construct_refined_space(space);
// Initialize the FE problem.
bool is_linear = false;
DiscreteProblem* dp = new DiscreteProblem(&wf, ref_space, is_linear);
if(JFNK == 0)
{
// Set up the solver, matrix, and rhs according to the solver selection.
SparseMatrix* matrix = create_matrix(matrix_solver);
Vector* rhs = create_vector(matrix_solver);
Solver* solver = create_linear_solver(matrix_solver, matrix, rhs);
// Newton's loop on the fine mesh.
info("Solving on fine mesh:");
// Fill vector coeff_vec using dof and coeffs arrays in elements.
double *coeff_vec = new double[Space::get_num_dofs(ref_space)];
get_coeff_vector(ref_space, coeff_vec);
int it = 1;
while (1)
{
// Obtain the number of degrees of freedom.
int ndof = Space::get_num_dofs(ref_space);
// Assemble the Jacobian matrix and residual vector.
dp->assemble(coeff_vec, matrix, rhs);
// Calculate the l2-norm of residual vector.
double res_l2_norm = get_l2_norm(rhs);
// Info for user.
info("---- Newton iter %d, ndof %d, res. l2 norm %g", it, Space::get_num_dofs(ref_space), res_l2_norm);
// If l2 norm of the residual vector is within tolerance, then quit.
// NOTE: at least one full iteration forced
// here because sometimes the initial
// residual on fine mesh is too small.
if(res_l2_norm < NEWTON_TOL_REF && it > 1) break;
// Multiply the residual vector with -1 since the matrix
// equation reads J(Y^n) \deltaY^{n+1} = -F(Y^n).
for(int i = 0; i < ndof; i++) rhs->set(i, -rhs->get(i));
// Solve the linear system.
if(!solver->solve())
error ("Matrix solver failed.\n");
// Add \deltaY^{n+1} to Y^n.
for (int i = 0; i < ndof; i++) coeff_vec[i] += solver->get_solution()[i];
// If the maximum number of iteration has been reached, then quit.
if (it >= NEWTON_MAX_ITER) error ("Newton method did not converge.");
// Copy coefficients from vector y to elements.
set_coeff_vector(coeff_vec, ref_space);
it++;
}
// Cleanup.
delete matrix;
delete rhs;
delete solver;
delete [] coeff_vec;
}
else
jfnk_cg(dp, ref_space, MATRIX_SOLVER_TOL, MATRIX_SOLVER_MAXITER,
JFNK_EPSILON, NEWTON_TOL_COARSE, NEWTON_MAX_ITER, matrix_solver);
// Cleanup.
delete dp;
// Starting with second adaptivity step, obtain new coarse
// mesh solution via projecting the fine mesh solution.
if(as > 1)
{
info("Projecting the fine mesh solution onto the coarse mesh.");
// Project the fine mesh solution (defined on space_ref) onto the coarse mesh (defined on space).
OGProjection::project_global(space, ref_space, matrix_solver);
}
double max_qoi_err_est = 0;
for (int i=0; i < space->get_n_active_elem(); i++)
{
if (GOAL_ORIENTED == 1)
{
// Use quantity of interest.
double qoi_est = quantity_of_interest(space, X_QOI);
double qoi_ref_est = quantity_of_interest(ref_space, X_QOI);
ftr_errors[i] = fabs(qoi_ref_est - qoi_est);
}
else
{
// Use global norm
double err_est_array[MAX_ELEM_NUM];
ftr_errors[i] = calc_err_est(NORM, space, ref_space, err_est_array);
}
// Info for user.
info("Elem [%d]: absolute error (est) = %g%%", i, ftr_errors[i]);
// Time measurement.
cpu_time.tick();
// Calculating maximum of QOI FTR error for plotting purposes
if (GOAL_ORIENTED == 1)
{
if (ftr_errors[i] > max_qoi_err_est)
max_qoi_err_est = ftr_errors[i];
}
else
{
double qoi_est = quantity_of_interest(space, X_QOI);
double qoi_ref_est = quantity_of_interest(ref_space, X_QOI);
double err_est = fabs(qoi_ref_est - qoi_est);
if (err_est > max_qoi_err_est)
max_qoi_err_est = err_est;
}
}
// Add entries to convergence graphs.
if (EXACT_SOL_PROVIDED)
{
double qoi_est = quantity_of_interest(space, X_QOI);
double u[MAX_EQN_NUM], dudx[MAX_EQN_NUM];
exact_sol(X_QOI, u, dudx);
double err_qoi_exact = fabs(u[0] - qoi_est);
// Info for user.
info("Relative error (exact) = %g %%", err_qoi_exact);
// Add entry to DOF and CPU convergence graphs.
graph_dof_exact.add_values(Space::get_num_dofs(space), err_qoi_exact);
graph_cpu_exact.add_values(cpu_time.accumulated(), err_qoi_exact);
}
// Add entry to DOF and CPU convergence graphs.
graph_dof_est.add_values(Space::get_num_dofs(space), max_qoi_err_est);
graph_cpu_est.add_values(cpu_time.accumulated(), max_qoi_err_est);
// Decide whether the max. FTR error in the quantity of interest
// is sufficiently small.
if(max_qoi_err_est < TOL_ERR_QOI) break;
// Returns updated coarse and fine meshes, with the last
// coarse and fine mesh solutions on them, respectively.
// The coefficient vectors and numbers of degrees of freedom
// on both meshes are also updated.
adapt(NORM, ADAPT_TYPE, THRESHOLD, ftr_errors, space, ref_space);
as++;
// Plot meshes, results, and errors.
adapt_plotting(space, ref_space, NORM, EXACT_SOL_PROVIDED, exact_sol);
// Cleanup.
delete ref_space;
}
while (done == false);
info("Total running time: %g s", cpu_time.accumulated());
// Save convergence graphs.
graph_dof_est.save("conv_dof_est.dat");
graph_cpu_est.save("conv_cpu_est.dat");
graph_dof_exact.save("conv_dof_exact.dat");
graph_cpu_exact.save("conv_cpu_exact.dat");
// Test variable.
bool success = true;
info("ndof = %d.", Space::get_num_dofs(space));
if (Space::get_num_dofs(space) > 150) success = false;
if (success)
{
info("Success!");
return ERROR_SUCCESS;
}
else
{
info("Failure!");
return ERROR_FAILURE;
}
}
int main() {
// Create coarse mesh, set Dirichlet BC, enumerate
// basis functions
Mesh *mesh = new Mesh(A, B, N_elem, P_init, N_eq);
mesh->set_bc_left_dirichlet(0, Val_dir_left);
mesh->set_bc_right_dirichlet(0, Val_dir_right);
mesh->assign_dofs();
// Create discrete problem on coarse mesh
DiscreteProblem *dp = new DiscreteProblem();
dp->add_matrix_form(0, 0, jacobian);
dp->add_vector_form(0, residual);
// Convergence graph wrt. the number of degrees of freedom
// (goal-oriented adaptivity)
GnuplotGraph graph_ftr;
graph_ftr.set_log_y();
graph_ftr.set_captions("Convergence History", "Degrees of Freedom", "QOI error");
graph_ftr.add_row("QOI error - FTR (exact)", "k", "-", "o");
graph_ftr.add_row("QOI error - FTR (est)", "k", "--");
// Main adaptivity loop
int adapt_iterations = 1;
double ftr_errors[MAX_ELEM_NUM]; // This array decides what
// elements will be refined.
ElemPtr2 ref_ftr_pairs[MAX_ELEM_NUM]; // To store element pairs from the
// FTR solution. Decides how
// elements will be hp-refined.
for (int i=0; i < MAX_ELEM_NUM; i++) {
ref_ftr_pairs[i][0] = new Element();
ref_ftr_pairs[i][1] = new Element();
}
while(1) {
printf("============ Adaptivity step %d ============\n", adapt_iterations);
printf("N_dof = %d\n", mesh->get_n_dof());
// Newton's loop on coarse mesh
int success;
if(JFNK == 0) {
newton(dp, mesh, NULL, NEWTON_TOL_COARSE, NEWTON_MAXITER);
}
else {
jfnk_cg(dp, mesh, MATRIX_SOLVER_TOL, MATRIX_SOLVER_MAXITER,
JFNK_EPSILON, NEWTON_TOL_COARSE, NEWTON_MAXITER);
}
// For every element perform its fast trial refinement (FTR),
// calculate the norm of the difference between the FTR
// solution and the coarse mesh solution, and store the
// error in the ftr_errors[] array.
int n_elem = mesh->get_n_active_elem();
double max_qoi_err_est = 0;
for (int i=0; i < n_elem; i++) {
printf("=== Starting FTR of Elem [%d]\n", i);
// Replicate coarse mesh including solution.
Mesh *mesh_ref_local = mesh->replicate();
// Perform FTR of element 'i'
mesh_ref_local->reference_refinement(i, 1);
printf("Elem [%d]: fine mesh created (%d DOF).\n",
i, mesh_ref_local->assign_dofs());
// Newton's loop on the FTR mesh
if(JFNK == 0) {
newton(dp, mesh_ref_local, NULL, NEWTON_TOL_COARSE, NEWTON_MAXITER);
}
else {
jfnk_cg(dp, mesh_ref_local, MATRIX_SOLVER_TOL, MATRIX_SOLVER_MAXITER,
JFNK_EPSILON, NEWTON_TOL_REF, NEWTON_MAXITER);
}
// Print FTR solution (enumerated)
Linearizer *lxx = new Linearizer(mesh_ref_local);
char out_filename[255];
sprintf(out_filename, "solution_ref_%d.gp", i);
lxx->plot_solution(out_filename);
delete lxx;
// Calculate FTR errors for refinement purposes
if (GOAL_ORIENTED == 1) {
// Use quantity of interest.
double qoi_est = quantity_of_interest(mesh, X_QOI);
double qoi_ref_est = quantity_of_interest(mesh_ref_local, X_QOI);
ftr_errors[i] = fabs(qoi_ref_est - qoi_est);
}
else {
// Use global norm
double err_est_array[MAX_ELEM_NUM];
ftr_errors[i] = calc_error_estimate(NORM, mesh, mesh_ref_local,
err_est_array);
}
// Calculating maximum of QOI FTR error for plotting purposes
if (GOAL_ORIENTED == 1) {
if (ftr_errors[i] > max_qoi_err_est)
max_qoi_err_est = ftr_errors[i];
}
else {
double qoi_est = quantity_of_interest(mesh, X_QOI);
double qoi_ref_est = quantity_of_interest(mesh_ref_local, X_QOI);
double err_est = fabs(qoi_ref_est - qoi_est);
if (err_est > max_qoi_err_est)
max_qoi_err_est = err_est;
}
// Copy the reference element pair for element 'i'
// into the ref_ftr_pairs[i][] array
Iterator *I = new Iterator(mesh);
Iterator *I_ref = new Iterator(mesh_ref_local);
Element *e, *e_ref;
while (1) {
e = I->next_active_element();
e_ref = I_ref->next_active_element();
if (e->id == i) {
e_ref->copy_into(ref_ftr_pairs[e->id][0]);
// coarse element 'e' was split in space
if (e->level != e_ref->level) {
e_ref = I_ref->next_active_element();
e_ref->copy_into(ref_ftr_pairs[e->id][1]);
}
break;
}
}
delete I;
delete I_ref;
delete mesh_ref_local;
}
// Add entries to convergence graphs
if (EXACT_SOL_PROVIDED) {
double qoi_est = quantity_of_interest(mesh, X_QOI);
double u[MAX_EQN_NUM], dudx[MAX_EQN_NUM];
exact_sol(X_QOI, u, dudx);
double err_qoi_exact = fabs(u[0] - qoi_est);
// plotting error in quantity of interest wrt. exact value
graph_ftr.add_values(0, mesh->get_n_dof(), err_qoi_exact);
}
graph_ftr.add_values(1, mesh->get_n_dof(), max_qoi_err_est);
// Decide whether the max. FTR error in the quantity of interest
// is sufficiently small
if(max_qoi_err_est < TOL_ERR_QOI) break;
// debug
if (adapt_iterations == 3) break;
// Returns updated coarse mesh with the last solution on it.
adapt(NORM, ADAPT_TYPE, THRESHOLD, ftr_errors,
mesh, ref_ftr_pairs);
adapt_iterations++;
}
// Plot meshes, results, and errors
adapt_plotting(mesh, ref_ftr_pairs,
NORM, EXACT_SOL_PROVIDED, exact_sol);
// Save convergence graph
graph_ftr.save("conv_dof.gp");
printf("Done.\n");
return 1;
}
int main(int argc, char* argv[])
{
#ifdef GRINS_USE_GRVY_TIMERS
GRVY::GRVY_Timer_Class grvy_timer;
grvy_timer.Init("GRINS Timer");
#endif
// Check command line count.
if( argc < 3 )
{
// TODO: Need more consistent error handling.
std::cerr << "Error: Must specify libMesh input file." << std::endl;
exit(1); // TODO: something more sophisticated for parallel runs?
}
// libMesh input file should be first argument
std::string libMesh_input_filename = argv[1];
// Create our GetPot object.
GetPot libMesh_inputfile( libMesh_input_filename );
// GetPot doesn't throw an error for a nonexistent file?
{
std::ifstream i(libMesh_input_filename.c_str());
if (!i)
{
std::cerr << "Error: Could not read from libMesh input file "
<< libMesh_input_filename << std::endl;
exit(1);
}
}
// Initialize libMesh library.
libMesh::LibMeshInit libmesh_init(argc, argv);
libMesh::out << "Starting GRINS with command:\n";
for (int i=0; i != argc; ++i)
libMesh::out << argv[i] << ' ';
libMesh::out << std::endl;
GRINS::SimulationBuilder sim_builder;
GRINS::Simulation grins( libMesh_inputfile,
sim_builder,
libmesh_init.comm() );
std::string system_name = libMesh_inputfile( "screen-options/system_name", "GRINS" );
// Get equation systems
GRINS::SharedPtr<libMesh::EquationSystems> es = grins.get_equation_system();
const libMesh::System& system = es->get_system(system_name);
libMesh::Parameters ¶ms = es->parameters;
system.project_solution( initial_values, NULL, params );
grins.run();
//es->write("suspended_cable_test.xdr");
// Create Exact solution object and attach exact solution quantities
libMesh::ExactSolution exact_sol(*es);
libMesh::EquationSystems es_ref( es->get_mesh() );
// Filename of file where comparison solution is stashed
std::string solution_file = std::string(argv[2]);
es_ref.read( solution_file );
exact_sol.attach_reference_solution( &es_ref );
// Compute error and get it in various norms
exact_sol.compute_error(system_name, "u");
exact_sol.compute_error(system_name, "v");
exact_sol.compute_error(system_name, "w");
double u_l2error = exact_sol.l2_error(system_name, "u");
double u_h1error = exact_sol.h1_error(system_name, "u");
double v_l2error = exact_sol.l2_error(system_name, "v");
double v_h1error = exact_sol.h1_error(system_name, "v");
double w_l2error = exact_sol.l2_error(system_name, "w");
double w_h1error = exact_sol.h1_error(system_name, "w");
int return_flag = 0;
double tol = 5.0e-8;
if( u_l2error > tol || u_h1error > tol ||
v_l2error > tol || v_h1error > tol ||
w_l2error > tol || w_h1error > tol )
{
return_flag = 1;
std::cout << "Tolerance exceeded for suspended cable test." << std::endl
<< "tolerance = " << tol << std::endl
<< "u l2 error = " << u_l2error << std::endl
<< "u h1 error = " << u_h1error << std::endl
<< "v l2 error = " << v_l2error << std::endl
<< "v h1 error = " << v_h1error << std::endl
<< "w l2 error = " << w_l2error << std::endl
<< "w h1 error = " << w_h1error << std::endl;
}
return return_flag;
}
