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Low storage runge kutta #259
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4f19280
First commit of new Low Storage RK ODESolver. [Does not compile]
jocelynpoon 93f71f1
low storage test
jocelynpoon 01d72b3
compiles
jocelynpoon ca60d55
this works
jocelynpoon 555565c
compiles
jocelynpoon 8cb35d8
compiles but time step does not change as expected
jocelynpoon 303cbf6
fixed w term need to fix dt
jocelynpoon d858fe7
this runs
jocelynpoon 35170cc
step size change
jocelynpoon 15ad87c
save
jocelynpoon 820d80c
works with mpi > 1
jocelynpoon e758b4a
update
jocelynpoon ee073a4
add test euler inviscid tgv largest stable cfl
jocelynpoon 7acd254
add 3s*+ method and RK3(2)5F[3S*+]
jocelynpoon 40d4e00
low storage algorithms, need to fix coefficients for RK3_2_5F_3SStarPlus
jocelynpoon 659719b
correct convergence for both algorithms (3S* and 3S*+)
jocelynpoon 4a99eac
add tolerances as parameters
jocelynpoon ac2b446
tolerance parameters work
jocelynpoon 8836f90
documentation and basic changes
jocelynpoon fa1c9ce
move code around
jocelynpoon ea7cc56
clean up code
jocelynpoon c633755
add code for automatic initial step size
jocelynpoon 59f3165
update to automatic initial time step, add ode_output param
jocelynpoon 940d163
add tolerance and beta parameters to own lsrk parameter subsection
jocelynpoon 26efcdf
Add RK4(3)9F[3S*+] method
jocelynpoon 48d3ff6
add RK5_4_10F_3SStarPlus scheme
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| Original file line number | Diff line number | Diff line change |
|---|---|---|
| @@ -0,0 +1,271 @@ | ||
| #include "low_storage_runge_kutta_ode_solver.h" | ||
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| namespace PHiLiP { | ||
| namespace ODE { | ||
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| template <int dim, typename real, int n_rk_stages, typename MeshType> | ||
| LowStorageRungeKuttaODESolver<dim,real,n_rk_stages, MeshType>::LowStorageRungeKuttaODESolver(std::shared_ptr< DGBase<dim, real, MeshType> > dg_input, | ||
| std::shared_ptr<LowStorageRKTableauBase<dim,real,MeshType>> rk_tableau_input, | ||
| std::shared_ptr<EmptyRRKBase<dim,real,MeshType>> RRK_object_input) | ||
| : ODESolverBase<dim,real,MeshType>(dg_input) | ||
| , butcher_tableau(rk_tableau_input) | ||
| , relaxation_runge_kutta(RRK_object_input) | ||
| { epsilon[0] = 1.0; | ||
| epsilon[1] = 1.0; | ||
| epsilon[2] = 1.0; | ||
| } | ||
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| template <int dim, typename real, int n_rk_stages, typename MeshType> | ||
| void LowStorageRungeKuttaODESolver<dim,real,n_rk_stages, MeshType>::step_in_time (real dt, const bool /*pseudotime*/) | ||
| { | ||
| this->original_time_step = dt; | ||
| this->solution_update = this->dg->solution; //storing u_n | ||
| double sum_delta = 0.0; | ||
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| storage_register_1.reinit(this->solution_update); | ||
| storage_register_2.reinit(this->solution_update); | ||
| storage_register_1 = this->dg->solution; | ||
| storage_register_2 *= 0; | ||
| storage_register_3 = storage_register_1; | ||
| rhs = storage_register_1; | ||
| if (is_3Sstarplus == true){ | ||
| storage_register_4 = storage_register_1; | ||
| } | ||
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| for (int i = 1; i < n_rk_stages +1; i++ ){ | ||
| storage_register_2.add(this->butcher_tableau->get_delta(i-1) , storage_register_1); | ||
| this->dg->solution = rhs; | ||
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| // Apply limiter at every RK stage | ||
| if (this->limiter) { | ||
| this->limiter->limit(this->dg->solution, | ||
| this->dg->dof_handler, | ||
| this->dg->fe_collection, | ||
| this->dg->volume_quadrature_collection, | ||
| this->dg->high_order_grid->fe_system.tensor_degree(), | ||
| this->dg->max_degree, | ||
| this->dg->oneD_fe_collection_1state, | ||
| this->dg->oneD_quadrature_collection); | ||
| } | ||
| this->dg->assemble_residual(); | ||
| this->dg->apply_inverse_global_mass_matrix(this->dg->right_hand_side, rhs); | ||
| storage_register_1 *= this->butcher_tableau->get_gamma(i, 0); | ||
| storage_register_1.add(this->butcher_tableau->get_gamma(i, 1), storage_register_2); | ||
| storage_register_1.add(this->butcher_tableau->get_gamma(i, 2), storage_register_3); | ||
| rhs *= dt; | ||
| storage_register_1.add(this->butcher_tableau->get_beta(i), rhs); | ||
| if (is_3Sstarplus == true){ | ||
| storage_register_4.add(this->butcher_tableau->get_b_hat(i-1), rhs); | ||
| } | ||
| rhs = storage_register_1; | ||
| } | ||
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| if (is_3Sstarplus == false){ | ||
| for (int i = 0; i < num_delta; i++){ | ||
| sum_delta = sum_delta + this->butcher_tableau->get_delta(i); | ||
| } | ||
| storage_register_2.add(this->butcher_tableau->get_delta(n_rk_stages), storage_register_1); | ||
| storage_register_2.add(this->butcher_tableau->get_delta(n_rk_stages+1), storage_register_3); | ||
| storage_register_2 /= sum_delta; | ||
| } | ||
| else if (is_3Sstarplus == true){ | ||
| this->dg->solution = rhs; | ||
| // Apply limiter at every RK stage | ||
| if (this->limiter) { | ||
| this->limiter->limit(this->dg->solution, | ||
| this->dg->dof_handler, | ||
| this->dg->fe_collection, | ||
| this->dg->volume_quadrature_collection, | ||
| this->dg->high_order_grid->fe_system.tensor_degree(), | ||
| this->dg->max_degree, | ||
| this->dg->oneD_fe_collection_1state, | ||
| this->dg->oneD_quadrature_collection); | ||
| } | ||
| this->dg->assemble_residual(); | ||
| this->dg->apply_inverse_global_mass_matrix(this->dg->right_hand_side, rhs); | ||
| rhs *= dt; | ||
| storage_register_4.add(this->butcher_tableau->get_b_hat(n_rk_stages), rhs); | ||
|
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| } | ||
| this->dg->solution = storage_register_1; | ||
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| // Apply limiter at every RK stage | ||
| if (this->limiter) { | ||
| this->limiter->limit(this->dg->solution, | ||
| this->dg->dof_handler, | ||
| this->dg->fe_collection, | ||
| this->dg->volume_quadrature_collection, | ||
| this->dg->high_order_grid->fe_system.tensor_degree(), | ||
| this->dg->max_degree, | ||
| this->dg->oneD_fe_collection_1state, | ||
| this->dg->oneD_quadrature_collection); | ||
| } | ||
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| if ((this->ode_param.ode_output) == Parameters::OutputEnum::verbose && | ||
| (this->current_iteration%this->ode_param.print_iteration_modulo) == 0 ) { | ||
| this->pcout << " Evaluating system update... " << std::endl; | ||
| } | ||
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| this->pcout << std::endl; | ||
| ++(this->current_iteration); | ||
| this->current_time += dt; | ||
| this->pcout << " Time is: " << this->current_time <<std::endl; | ||
| this->pcout << std::endl; | ||
| } | ||
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| template <int dim, typename real, int n_rk_stages, typename MeshType> | ||
| double LowStorageRungeKuttaODESolver<dim,real,n_rk_stages, MeshType>::get_automatic_error_adaptive_step_size (real dt, const bool /*pseudotime*/) | ||
| { | ||
| double error = 0.0; | ||
| w = 0.0; | ||
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| // error based step size | ||
| if (is_3Sstarplus == false){ | ||
| // loop sums elements at each mpi processor | ||
| for (dealii::LinearAlgebra::distributed::Vector<double>::size_type i = 0; i < storage_register_1.local_size(); ++i) { | ||
| error = storage_register_1.local_element(i) - storage_register_2.local_element(i); | ||
| w = w + pow(error / (atol + rtol * std::max(std::abs(storage_register_1.local_element(i)), std::abs(storage_register_2.local_element(i)))), 2); | ||
| } | ||
| } | ||
| else if (is_3Sstarplus == true){ | ||
| // loop sums elements at each mpi processor | ||
| for (dealii::LinearAlgebra::distributed::Vector<double>::size_type i = 0; i < storage_register_1.local_size(); ++i) { | ||
| error = storage_register_1.local_element(i) - storage_register_4.local_element(i); | ||
| w = w + pow(error / (atol + rtol * std::max(std::abs(storage_register_1.local_element(i)), std::abs(storage_register_4.local_element(i)))), 2); | ||
| } | ||
| } | ||
| this->pcout << std::endl; | ||
|
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| // sum over all elements | ||
| w = dealii::Utilities::MPI::sum(w, this->mpi_communicator); | ||
| w = pow(w / global_size, 0.5); | ||
| epsilon[2] = epsilon[1]; | ||
| epsilon[1] = epsilon[0]; | ||
| epsilon[0] = 1.0 / w; | ||
| dt = pow(epsilon[0], 1.0 * beta1/rk_order) * pow(epsilon[1], 1.0 * beta2/rk_order) * pow(epsilon[2], 1.0 * beta3/rk_order) * dt; | ||
| return dt; | ||
| } | ||
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| template <int dim, typename real, int n_rk_stages, typename MeshType> | ||
| double LowStorageRungeKuttaODESolver<dim,real,n_rk_stages, MeshType>::get_automatic_initial_step_size (real dt, const bool /*pseudotime*/) | ||
| { | ||
| // h will store the starting step size | ||
| double h0 = 0.0; | ||
| double h1 = 0.0; | ||
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| // d estimates the derivate of the solution | ||
| double d0 = 0.0; | ||
| double d1 = 0.0; | ||
| double d2 = 0.0; | ||
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| /// Storage of the solution to calculate the initial time step | ||
| dealii::LinearAlgebra::distributed::Vector<double> u_n; | ||
| dealii::LinearAlgebra::distributed::Vector<double> rhs_initial; | ||
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| this->solution_update = this->dg->solution; | ||
| u_n.reinit(this->solution_update); | ||
| rhs_initial.reinit(this->solution_update); | ||
| storage_register_1.reinit(this->solution_update); | ||
| storage_register_1 = this->dg->solution; | ||
| u_n = storage_register_1; | ||
| rhs_initial = storage_register_1; | ||
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| d0 = u_n.linfty_norm(); | ||
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| this->dg->solution = rhs_initial; | ||
| this->dg->assemble_residual(); | ||
| this->dg->apply_inverse_global_mass_matrix(this->dg->right_hand_side, rhs_initial); | ||
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| d1 = rhs_initial.linfty_norm(); | ||
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| if (d0 < pow(10, -5) || d1 < pow(10, -5)){ | ||
| h0 = pow(10, -6); | ||
| }else{ | ||
| h0 = 0.01 * d0 / d1; | ||
| } | ||
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| u_n.add(h0, rhs_initial); | ||
| this->dg->solution = u_n; | ||
| this->dg->assemble_residual(); | ||
| this->dg->apply_inverse_global_mass_matrix(this->dg->right_hand_side, u_n); | ||
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| // Calculate d2 | ||
| u_n.add(-1, rhs_initial); | ||
| d2 = u_n.linfty_norm(); | ||
| d2 /= h0; | ||
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| if (std::max(d1, d2) <= pow(10, -15)) | ||
| { | ||
| h1 = std::max(pow(10, -6), pow(10, -3)); | ||
| } | ||
| else | ||
| { | ||
| h1 = 0.01 / std::max(d1, d2); | ||
| } | ||
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| dt = std::min(100 * h0, h1); | ||
| this->dg->solution = storage_register_1; | ||
| return dt; | ||
| } | ||
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| template <int dim, typename real, int n_rk_stages, typename MeshType> | ||
| void LowStorageRungeKuttaODESolver<dim,real,n_rk_stages, MeshType>::allocate_ode_system () | ||
| { | ||
| this->solution_update.reinit(this->dg->solution); | ||
| storage_register_1.reinit(this->solution_update); | ||
|
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| atol = this->ode_param.atol; | ||
| rtol = this->ode_param.rtol; | ||
| rk_order = this->ode_param.rk_order; | ||
| is_3Sstarplus = this->ode_param.is_3Sstarplus; | ||
| num_delta = this->ode_param.num_delta; | ||
| beta1 = this->ode_param.beta1; | ||
| beta2 = this->ode_param.beta2; | ||
| beta3 = this->ode_param.beta3; | ||
|
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| global_size = dealii::Utilities::MPI::sum(storage_register_1.local_size(), this->mpi_communicator); | ||
| this->pcout << "Allocating ODE system..." << std::flush; | ||
| this->solution_update.reinit(this->dg->right_hand_side); | ||
| if(this->all_parameters->use_inverse_mass_on_the_fly == false) { | ||
| this->pcout << " evaluating inverse mass matrix..." << std::flush; | ||
| this->dg->evaluate_mass_matrices(true); // creates and stores global inverse mass matrix | ||
| //RRK needs both mass matrix and inverse mass matrix | ||
| using ODEEnum = Parameters::ODESolverParam::ODESolverEnum; | ||
| ODEEnum ode_type = this->ode_param.ode_solver_type; | ||
| if (ode_type == ODEEnum::rrk_explicit_solver){ | ||
| this->dg->evaluate_mass_matrices(false); // creates and stores global mass matrix | ||
| } | ||
| } | ||
|
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| this->pcout << std::endl; | ||
|
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| this->butcher_tableau->set_tableau(); | ||
| } | ||
|
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| template class LowStorageRungeKuttaODESolver<PHILIP_DIM, double,1, dealii::Triangulation<PHILIP_DIM> >; | ||
| template class LowStorageRungeKuttaODESolver<PHILIP_DIM, double,2, dealii::Triangulation<PHILIP_DIM> >; | ||
| template class LowStorageRungeKuttaODESolver<PHILIP_DIM, double,3, dealii::Triangulation<PHILIP_DIM> >; | ||
| template class LowStorageRungeKuttaODESolver<PHILIP_DIM, double,4, dealii::Triangulation<PHILIP_DIM> >; | ||
| template class LowStorageRungeKuttaODESolver<PHILIP_DIM, double,5, dealii::Triangulation<PHILIP_DIM> >; | ||
| template class LowStorageRungeKuttaODESolver<PHILIP_DIM, double,9, dealii::Triangulation<PHILIP_DIM> >; | ||
| template class LowStorageRungeKuttaODESolver<PHILIP_DIM, double,10, dealii::Triangulation<PHILIP_DIM> >; | ||
| template class LowStorageRungeKuttaODESolver<PHILIP_DIM, double,1, dealii::parallel::shared::Triangulation<PHILIP_DIM> >; | ||
| template class LowStorageRungeKuttaODESolver<PHILIP_DIM, double,2, dealii::parallel::shared::Triangulation<PHILIP_DIM> >; | ||
| template class LowStorageRungeKuttaODESolver<PHILIP_DIM, double,3, dealii::parallel::shared::Triangulation<PHILIP_DIM> >; | ||
| template class LowStorageRungeKuttaODESolver<PHILIP_DIM, double,4, dealii::parallel::shared::Triangulation<PHILIP_DIM> >; | ||
| template class LowStorageRungeKuttaODESolver<PHILIP_DIM, double,5, dealii::parallel::shared::Triangulation<PHILIP_DIM> >; | ||
| template class LowStorageRungeKuttaODESolver<PHILIP_DIM, double,9, dealii::parallel::shared::Triangulation<PHILIP_DIM> >; | ||
| template class LowStorageRungeKuttaODESolver<PHILIP_DIM, double,10, dealii::parallel::shared::Triangulation<PHILIP_DIM> >; | ||
| #if PHILIP_DIM != 1 | ||
| template class LowStorageRungeKuttaODESolver<PHILIP_DIM, double,1, dealii::parallel::distributed::Triangulation<PHILIP_DIM> >; | ||
| template class LowStorageRungeKuttaODESolver<PHILIP_DIM, double,2, dealii::parallel::distributed::Triangulation<PHILIP_DIM> >; | ||
| template class LowStorageRungeKuttaODESolver<PHILIP_DIM, double,3, dealii::parallel::distributed::Triangulation<PHILIP_DIM> >; | ||
| template class LowStorageRungeKuttaODESolver<PHILIP_DIM, double,4, dealii::parallel::distributed::Triangulation<PHILIP_DIM> >; | ||
| template class LowStorageRungeKuttaODESolver<PHILIP_DIM, double,5, dealii::parallel::distributed::Triangulation<PHILIP_DIM> >; | ||
| template class LowStorageRungeKuttaODESolver<PHILIP_DIM, double,9, dealii::parallel::distributed::Triangulation<PHILIP_DIM> >; | ||
| template class LowStorageRungeKuttaODESolver<PHILIP_DIM, double,10, dealii::parallel::distributed::Triangulation<PHILIP_DIM> >; | ||
| #endif | ||
|
|
||
| } // ODESolver namespace | ||
| } // PHiLiP namespace | ||
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Nice! The organization looks good.