integrate_fast Subroutine

  1. foodie_integrator_runge_kutta_embedded.f90
  2. foodie_integrator_runge_kutta_emd
  3. integrate_fast

private subroutine integrate_fast(self, U, Dt, t, new_Dt)

Integrate field with explicit embedded Runge-Kutta scheme, fast mode.

The time steps is adaptively resized using the local truncation error estimation by means of the embedded pairs of RK schemes.

Arguments

Type IntentOptional AttributesName
class(integrator_runge_kutta_emd), intent(inout) :: self

Integrator.
class(integrand_object), intent(inout) :: U

Field to be integrated.
real(kind=R_P), intent(in) :: Dt

Time step.
real(kind=R_P), intent(in) :: t

Time.
real(kind=R_P), intent(out), optional :: new_Dt

New adapted time step.

Source Code

integrate_fast

Source Code

  subroutine integrate_fast(self, U, Dt, t, new_Dt)
  !< Integrate field with explicit embedded Runge-Kutta scheme, fast mode.
  !<
  !< The time steps is adaptively resized using the local truncation error estimation by means of the embedded pairs of RK schemes.
  class(integrator_runge_kutta_emd), intent(inout)         :: self   !< Integrator.
  class(integrand_object),           intent(inout)         :: U      !< Field to be integrated.
  real(R_P),                         intent(in)            :: Dt     !< Time step.
  real(R_P),                         intent(in)            :: t      !< Time.
  real(R_P),                         intent(out), optional :: new_Dt !< New adapted time step.
  real(R_P)                                                :: Dt_    !< Time step, local variable.
  real(R_P)                                                :: error  !< Local truncation error estimation.
  integer(I_P)                                             :: s      !< First stages counter.
  integer(I_P)                                             :: ss     !< Second stages counter.

  Dt_ = Dt
  do
     ! compute stages
     do s=1, self%stages
        self%stage(s) = U
        do ss=1, s - 1
           call self%buffer%multiply_fast(lhs=self%stage(ss), rhs=Dt_ * self%alph(s, ss))
           call self%stage(s)%add_fast(lhs=self%stage(s), rhs=self%buffer)
        enddo
        call self%stage(s)%t_fast(t=t + self%gamm(s) * Dt_)
     enddo
     ! compute new time step
     self%U1 = U
     self%U2 = U
     do s=1, self%stages
        call self%buffer%multiply_fast(lhs=self%stage(s), rhs=Dt_ * self%beta(s, 1))
        call self%U1%add_fast(lhs=self%U1, rhs=self%buffer)
        call self%buffer%multiply_fast(lhs=self%stage(s), rhs=Dt_ * self%beta(s, 2))
        call self%U2%add_fast(lhs=self%U2, rhs=self%buffer)
     enddo
     error = self%U2.lterror.self%U1
     if (error <= self%tolerance) exit
     call self%new_Dt(error=error, Dt=Dt_)
  enddo
  U = self%U1
  if (present(new_Dt)) new_Dt = Dt_
  endsubroutine integrate_fast

All Procedures

a a a a a add_burgers add_euler add_euler add_euler add_lorenz allocate_integrand_members allocate_integrand_members allocate_integrand_members allocate_integrand_members allocate_integrand_members amplitude_phase assign_abstract assign_integrand assign_integrand assign_integrand assign_multistage assign_multistage_multistep assign_multistep assign_real assign_real assign_real average_solution burgers_assign_burgers burgers_assign_real burgers_local_error burgers_multiply_burgers burgers_multiply_real check_error check_scheme_has_fast_mode check_scheme_has_fast_mode check_scheme_has_fast_mode class_name class_name class_name class_name class_name class_name class_name class_name class_name class_name class_name class_name class_name compute_dt compute_dt compute_dt compute_dt compute_dt compute_dt compute_dt compute_dx compute_inter_states compute_inter_states compute_inter_states compute_inter_states compute_inter_states conservative2primitive conservative2primitive conservative2primitive conservative2primitive conservative2primitive d2Burgers_dx2 dBurgers_dt dBurgers_dx description description description description destroy destroy destroy destroy destroy destroy destroy destroy destroy destroy destroy destroy destroy destroy destroy destroy destroy destroy destroy destroy_abstract destroy_multistage destroy_multistage_multistep destroy_multistep destroy_rk destroy_rk dEuler_dt dEuler_dt dEuler_dt dEuler_dt dEuler_dt dLorenz_dt dt_ratio dU_dt dU_dt dU_dt E E E E E error error error euler_assign_euler euler_assign_euler euler_assign_euler euler_assign_euler euler_assign_euler euler_assign_real euler_assign_real euler_assign_real euler_local_error euler_local_error euler_local_error euler_multiply_euler euler_multiply_euler euler_multiply_euler euler_multiply_real euler_multiply_real euler_multiply_real exact_solution exact_solution exact_solution execute execute execute export_tecplot export_tecplot export_tecplot foodie_integrator_class_names foodie_integrator_factory foodie_integrator_schemes H H H H H has_fast_mode has_fast_mode has_fast_mode has_fast_mode has_fast_mode has_fast_mode has_fast_mode has_fast_mode has_fast_mode has_fast_mode has_fast_mode has_fast_mode has_fast_mode impose_boundary_conditions impose_boundary_conditions impose_boundary_conditions impose_boundary_conditions impose_boundary_conditions impose_boundary_conditions init init init init init init init init init init init init init init_rk init_rk initialize initialize initialize initialize initialize initialize initialize initialize initialize initialize initialize initialize initialize initialize initialize initialize initialize initialize initialize initialize_order_s initialize_order_s_1 integr_assign_integr integr_assign_integr integr_assign_integr integr_assign_integr integr_assign_integr integr_assign_integr integr_assign_integr integr_assign_integr integr_assign_integr integr_assign_integr integr_assign_integr integr_assign_integr integr_assign_integr integrand_add_integrand integrand_add_integrand integrand_add_integrand integrand_add_integrand_fast integrand_add_integrand_fast integrand_add_integrand_fast integrand_add_real integrand_add_real integrand_add_real integrand_dimension integrand_dimension integrand_dimension integrand_multiply_integrand integrand_multiply_integrand integrand_multiply_integrand integrand_multiply_integrand_fast integrand_multiply_integrand_fast integrand_multiply_integrand_fast integrand_multiply_real integrand_multiply_real integrand_multiply_real integrand_multiply_real_scalar integrand_multiply_real_scalar integrand_multiply_real_scalar integrand_multiply_real_scalar_fast integrand_multiply_real_scalar_fast integrand_multiply_real_scalar_fast integrand_sub_integrand integrand_sub_integrand integrand_sub_integrand integrand_sub_real integrand_sub_real integrand_sub_real integrand_subtract_integrand_fast integrand_subtract_integrand_fast integrand_subtract_integrand_fast integrate integrate integrate integrate integrate integrate integrate integrate integrate integrate integrate integrate integrate integrate integrate integrate integrate_fast integrate_fast integrate_fast integrate_fast integrate_fast integrate_fast integrate_fast integrate_fast integrate_fast integrate_fast integrate_fast integrate_fast integrate_fast integrate_order_2 integrate_order_2_fast integrate_order_3 integrate_order_3_fast integrate_order_s integrate_order_s_1 integrate_order_s_1_fast integrate_order_s_fast integrate_rk integrate_rk is_admissible is_available is_class_available is_multistage is_multistage is_multistage is_multistep is_multistep is_multistep is_scheme_available is_supported is_supported is_supported is_supported is_supported is_supported is_supported is_supported is_supported is_supported is_supported is_supported is_supported local_error local_error local_error lorenz_assign_lorenz lorenz_assign_real lorenz_local_error lorenz_multiply_lorenz lorenz_multiply_real new_Dt observed_order observed_order observed_order omega output output output output output output output output output output p p p p p parse_cli parse_cli parse_cli previous_step previous_step previous_step primitive2conservative primitive2conservative primitive2conservative primitive2conservative primitive2conservative r r r r r real_add_integrand real_add_integrand real_add_integrand real_multiply_burgers real_multiply_euler real_multiply_euler real_multiply_euler real_multiply_integrand real_multiply_integrand real_multiply_integrand real_multiply_lorenz real_scalar_multiply_integrand real_scalar_multiply_integrand real_scalar_multiply_integrand real_sub_integrand real_sub_integrand real_sub_integrand reconstruct_interfaces reconstruct_interfaces_states reconstruct_interfaces_states reconstruct_interfaces_states reconstruct_interfaces_states reconstruct_interfaces_states registers_number riemann_solver riemann_solver riemann_solver riemann_solver riemann_solver save_results save_results save_results save_results save_results save_results save_results save_results save_results save_time_serie save_time_serie save_time_serie save_time_serie save_time_serie scheme_number set_cli set_cli set_cli set_sin_wave_initial_state set_square_wave_initial_state stages_number stages_number stages_number steps_number steps_number steps_number sub_burgers sub_euler sub_euler sub_euler sub_lorenz supported_schemes supported_schemes supported_schemes supported_schemes supported_schemes supported_schemes supported_schemes supported_schemes supported_schemes supported_schemes supported_schemes supported_schemes supported_schemes synchronize synchronize synchronize synchronize t_fast t_fast t_fast test test test_ab test_ab test_ab test_euler test_euler test_euler test_leapfrog test_leapfrog test_leapfrog test_ls_rk test_ls_rk test_ls_rk test_tvd_rk test_tvd_rk test_tvd_rk tokenize trigger_error update_previous update_previous update_previous_steps update_previous_steps update_previous_steps