PHiLiP::DGBase< dim, nspecies, real, MeshType > Class Template Reference

DGBase is independent of the number of state variables. More...

#include <dg_base.hpp>

Inheritance diagram for PHiLiP::DGBase< dim, nspecies, real, MeshType >:

Collaboration diagram for PHiLiP::DGBase< dim, nspecies, real, MeshType >:

Public Types
using	Triangulation = MeshType
using	MassiveCollectionTuple = std::tuple< dealii::hp::FECollection< dim >, dealii::hp::QCollection< dim >, dealii::hp::QCollection< dim-1 >, dealii::hp::FECollection< dim >, dealii::hp::FECollection< 1 >, dealii::hp::FECollection< 1 >, dealii::hp::FECollection< 1 >, dealii::hp::QCollection< 1 > >
	Makes for cleaner doxygen documentation.

Public Member Functions
virtual	~DGBase ()=default
	Destructor.
	DGBase (const int nstate_input, const Parameters::AllParameters *const parameters_input, const unsigned int degree, const unsigned int max_degree_input, const unsigned int grid_degree_input, const std::shared_ptr< Triangulation > triangulation_input)
	Principal constructor that will call delegated constructor. More...
void	reinit ()
	Reinitializes the DG object after a change of triangulation. More...
	DGBase (const int nstate_input, const Parameters::AllParameters *const parameters_input, const unsigned int degree, const unsigned int max_degree_input, const unsigned int grid_degree_input, const std::shared_ptr< Triangulation > triangulation_input, const MassiveCollectionTuple collection_tuple)
	Delegated constructor that initializes collections. More...
void	set_high_order_grid (std::shared_ptr< HighOrderGrid< dim, real, MeshType >> new_high_order_grid)
	Sets the associated high order grid with the provided one.
void	set_all_cells_fe_degree (const unsigned int degree)
	Refers to a collection Mappings, which represents the high-order grid. More...
unsigned int	get_max_fe_degree ()
	Gets the maximum value of currently active FE degree.
unsigned int	get_min_fe_degree ()
	Gets the minimum value of currently active FE degree.
dealii::Point< dim >	coordinates_of_highest_refined_cell (bool check_for_p_refined_cell=false)
	Returns the coordinates of the most refined cell.
virtual void	allocate_system (const bool compute_dRdW=true, const bool compute_dRdX=true, const bool compute_d2R=true)
	Allocates the system. More...
void	time_scale_solution_update (dealii::LinearAlgebra::distributed::Vector< double > &solution_update, const real CFL) const
	Scales a solution update with the appropriate maximum time step. More...
void	time_scaled_mass_matrices (const real scale)
void	reinit_operators_for_cell_residual_loop (const unsigned int poly_degree_int, const unsigned int poly_degree_ext, const unsigned int grid_degree, OPERATOR::basis_functions< dim, 2 *dim > &soln_basis_int, OPERATOR::basis_functions< dim, 2 *dim > &soln_basis_ext, OPERATOR::basis_functions< dim, 2 *dim > &flux_basis_int, OPERATOR::basis_functions< dim, 2 *dim > &flux_basis_ext, OPERATOR::local_basis_stiffness< dim, 2 *dim > &flux_basis_stiffness, OPERATOR::vol_projection_operator< dim, 2 *dim > &soln_basis_projection_oper_int, OPERATOR::vol_projection_operator< dim, 2 *dim > &soln_basis_projection_oper_ext, OPERATOR::mapping_shape_functions< dim, 2 *dim > &mapping_basis)
	Builds needed operators for cell residual loop.
void	reinit_operators_for_mass_matrix (const bool Cartesian_element, const unsigned int poly_degree, const unsigned int grid_degree, OPERATOR::mapping_shape_functions< dim, 2 *dim > &mapping_basis, OPERATOR::basis_functions< dim, 2 *dim > &basis, OPERATOR::local_mass< dim, 2 *dim > &reference_mass_matrix, OPERATOR::local_Flux_Reconstruction_operator< dim, 2 *dim > &reference_FR, OPERATOR::local_Flux_Reconstruction_operator_aux< dim, 2 *dim > &reference_FR_aux, OPERATOR::derivative_p< dim, 2 *dim > &deriv_p)
	Builds needed operators to compute mass matrices/inverses efficiently.
void	evaluate_mass_matrices (bool do_inverse_mass_matrix=false)
	Allocates and evaluates the mass matrices for the entire grid.
void	evaluate_local_metric_dependent_mass_matrix_and_set_in_global_mass_matrix (const bool Cartesian_element, const bool do_inverse_mass_matrix, const unsigned int poly_degree, const unsigned int curr_grid_degree, const unsigned int n_quad_pts, const unsigned int n_dofs_cell, const std::vector< dealii::types::global_dof_index > dofs_indices, OPERATOR::metric_operators< real, dim, 2 *dim > &metric_oper, OPERATOR::basis_functions< dim, 2 *dim > &basis, OPERATOR::local_mass< dim, 2 *dim > &reference_mass_matrix, OPERATOR::local_Flux_Reconstruction_operator< dim, 2 *dim > &reference_FR, OPERATOR::local_Flux_Reconstruction_operator_aux< dim, 2 *dim > &reference_FR_aux, OPERATOR::derivative_p< dim, 2 *dim > &deriv_p)
	Evaluates the metric dependent local mass matrices and inverses, then sets them in the global matrices.
void	apply_inverse_global_mass_matrix (const dealii::LinearAlgebra::distributed::Vector< double > &input_vector, dealii::LinearAlgebra::distributed::Vector< double > &output_vector, const bool use_auxiliary_eq=false)
	Applies the inverse of the local metric dependent mass matrices when the global is not stored. More...
void	apply_global_mass_matrix (const dealii::LinearAlgebra::distributed::Vector< double > &input_vector, dealii::LinearAlgebra::distributed::Vector< double > &output_vector, const bool use_auxiliary_eq=false, const bool use_unmodified_mass_matrix=false)
	Applies the local metric dependent mass matrices when the global is not stored. More...
std::vector< real >	evaluate_time_steps (const bool exact_time_stepping)
	Evaluates the maximum stable time step. More...
void	add_mass_matrices (const real scale)
	Add mass matrices to the system scaled by a factor (likely time-step) More...
void	add_time_scaled_mass_matrices ()
	Add time scaled mass matrices to the system. More...
double	get_residual_l2norm () const
	Returns the L2-norm of the right_hand_side vector.
double	get_residual_linfnorm () const
	Returns the Linf-norm of the right_hand_side vector.
unsigned int	n_dofs () const
	Number of degrees of freedom.
void	set_anisotropic_flags ()
	Set anisotropic flags based on jump indicator. More...
template<typename real2 >
real2	discontinuity_sensor (const dealii::Quadrature< dim > &volume_quadrature, const std::vector< real2 > &soln_coeff_high, const dealii::FiniteElement< dim, dim > &fe_high, const std::vector< real2 > &jac_det)
void	set_dual (const dealii::LinearAlgebra::distributed::Vector< real > &dual_input)
	Sets the stored dual variables used to compute the dual dotted with the residual Hessians.
dealii::SparsityPattern	get_dRdX_sparsity_pattern ()
	Evaluate SparsityPattern of dRdX.
dealii::SparsityPattern	get_dRdW_sparsity_pattern ()
	Evaluate SparsityPattern of dRdW.
dealii::SparsityPattern	get_d2RdWdW_sparsity_pattern ()
	Evaluate SparsityPattern of the residual Hessian dual.d2RdWdW.
dealii::SparsityPattern	get_d2RdXdX_sparsity_pattern ()
	Evaluate SparsityPattern of the residual Hessian dual.d2RdXdX.
dealii::SparsityPattern	get_d2RdWdX_sparsity_pattern ()
	Evaluate SparsityPattern of the residual Hessian dual.d2RdXdW.
dealii::SparsityPattern	get_dRdXs_sparsity_pattern ()
	Evaluate SparsityPattern of dRdXs.
dealii::SparsityPattern	get_d2RdXsdXs_sparsity_pattern ()
	Evaluate SparsityPattern of the residual Hessian dual.d2RdXsdXs.
dealii::SparsityPattern	get_d2RdWdXs_sparsity_pattern ()
	Evaluate SparsityPattern of the residual Hessian dual.d2RdXsdW.
dealii::TrilinosWrappers::SparseMatrix	get_dRdX_finite_differences (dealii::SparsityPattern dRdX_sparsity_pattern)
	Evaluate dRdX using finite-differences.
void	initialize_manufactured_solution ()
	Virtual function defined in DG.
void	output_results_vtk (const unsigned int cycle, const double current_time=0.0, const bool output_time_averaged_solution=false, const bool output_fluctuating_quantities=false)
	Output solution.
void	output_face_results_vtk (const unsigned int cycle, const double current_time=0.0, const bool output_time_averaged_solution=false, const bool output_fluctuating_quantities=false)
	Output Euler face solution.
void	assemble_residual (const bool compute_dRdW=false, const bool compute_dRdX=false, const bool compute_d2R=false, const double CFL_mass=0.0)
	Main loop of the DG class. More...
template<typename adtype >
void	assemble_cell_residual_and_ad_derivatives (const dealii::TriaActiveIterator< dealii::DoFCellAccessor< dim, dim, false >> &current_cell, const dealii::TriaActiveIterator< dealii::DoFCellAccessor< dim, dim, false >> &current_metric_cell, const bool compute_dRdW, const bool compute_dRdX, const bool compute_d2R, dealii::hp::FEValues< dim, dim > &fe_values_collection_volume, dealii::hp::FEFaceValues< dim, dim > &fe_values_collection_face_int, dealii::hp::FEFaceValues< dim, dim > &fe_values_collection_face_ext, dealii::hp::FESubfaceValues< dim, dim > &fe_values_collection_subface, dealii::hp::FEValues< dim, dim > &fe_values_collection_volume_lagrange, OPERATOR::basis_functions< dim, 2 *dim > &soln_basis_int, OPERATOR::basis_functions< dim, 2 *dim > &soln_basis_ext, OPERATOR::basis_functions< dim, 2 *dim > &flux_basis_int, OPERATOR::basis_functions< dim, 2 *dim > &flux_basis_ext, OPERATOR::local_basis_stiffness< dim, 2 *dim > &flux_basis_stiffness, OPERATOR::vol_projection_operator< dim, 2 *dim > &soln_basis_projection_oper_int, OPERATOR::vol_projection_operator< dim, 2 *dim > &soln_basis_projection_oper_ext, OPERATOR::mapping_shape_functions< dim, 2 *dim > &mapping_basis, const bool compute_auxiliary_right_hand_side, dealii::LinearAlgebra::distributed::Vector< double > &rhs, std::array< dealii::LinearAlgebra::distributed::Vector< double >, dim > &rhs_aux)
	Used in assemble_residual(). More...
template<typename adtype >
std::enable_if<!std::is_same< adtype, double >::value, void >::type	assemble_volume_codi_taped_derivatives_ad (typename dealii::DoFHandler< dim >::active_cell_iterator cell, const dealii::types::global_dof_index current_cell_index, const std::vector< dealii::types::global_dof_index > &soln_dofs_indices, const std::vector< dealii::types::global_dof_index > &metric_dof_indices, const unsigned int poly_degree, const unsigned int grid_degree, OPERATOR::basis_functions< dim, 2 *dim > &soln_basis, OPERATOR::basis_functions< dim, 2 *dim > &flux_basis, OPERATOR::local_basis_stiffness< dim, 2 *dim > &flux_basis_stiffness, OPERATOR::vol_projection_operator< dim, 2 *dim > &soln_basis_projection_oper_int, OPERATOR::vol_projection_operator< dim, 2 *dim > &soln_basis_projection_oper_ext, OPERATOR::metric_operators< adtype, dim, 2 *dim > &metric_oper, OPERATOR::mapping_shape_functions< dim, 2 *dim > &mapping_basis, std::array< std::vector< adtype >, dim > &mapping_support_points, dealii::hp::FEValues< dim, dim > &fe_values_collection_volume, dealii::hp::FEValues< dim, dim > &fe_values_collection_volume_lagrange, const dealii::FESystem< dim, dim > &fe_soln, std::vector< real > &local_rhs_cell, dealii::Tensor< 1, dim, std::vector< real >> &local_auxiliary_RHS, const bool compute_auxiliary_right_hand_side, const bool compute_dRdW, const bool compute_dRdX, const bool compute_d2R)
	Computes the volume term of the cell and performs automatic differentiation.
void	assemble_volume_codi_taped_derivatives_ad (typename dealii::DoFHandler< dim >::active_cell_iterator cell, const dealii::types::global_dof_index current_cell_index, const std::vector< dealii::types::global_dof_index > &soln_dofs_indices, const std::vector< dealii::types::global_dof_index > &metric_dof_indices, const unsigned int poly_degree, const unsigned int grid_degree, OPERATOR::basis_functions< dim, 2 *dim > &soln_basis, OPERATOR::basis_functions< dim, 2 *dim > &flux_basis, OPERATOR::local_basis_stiffness< dim, 2 *dim > &flux_basis_stiffness, OPERATOR::vol_projection_operator< dim, 2 *dim > &soln_basis_projection_oper_int, OPERATOR::vol_projection_operator< dim, 2 *dim > &soln_basis_projection_oper_ext, OPERATOR::metric_operators< double, dim, 2 *dim > &metric_oper, OPERATOR::mapping_shape_functions< dim, 2 *dim > &mapping_basis, std::array< std::vector< double >, dim > &mapping_support_points, dealii::hp::FEValues< dim, dim > &fe_values_collection_volume, dealii::hp::FEValues< dim, dim > &fe_values_collection_volume_lagrange, const dealii::FESystem< dim, dim > &fe_soln, std::vector< real > &local_rhs_cell, dealii::Tensor< 1, dim, std::vector< real >> &local_auxiliary_RHS, const bool compute_auxiliary_right_hand_side, const bool compute_dRdW, const bool compute_dRdX, const bool compute_d2R)
	Computes the volume term of the cell.
template<typename adtype >
std::enable_if<!std::is_same< adtype, double >::value, void >::type	assemble_boundary_codi_taped_derivatives_ad (typename dealii::DoFHandler< dim >::active_cell_iterator cell, const dealii::types::global_dof_index current_cell_index, const unsigned int iface, const unsigned int boundary_id, const real penalty, const std::vector< dealii::types::global_dof_index > &soln_dofs_indices, const std::vector< dealii::types::global_dof_index > &metric_dof_indices, const unsigned int poly_degree, const unsigned int grid_degree, OPERATOR::basis_functions< dim, 2 *dim > &soln_basis, OPERATOR::basis_functions< dim, 2 *dim > &flux_basis, OPERATOR::vol_projection_operator< dim, 2 *dim > &soln_basis_projection_oper_int, OPERATOR::metric_operators< adtype, dim, 2 *dim > &metric_oper, OPERATOR::mapping_shape_functions< dim, 2 *dim > &mapping_basis, std::array< std::vector< adtype >, dim > &mapping_support_points, dealii::hp::FEFaceValues< dim, dim > &fe_values_collection_face_int, const dealii::FESystem< dim, dim > &fe_soln, std::vector< real > &local_rhs_cell, dealii::Tensor< 1, dim, std::vector< real >> &local_auxiliary_RHS, const bool compute_auxiliary_right_hand_side, const bool compute_dRdW, const bool compute_dRdX, const bool compute_d2R)
	Computes boundary term of the cell if the cell has a face at the boundary and performs automatic differentiation. More...
void	assemble_boundary_codi_taped_derivatives_ad (typename dealii::DoFHandler< dim >::active_cell_iterator cell, const dealii::types::global_dof_index current_cell_index, const unsigned int iface, const unsigned int boundary_id, const real penalty, const std::vector< dealii::types::global_dof_index > &soln_dofs_indices, const std::vector< dealii::types::global_dof_index > &metric_dof_indices, const unsigned int poly_degree, const unsigned int grid_degree, OPERATOR::basis_functions< dim, 2 *dim > &soln_basis, OPERATOR::basis_functions< dim, 2 *dim > &flux_basis, OPERATOR::vol_projection_operator< dim, 2 *dim > &soln_basis_projection_oper_int, OPERATOR::metric_operators< double, dim, 2 *dim > &metric_oper, OPERATOR::mapping_shape_functions< dim, 2 *dim > &mapping_basis, std::array< std::vector< double >, dim > &mapping_support_points, dealii::hp::FEFaceValues< dim, dim > &fe_values_collection_face_int, const dealii::FESystem< dim, dim > &fe_soln, std::vector< real > &local_rhs_cell, dealii::Tensor< 1, dim, std::vector< real >> &local_auxiliary_RHS, const bool compute_auxiliary_right_hand_side, const bool compute_dRdW, const bool compute_dRdX, const bool compute_d2R)
	Computes boundary term of the cell if the cell has a face at the boundary.
template<typename adtype >
std::enable_if<!std::is_same< adtype, double >::value, void >::type	assemble_face_codi_taped_derivatives_ad (typename dealii::DoFHandler< dim >::active_cell_iterator cell, typename dealii::DoFHandler< dim >::active_cell_iterator neighbor_cell, const dealii::types::global_dof_index current_cell_index, const dealii::types::global_dof_index neighbor_cell_index, const unsigned int iface, const unsigned int neighbor_iface, const real penalty, dealii::hp::FEFaceValues< dim, dim > &fe_values_collection_face_int, dealii::hp::FEFaceValues< dim, dim > &fe_values_collection_face_ext, dealii::hp::FESubfaceValues< dim, dim > &fe_values_collection_subface, const dealii::FESystem< dim, dim > &fe_int, const dealii::FESystem< dim, dim > &fe_ext, const std::vector< dealii::types::global_dof_index > &soln_dofs_indices_int, const std::vector< dealii::types::global_dof_index > &soln_dofs_indices_ext, const std::vector< dealii::types::global_dof_index > &metric_dofs_indices_int, const std::vector< dealii::types::global_dof_index > &metric_dofs_indices_ext, const unsigned int poly_degree_int, const unsigned int poly_degree_ext, const unsigned int grid_degree_int, const unsigned int grid_degree_ext, OPERATOR::basis_functions< dim, 2 *dim > &soln_basis_int, OPERATOR::basis_functions< dim, 2 *dim > &soln_basis_ext, OPERATOR::basis_functions< dim, 2 *dim > &flux_basis_int, OPERATOR::basis_functions< dim, 2 *dim > &flux_basis_ext, OPERATOR::local_basis_stiffness< dim, 2 *dim > &flux_basis_stiffness, OPERATOR::vol_projection_operator< dim, 2 *dim > &soln_basis_projection_oper_int, OPERATOR::vol_projection_operator< dim, 2 *dim > &soln_basis_projection_oper_ext, OPERATOR::metric_operators< adtype, dim, 2 *dim > &metric_oper_int, OPERATOR::metric_operators< adtype, dim, 2 *dim > &metric_oper_ext, OPERATOR::mapping_shape_functions< dim, 2 *dim > &mapping_basis, std::array< std::vector< adtype >, dim > &mapping_support_points, std::vector< real > &local_rhs_int_cell, std::vector< real > &local_rhs_ext_cell, dealii::Tensor< 1, dim, std::vector< real >> &current_cell_rhs_aux, dealii::LinearAlgebra::distributed::Vector< double > &rhs, std::array< dealii::LinearAlgebra::distributed::Vector< double >, dim > &rhs_aux, const bool compute_auxiliary_right_hand_side, const bool compute_dRdW, const bool compute_dRdX, const bool compute_d2R, const bool is_a_subface=false, const unsigned int neighbor_i_subface=0)
	Computes face term of the cell and performs automatic differentiation.
void	assemble_face_codi_taped_derivatives_ad (typename dealii::DoFHandler< dim >::active_cell_iterator cell, typename dealii::DoFHandler< dim >::active_cell_iterator neighbor_cell, const dealii::types::global_dof_index current_cell_index, const dealii::types::global_dof_index neighbor_cell_index, const unsigned int iface, const unsigned int neighbor_iface, const real penalty, dealii::hp::FEFaceValues< dim, dim > &fe_values_collection_face_int, dealii::hp::FEFaceValues< dim, dim > &fe_values_collection_face_ext, dealii::hp::FESubfaceValues< dim, dim > &fe_values_collection_subface, const dealii::FESystem< dim, dim > &fe_int, const dealii::FESystem< dim, dim > &fe_ext, const std::vector< dealii::types::global_dof_index > &soln_dofs_indices_int, const std::vector< dealii::types::global_dof_index > &soln_dofs_indices_ext, const std::vector< dealii::types::global_dof_index > &metric_dofs_indices_int, const std::vector< dealii::types::global_dof_index > &metric_dofs_indices_ext, const unsigned int poly_degree_int, const unsigned int poly_degree_ext, const unsigned int grid_degree_int, const unsigned int grid_degree_ext, OPERATOR::basis_functions< dim, 2 *dim > &soln_basis_int, OPERATOR::basis_functions< dim, 2 *dim > &soln_basis_ext, OPERATOR::basis_functions< dim, 2 *dim > &flux_basis_int, OPERATOR::basis_functions< dim, 2 *dim > &flux_basis_ext, OPERATOR::local_basis_stiffness< dim, 2 *dim > &flux_basis_stiffness, OPERATOR::vol_projection_operator< dim, 2 *dim > &soln_basis_projection_oper_int, OPERATOR::vol_projection_operator< dim, 2 *dim > &soln_basis_projection_oper_ext, OPERATOR::metric_operators< double, dim, 2 *dim > &metric_oper_int, OPERATOR::metric_operators< double, dim, 2 *dim > &metric_oper_ext, OPERATOR::mapping_shape_functions< dim, 2 *dim > &mapping_basis, std::array< std::vector< double >, dim > &mapping_support_points, std::vector< real > &local_rhs_int_cell, std::vector< real > &local_rhs_ext_cell, dealii::Tensor< 1, dim, std::vector< real >> &current_cell_rhs_aux, dealii::LinearAlgebra::distributed::Vector< double > &rhs, std::array< dealii::LinearAlgebra::distributed::Vector< double >, dim > &rhs_aux, const bool compute_auxiliary_right_hand_side, const bool compute_dRdW, const bool compute_dRdX, const bool compute_d2R, const bool is_a_subface=false, const unsigned int neighbor_i_subface=0)
	Computes face term of the cell.
virtual void	assemble_volume_term_and_build_operators_ad (typename dealii::DoFHandler< dim >::active_cell_iterator cell, const dealii::types::global_dof_index current_cell_index, const std::vector< double > &soln_coeffs, const dealii::Tensor< 1, dim, std::vector< double >> &aux_soln_coeffs, const std::vector< double > &metric_coeffs, const std::vector< real > &local_dual, const std::vector< dealii::types::global_dof_index > &soln_dofs_indices, const std::vector< dealii::types::global_dof_index > &metric_dofs_indices, const unsigned int poly_degree, const unsigned int grid_degree, OPERATOR::basis_functions< dim, 2 *dim > &soln_basis, OPERATOR::basis_functions< dim, 2 *dim > &flux_basis, OPERATOR::local_basis_stiffness< dim, 2 *dim > &flux_basis_stiffness, OPERATOR::vol_projection_operator< dim, 2 *dim > &soln_basis_projection_oper_int, OPERATOR::vol_projection_operator< dim, 2 *dim > &soln_basis_projection_oper_ext, OPERATOR::metric_operators< double, dim, 2 *dim > &metric_oper, OPERATOR::mapping_shape_functions< dim, 2 *dim > &mapping_basis, std::array< std::vector< double >, dim > &mapping_support_points, dealii::hp::FEValues< dim, dim > &fe_values_collection_volume, dealii::hp::FEValues< dim, dim > &fe_values_collection_volume_lagrange, const dealii::FESystem< dim, dim > &fe_soln, std::vector< double > &rhs, dealii::Tensor< 1, dim, std::vector< double >> &local_auxiliary_RHS, const bool compute_auxiliary_right_hand_side, double &dual_dot_residual)=0
	Builds the necessary operators/fe values and assembles volume residual. For double type.
virtual void	assemble_volume_term_and_build_operators_ad (typename dealii::DoFHandler< dim >::active_cell_iterator cell, const dealii::types::global_dof_index current_cell_index, const std::vector< codi_JacobianComputationType > &soln_coeffs, const dealii::Tensor< 1, dim, std::vector< codi_JacobianComputationType >> &aux_soln_coeffs, const std::vector< codi_JacobianComputationType > &metric_coeffs, const std::vector< real > &local_dual, const std::vector< dealii::types::global_dof_index > &soln_dofs_indices, const std::vector< dealii::types::global_dof_index > &metric_dofs_indices, const unsigned int poly_degree, const unsigned int grid_degree, OPERATOR::basis_functions< dim, 2 *dim > &soln_basis, OPERATOR::basis_functions< dim, 2 *dim > &flux_basis, OPERATOR::local_basis_stiffness< dim, 2 *dim > &flux_basis_stiffness, OPERATOR::vol_projection_operator< dim, 2 *dim > &soln_basis_projection_oper_int, OPERATOR::vol_projection_operator< dim, 2 *dim > &soln_basis_projection_oper_ext, OPERATOR::metric_operators< codi_JacobianComputationType, dim, 2 *dim > &metric_oper, OPERATOR::mapping_shape_functions< dim, 2 *dim > &mapping_basis, std::array< std::vector< codi_JacobianComputationType >, dim > &mapping_support_points, dealii::hp::FEValues< dim, dim > &fe_values_collection_volume, dealii::hp::FEValues< dim, dim > &fe_values_collection_volume_lagrange, const dealii::FESystem< dim, dim > &fe_soln, std::vector< codi_JacobianComputationType > &rhs, dealii::Tensor< 1, dim, std::vector< codi_JacobianComputationType >> &local_auxiliary_RHS, const bool compute_auxiliary_right_hand_side, codi_JacobianComputationType &dual_dot_residual)=0
	Builds the necessary operators/fe values and assembles volume residual. For codi_JacobianComputationType.
virtual void	assemble_volume_term_and_build_operators_ad (typename dealii::DoFHandler< dim >::active_cell_iterator cell, const dealii::types::global_dof_index current_cell_index, const std::vector< codi_HessianComputationType > &soln_coeffs, const dealii::Tensor< 1, dim, std::vector< codi_HessianComputationType >> &aux_soln_coeffs, const std::vector< codi_HessianComputationType > &metric_coeffs, const std::vector< real > &local_dual, const std::vector< dealii::types::global_dof_index > &soln_dofs_indices, const std::vector< dealii::types::global_dof_index > &metric_dofs_indices, const unsigned int poly_degree, const unsigned int grid_degree, OPERATOR::basis_functions< dim, 2 *dim > &soln_basis, OPERATOR::basis_functions< dim, 2 *dim > &flux_basis, OPERATOR::local_basis_stiffness< dim, 2 *dim > &flux_basis_stiffness, OPERATOR::vol_projection_operator< dim, 2 *dim > &soln_basis_projection_oper_int, OPERATOR::vol_projection_operator< dim, 2 *dim > &soln_basis_projection_oper_ext, OPERATOR::metric_operators< codi_HessianComputationType, dim, 2 *dim > &metric_oper, OPERATOR::mapping_shape_functions< dim, 2 *dim > &mapping_basis, std::array< std::vector< codi_HessianComputationType >, dim > &mapping_support_points, dealii::hp::FEValues< dim, dim > &fe_values_collection_volume, dealii::hp::FEValues< dim, dim > &fe_values_collection_volume_lagrange, const dealii::FESystem< dim, dim > &fe_soln, std::vector< codi_HessianComputationType > &rhs, dealii::Tensor< 1, dim, std::vector< codi_HessianComputationType >> &local_auxiliary_RHS, const bool compute_auxiliary_right_hand_side, codi_HessianComputationType &dual_dot_residual)=0
	Builds the necessary operators/fe values and assembles volume residual. For codi_HessianComputationType.
virtual void	assemble_boundary_term_and_build_operators_ad (typename dealii::DoFHandler< dim >::active_cell_iterator cell, const dealii::types::global_dof_index current_cell_index, const std::vector< double > &soln_coeffs, const dealii::Tensor< 1, dim, std::vector< double >> &aux_soln_coeffs, const std::vector< double > &metric_coeffs, const std::vector< real > &local_dual, const unsigned int face_number, const unsigned int boundary_id, const unsigned int poly_degree, const unsigned int grid_degree, OPERATOR::basis_functions< dim, 2 *dim > &soln_basis, OPERATOR::basis_functions< dim, 2 *dim > &flux_basis, OPERATOR::vol_projection_operator< dim, 2 *dim > &soln_basis_projection_oper_int, OPERATOR::metric_operators< double, dim, 2 *dim > &metric_oper, OPERATOR::mapping_shape_functions< dim, 2 *dim > &mapping_basis, std::array< std::vector< double >, dim > &mapping_support_points, dealii::hp::FEFaceValues< dim, dim > &fe_values_collection_face_int, const dealii::FESystem< dim, dim > &fe_soln, const real penalty, std::vector< double > &rhs, dealii::Tensor< 1, dim, std::vector< double >> &local_auxiliary_RHS, const bool compute_auxiliary_right_hand_side, double &dual_dot_residual)=0
	Builds the necessary operators/fe values and assembles boundary residual. For double type.
virtual void	assemble_boundary_term_and_build_operators_ad (typename dealii::DoFHandler< dim >::active_cell_iterator cell, const dealii::types::global_dof_index current_cell_index, const std::vector< codi_JacobianComputationType > &soln_coeffs, const dealii::Tensor< 1, dim, std::vector< codi_JacobianComputationType >> &aux_soln_coeffs, const std::vector< codi_JacobianComputationType > &metric_coeffs, const std::vector< real > &local_dual, const unsigned int face_number, const unsigned int boundary_id, const unsigned int poly_degree, const unsigned int grid_degree, OPERATOR::basis_functions< dim, 2 *dim > &soln_basis, OPERATOR::basis_functions< dim, 2 *dim > &flux_basis, OPERATOR::vol_projection_operator< dim, 2 *dim > &soln_basis_projection_oper_int, OPERATOR::metric_operators< codi_JacobianComputationType, dim, 2 *dim > &metric_oper, OPERATOR::mapping_shape_functions< dim, 2 *dim > &mapping_basis, std::array< std::vector< codi_JacobianComputationType >, dim > &mapping_support_points, dealii::hp::FEFaceValues< dim, dim > &fe_values_collection_face_int, const dealii::FESystem< dim, dim > &fe_soln, const real penalty, std::vector< codi_JacobianComputationType > &rhs, dealii::Tensor< 1, dim, std::vector< codi_JacobianComputationType >> &local_auxiliary_RHS, const bool compute_auxiliary_right_hand_side, codi_JacobianComputationType &dual_dot_residual)=0
	Builds the necessary operators/fe values and assembles boundary residual. For codi_JacobianComputationType.
virtual void	assemble_boundary_term_and_build_operators_ad (typename dealii::DoFHandler< dim >::active_cell_iterator cell, const dealii::types::global_dof_index current_cell_index, const std::vector< codi_HessianComputationType > &soln_coeffs, const dealii::Tensor< 1, dim, std::vector< codi_HessianComputationType >> &aux_soln_coeffs, const std::vector< codi_HessianComputationType > &metric_coeffs, const std::vector< real > &local_dual, const unsigned int face_number, const unsigned int boundary_id, const unsigned int poly_degree, const unsigned int grid_degree, OPERATOR::basis_functions< dim, 2 *dim > &soln_basis, OPERATOR::basis_functions< dim, 2 *dim > &flux_basis, OPERATOR::vol_projection_operator< dim, 2 *dim > &soln_basis_projection_oper_int, OPERATOR::metric_operators< codi_HessianComputationType, dim, 2 *dim > &metric_oper, OPERATOR::mapping_shape_functions< dim, 2 *dim > &mapping_basis, std::array< std::vector< codi_HessianComputationType >, dim > &mapping_support_points, dealii::hp::FEFaceValues< dim, dim > &fe_values_collection_face_int, const dealii::FESystem< dim, dim > &fe_soln, const real penalty, std::vector< codi_HessianComputationType > &rhs, dealii::Tensor< 1, dim, std::vector< codi_HessianComputationType >> &local_auxiliary_RHS, const bool compute_auxiliary_right_hand_side, codi_HessianComputationType &dual_dot_residual)=0
	Builds the necessary operators/fe values and assembles boundary residual. For codi_HessianComputationType.
virtual void	assemble_face_term_and_build_operators_ad (typename dealii::DoFHandler< dim >::active_cell_iterator cell, typename dealii::DoFHandler< dim >::active_cell_iterator neighbor_cell, const dealii::types::global_dof_index current_cell_index, const dealii::types::global_dof_index neighbor_cell_index, const unsigned int iface, const unsigned int neighbor_iface, const std::vector< double > &soln_coeff_int, const std::vector< double > &soln_coeff_ext, const dealii::Tensor< 1, dim, std::vector< double >> &aux_soln_coeff_int, const dealii::Tensor< 1, dim, std::vector< double >> &aux_soln_coeff_ext, const std::vector< double > &metric_coefF_int, const std::vector< double > &metric_coefF_ext, const std::vector< double > &dual_int, const std::vector< double > &dual_ext, const unsigned int poly_degree_int, const unsigned int poly_degree_ext, const unsigned int grid_degree_int, const unsigned int grid_degree_ext, OPERATOR::basis_functions< dim, 2 *dim > &soln_basis_int, OPERATOR::basis_functions< dim, 2 *dim > &soln_basis_ext, OPERATOR::basis_functions< dim, 2 *dim > &flux_basis_int, OPERATOR::basis_functions< dim, 2 *dim > &flux_basis_ext, OPERATOR::local_basis_stiffness< dim, 2 *dim > &flux_basis_stiffness, OPERATOR::vol_projection_operator< dim, 2 *dim > &soln_basis_projection_oper_int, OPERATOR::vol_projection_operator< dim, 2 *dim > &soln_basis_projection_oper_ext, OPERATOR::metric_operators< double, dim, 2 *dim > &metric_oper_int, OPERATOR::metric_operators< double, dim, 2 *dim > &metric_oper_ext, OPERATOR::mapping_shape_functions< dim, 2 *dim > &mapping_basis, std::array< std::vector< double >, dim > &mapping_support_points, dealii::hp::FEFaceValues< dim, dim > &fe_values_collection_face_int, dealii::hp::FEFaceValues< dim, dim > &fe_values_collection_face_ext, dealii::hp::FESubfaceValues< dim, dim > &fe_values_collection_subface, const dealii::FESystem< dim, dim > &fe_int, const dealii::FESystem< dim, dim > &fe_ext, const real penalty, std::vector< double > &rhs_int, std::vector< double > &rhs_ext, dealii::Tensor< 1, dim, std::vector< double >> &aux_rhs_int, dealii::Tensor< 1, dim, std::vector< double >> &aux_rhs_ext, const bool compute_auxiliary_right_hand_side, double &dual_dot_residual, const bool compute_dRdW, const bool compute_dRdX, const bool compute_d2R, const bool is_a_subface, const unsigned int neighbor_i_subface)=0
	Builds the necessary operators/fe values and assembles face residual. For double type.
virtual void	assemble_face_term_and_build_operators_ad (typename dealii::DoFHandler< dim >::active_cell_iterator cell, typename dealii::DoFHandler< dim >::active_cell_iterator neighbor_cell, const dealii::types::global_dof_index current_cell_index, const dealii::types::global_dof_index neighbor_cell_index, const unsigned int iface, const unsigned int neighbor_iface, const std::vector< codi_JacobianComputationType > &soln_coeff_int, const std::vector< codi_JacobianComputationType > &soln_coeff_ext, const dealii::Tensor< 1, dim, std::vector< codi_JacobianComputationType >> &aux_soln_coeff_int, const dealii::Tensor< 1, dim, std::vector< codi_JacobianComputationType >> &aux_soln_coeff_ext, const std::vector< codi_JacobianComputationType > &metric_coefF_int, const std::vector< codi_JacobianComputationType > &metric_coefF_ext, const std::vector< double > &dual_int, const std::vector< double > &dual_ext, const unsigned int poly_degree_int, const unsigned int poly_degree_ext, const unsigned int grid_degree_int, const unsigned int grid_degree_ext, OPERATOR::basis_functions< dim, 2 *dim > &soln_basis_int, OPERATOR::basis_functions< dim, 2 *dim > &soln_basis_ext, OPERATOR::basis_functions< dim, 2 *dim > &flux_basis_int, OPERATOR::basis_functions< dim, 2 *dim > &flux_basis_ext, OPERATOR::local_basis_stiffness< dim, 2 *dim > &flux_basis_stiffness, OPERATOR::vol_projection_operator< dim, 2 *dim > &soln_basis_projection_oper_int, OPERATOR::vol_projection_operator< dim, 2 *dim > &soln_basis_projection_oper_ext, OPERATOR::metric_operators< codi_JacobianComputationType, dim, 2 *dim > &metric_oper_int, OPERATOR::metric_operators< codi_JacobianComputationType, dim, 2 *dim > &metric_oper_ext, OPERATOR::mapping_shape_functions< dim, 2 *dim > &mapping_basis, std::array< std::vector< codi_JacobianComputationType >, dim > &mapping_support_points, dealii::hp::FEFaceValues< dim, dim > &fe_values_collection_face_int, dealii::hp::FEFaceValues< dim, dim > &fe_values_collection_face_ext, dealii::hp::FESubfaceValues< dim, dim > &fe_values_collection_subface, const dealii::FESystem< dim, dim > &fe_int, const dealii::FESystem< dim, dim > &fe_ext, const real penalty, std::vector< codi_JacobianComputationType > &rhs_int, std::vector< codi_JacobianComputationType > &rhs_ext, dealii::Tensor< 1, dim, std::vector< codi_JacobianComputationType >> &aux_rhs_int, dealii::Tensor< 1, dim, std::vector< codi_JacobianComputationType >> &aux_rhs_ext, const bool compute_auxiliary_right_hand_side, codi_JacobianComputationType &dual_dot_residual, const bool compute_dRdW, const bool compute_dRdX, const bool compute_d2R, const bool is_a_subface, const unsigned int neighbor_i_subface)=0
	Builds the necessary operators/fe values and assembles face residual. For codi_JacobianComputationType.
virtual void	assemble_face_term_and_build_operators_ad (typename dealii::DoFHandler< dim >::active_cell_iterator cell, typename dealii::DoFHandler< dim >::active_cell_iterator neighbor_cell, const dealii::types::global_dof_index current_cell_index, const dealii::types::global_dof_index neighbor_cell_index, const unsigned int iface, const unsigned int neighbor_iface, const std::vector< codi_HessianComputationType > &soln_coeff_int, const std::vector< codi_HessianComputationType > &soln_coeff_ext, const dealii::Tensor< 1, dim, std::vector< codi_HessianComputationType >> &aux_soln_coeff_int, const dealii::Tensor< 1, dim, std::vector< codi_HessianComputationType >> &aux_soln_coeff_ext, const std::vector< codi_HessianComputationType > &metric_coefF_int, const std::vector< codi_HessianComputationType > &metric_coefF_ext, const std::vector< double > &dual_int, const std::vector< double > &dual_ext, const unsigned int poly_degree_int, const unsigned int poly_degree_ext, const unsigned int grid_degree_int, const unsigned int grid_degree_ext, OPERATOR::basis_functions< dim, 2 *dim > &soln_basis_int, OPERATOR::basis_functions< dim, 2 *dim > &soln_basis_ext, OPERATOR::basis_functions< dim, 2 *dim > &flux_basis_int, OPERATOR::basis_functions< dim, 2 *dim > &flux_basis_ext, OPERATOR::local_basis_stiffness< dim, 2 *dim > &flux_basis_stiffness, OPERATOR::vol_projection_operator< dim, 2 *dim > &soln_basis_projection_oper_int, OPERATOR::vol_projection_operator< dim, 2 *dim > &soln_basis_projection_oper_ext, OPERATOR::metric_operators< codi_HessianComputationType, dim, 2 *dim > &metric_oper_int, OPERATOR::metric_operators< codi_HessianComputationType, dim, 2 *dim > &metric_oper_ext, OPERATOR::mapping_shape_functions< dim, 2 *dim > &mapping_basis, std::array< std::vector< codi_HessianComputationType >, dim > &mapping_support_points, dealii::hp::FEFaceValues< dim, dim > &fe_values_collection_face_int, dealii::hp::FEFaceValues< dim, dim > &fe_values_collection_face_ext, dealii::hp::FESubfaceValues< dim, dim > &fe_values_collection_subface, const dealii::FESystem< dim, dim > &fe_int, const dealii::FESystem< dim, dim > &fe_ext, const real penalty, std::vector< codi_HessianComputationType > &rhs_int, std::vector< codi_HessianComputationType > &rhs_ext, dealii::Tensor< 1, dim, std::vector< codi_HessianComputationType >> &aux_rhs_int, dealii::Tensor< 1, dim, std::vector< codi_HessianComputationType >> &aux_rhs_ext, const bool compute_auxiliary_right_hand_side, codi_HessianComputationType &dual_dot_residual, const bool compute_dRdW, const bool compute_dRdX, const bool compute_d2R, const bool is_a_subface, const unsigned int neighbor_i_subface)=0
	Builds the necessary operators/fe values and assembles face residual. For codi_HessianComputationType.
template<typename real2 >
double	getValue (const real2 &x)
	Returns the value from a CoDiPack variable. More...
void	automatic_differentiation_indexing_1 (const bool compute_dRdW, const bool compute_dRdX, const bool compute_d2R, const unsigned int n_soln_dofs, const unsigned int n_metric_dofs, unsigned int &w_start, unsigned int &w_end, unsigned int &x_start, unsigned int &x_end)
void	automatic_differentiation_indexing_2 (const bool compute_dRdW, const bool compute_dRdX, const bool compute_d2R, const unsigned int n_soln_dofs_int, const unsigned int n_soln_dofs_ext, const unsigned int n_metric_dofs, unsigned int &w_int_start, unsigned int &w_int_end, unsigned int &w_ext_start, unsigned int &w_ext_end, unsigned int &x_int_start, unsigned int &x_int_end, unsigned int &x_ext_start, unsigned int &x_ext_end)
void	set_current_time (const real current_time_input)
	Sets the current time within DG to be used for unsteady source terms.
void	allocate_auxiliary_equation ()
	Allocates the auxiliary equations' variables and right hand side (primarily for Strong form diffusive)
virtual void	assemble_auxiliary_residual (const bool compute_dRdW, const bool compute_dRdX, const bool compute_d2R)=0
	Asembles the auxiliary equations' residuals and solves. Note: This function cannot be automatically differentiated.
virtual void	allocate_dual_vector (const bool compute_d2R)=0
	Allocate the dual vector for optimization.
virtual void	build_volume_metric_operators (const unsigned int poly_degree, const unsigned int grid_degree, const std::vector< double > &metric_coeffs, OPERATOR::metric_operators< double, dim, 2 *dim > &metric_oper, OPERATOR::mapping_shape_functions< dim, 2 *dim > &mapping_basis, std::array< std::vector< double >, dim > &mapping_support_points)=0
	Builds volume metric operators (metric cofactor and determinant of metric Jacobian). For double type.
virtual void	build_volume_metric_operators (const unsigned int poly_degree, const unsigned int grid_degree, const std::vector< codi_JacobianComputationType > &metric_coeffs, OPERATOR::metric_operators< codi_JacobianComputationType, dim, 2 *dim > &metric_oper, OPERATOR::mapping_shape_functions< dim, 2 *dim > &mapping_basis, std::array< std::vector< codi_JacobianComputationType >, dim > &mapping_support_points)=0
	Builds volume metric operators (metric cofactor and determinant of metric Jacobian). For codi_JacobianComputationType.
virtual void	build_volume_metric_operators (const unsigned int poly_degree, const unsigned int grid_degree, const std::vector< codi_HessianComputationType > &metric_coeffs, OPERATOR::metric_operators< codi_HessianComputationType, dim, 2 *dim > &metric_oper, OPERATOR::mapping_shape_functions< dim, 2 *dim > &mapping_basis, std::array< std::vector< codi_HessianComputationType >, dim > &mapping_support_points)=0
	Builds volume metric operators (metric cofactor and determinant of metric Jacobian). For codi_HessianComputationType.
void	update_artificial_dissipation_discontinuity_sensor ()
	Update discontinuity sensor. More...
virtual void	allocate_model_variables ()=0
	Allocate the necessary variables declared in src/physics/model.h.
virtual void	update_model_variables ()=0
	Update the necessary variables declared in src/physics/model.h.
virtual void	set_unsteady_model_time_step (const double time_step)=0
	Set the unsteady time step variable declared in src/physics/model.h.
virtual void	set_use_auxiliary_eq ()=0
	Set use_auxiliary_eq flag.
virtual void	set_store_vol_flux_nodes ()=0
	Set store_vol_flux_nodes flag.
virtual void	set_store_surf_flux_nodes ()=0
	Set store_surf_flux_nodes flag.

Public Attributes
const Parameters::AllParameters *const	all_parameters
	Pointer to all parameters.
const int	nstate
	Number of state variables. More...
const unsigned int	initial_degree
	Initial polynomial degree assigned during constructor.
const unsigned int	max_degree
	Maximum degree used for p-refi1nement. More...
const unsigned int	max_grid_degree
	Maximum grid degree used for hp-refi1nement. More...
std::shared_ptr< Triangulation >	triangulation
	Mesh.
dealii::SparsityPattern	sparsity_pattern
	Sparsity pattern used on the system_matrix. More...
dealii::SparsityPattern	mass_sparsity_pattern
	Sparsity pattern used on the system_matrix. More...
dealii::TrilinosWrappers::SparseMatrix	time_scaled_global_mass_matrix
	Global mass matrix divided by the time scales. More...
dealii::TrilinosWrappers::SparseMatrix	global_mass_matrix
	Global mass matrix. More...
dealii::TrilinosWrappers::SparseMatrix	global_inverse_mass_matrix
	Global inverser mass matrix. More...
dealii::TrilinosWrappers::SparseMatrix	global_mass_matrix_auxiliary
	Global auxiliary mass matrix. More...
dealii::TrilinosWrappers::SparseMatrix	global_inverse_mass_matrix_auxiliary
	Global inverse of the auxiliary mass matrix.
dealii::TrilinosWrappers::SparseMatrix	system_matrix
dealii::TrilinosWrappers::SparseMatrix	system_matrix_transpose
std::unique_ptr< Epetra_RowMatrixTransposer >	epetra_rowmatrixtransposer_dRdW
	Epetra_RowMatrixTransposer used to transpose the system_matrix.
dealii::TrilinosWrappers::SparseMatrix	dRdXv
dealii::TrilinosWrappers::SparseMatrix	d2RdWdW
dealii::TrilinosWrappers::SparseMatrix	d2RdXdX
dealii::TrilinosWrappers::SparseMatrix	d2RdWdX
dealii::LinearAlgebra::distributed::Vector< double >	right_hand_side
	Residual of the current solution. More...
dealii::IndexSet	locally_owned_dofs
	Locally own degrees of freedom.
dealii::IndexSet	ghost_dofs
	Locally relevant ghost degrees of freedom.
dealii::IndexSet	locally_relevant_dofs
	Union of locally owned degrees of freedom and relevant ghost degrees of freedom.
dealii::IndexSet	locally_owned_dofs_grid
	Locally own degrees of freedom for the grid.
dealii::IndexSet	ghost_dofs_grid
	Locally relevant ghost degrees of freedom for the grid.
dealii::IndexSet	locally_relevant_dofs_grid
dealii::LinearAlgebra::distributed::Vector< double >	solution
	Current modal coefficients of the solution. More...
dealii::LinearAlgebra::distributed::Vector< double >	time_averaged_solution
dealii::LinearAlgebra::distributed::Vector< double >	fluctuating_quantities
std::array< dealii::LinearAlgebra::distributed::Vector< double >, dim >	auxiliary_right_hand_side
	The auxiliary equations' right hand sides.
std::array< dealii::LinearAlgebra::distributed::Vector< double >, dim >	auxiliary_solution
	The auxiliary equations' solution.
dealii::Vector< double >	cell_volume
	Time it takes for the maximum wavespeed to cross the cell domain. More...
dealii::Vector< double >	max_dt_cell
	Time it takes for the maximum wavespeed to cross the cell domain. More...
dealii::Vector< double >	reduced_mesh_weights
dealii::Vector< double >	artificial_dissipation_coeffs
	Artificial dissipation in each cell.
dealii::Vector< double >	artificial_dissipation_se
	Artificial dissipation error ratio sensor in each cell.
dealii::LinearAlgebra::distributed::Vector< real >	dual
	Current optimization dual variables corresponding to the residual constraints also known as the adjoint. More...
bool	update_artificial_diss
const dealii::hp::FECollection< dim >	fe_collection
	Finite Element Collection for p-finite-element to represent the solution. More...
dealii::hp::QCollection< dim >	volume_quadrature_collection
	Finite Element Collection to represent the high-order grid. More...
dealii::hp::QCollection< dim-1 >	face_quadrature_collection
	Quadrature used to evaluate face integrals.
const dealii::hp::FECollection< dim >	fe_collection_lagrange
	Lagrange basis used in strong form. More...
const dealii::hp::FECollection< 1 >	oneD_fe_collection
	1D Finite Element Collection for p-finite-element to represent the solution More...
const dealii::hp::FECollection< 1 >	oneD_fe_collection_1state
	1D Finite Element Collection for p-finite-element to represent the solution for a single state. More...
const dealii::hp::FECollection< 1 >	oneD_fe_collection_flux
	1D collocated flux basis used in strong form More...
dealii::hp::QCollection< 1 >	oneD_quadrature_collection
	1D quadrature to generate Lagrange polynomials for the sake of flux interpolation.
dealii::QGauss< 0 >	oneD_face_quadrature
	1D surface quadrature is always one single point for all poly degrees.
dealii::DoFHandler< dim >	dof_handler
	Finite Element Collection to represent the high-order grid. More...
std::shared_ptr< HighOrderGrid< dim, real, MeshType > >	high_order_grid
	High order grid that will provide the MappingFEField.
double	assemble_residual_time
	Computational time for assembling residual.
bool	freeze_artificial_dissipation
	Flag to freeze artificial dissipation.
double	max_artificial_dissipation_coeff
	Stores maximum artificial dissipation while assembling the residual.
bool	use_auxiliary_eq
	Flag for using the auxiliary equation.
bool	store_vol_flux_nodes
	Flag for storing volume flux nodes.
bool	store_surf_flux_nodes
	Flag for storing surface flux nodes.

Protected Member Functions
virtual void	assemble_volume_term_explicit (typename dealii::DoFHandler< dim >::active_cell_iterator cell, const dealii::types::global_dof_index current_cell_index, const dealii::FEValues< dim, dim > &fe_values_volume, const std::vector< dealii::types::global_dof_index > &current_dofs_indices, const std::vector< dealii::types::global_dof_index > &metric_dof_indices, const unsigned int poly_degree, const unsigned int grid_degree, dealii::Vector< real > &current_cell_rhs, const dealii::FEValues< dim, dim > &fe_values_lagrange)=0
	Evaluate the integral over the cell volume.

Protected Attributes
real	current_time
	The current time set in set_current_time()
const dealii::FE_Q< dim >	fe_q_artificial_dissipation
	Continuous distribution of artificial dissipation.
dealii::DoFHandler< dim >	dof_handler_artificial_dissipation
	Degrees of freedom handler for C0 artificial dissipation.
dealii::LinearAlgebra::distributed::Vector< double >	artificial_dissipation_c0
	Artificial dissipation coefficients.
const dealii::UpdateFlags	volume_update_flags
	Update flags needed at volume points. More...
const dealii::UpdateFlags	face_update_flags
	Update flags needed at face points. More...
const dealii::UpdateFlags	neighbor_face_update_flags = dealii::update_values | dealii::update_gradients | dealii::update_quadrature_points | dealii::update_JxW_values
	Update flags needed at neighbor' face points. More...
MPI_Comm	mpi_communicator
	MPI communicator.
dealii::ConditionalOStream	pcout
	Parallel std::cout that only outputs on mpi_rank==0.

Private Member Functions
virtual void	allocate_second_derivatives ()
	Allocates the second derivatives. More...
virtual void	allocate_dRdX ()
	Allocates the residual derivatives w.r.t the volume nodes. More...
void	allocate_artificial_dissipation ()
	Allocates variables of artificial dissipation. More...
template<typename DoFCellAccessorType >
real	evaluate_penalty_scaling (const DoFCellAccessorType &cell, const int iface, const dealii::hp::FECollection< dim > fe_collection) const
template<typename DoFCellAccessorType1 , typename DoFCellAccessorType2 >
bool	current_cell_should_do_the_work (const DoFCellAccessorType1 &current_cell, const DoFCellAccessorType2 &neighbor_cell) const
	In the case that two cells have the same coarseness, this function decides if the current cell should perform the work. More...
MassiveCollectionTuple	create_collection_tuple (const unsigned int max_degree, const int nstate, const Parameters::AllParameters *const parameters_input) const
	Used in the delegated constructor. More...

Private Attributes
dealii::LinearAlgebra::distributed::Vector< double >	solution_dRdW
dealii::LinearAlgebra::distributed::Vector< double >	volume_nodes_dRdW
double	CFL_mass_dRdW
	CFL used to add mass matrix in the optimization FlowConstraints class.
dealii::LinearAlgebra::distributed::Vector< double >	solution_dRdX
dealii::LinearAlgebra::distributed::Vector< double >	volume_nodes_dRdX
dealii::LinearAlgebra::distributed::Vector< double >	solution_d2R
dealii::LinearAlgebra::distributed::Vector< double >	volume_nodes_d2R
dealii::LinearAlgebra::distributed::Vector< double >	dual_d2R

Detailed Description

template<int dim, int nspecies, typename real, typename MeshType = dealii::parallel::distributed::Triangulation<dim>>
class PHiLiP::DGBase< dim, nspecies, real, MeshType >

DGBase is independent of the number of state variables.

This base class allows the use of arrays to efficiently allocate the data structures through std::array in the derived class DGBaseState. This class is the one being returned by the DGFactory and is the main interface for a user to call its main functions such as "assemble_residual".

Discretizes the problem

\[ \frac{\partial \mathbf{u}}{\partial t} + \boldsymbol\nabla \cdot ( \mathbf{F}_{conv}(\mathbf{u}) + \mathbf{F}_{diss}(\mathbf{u},\boldsymbol\nabla\mathbf{u}) ) = \mathbf{q} \]

Definition at line 82 of file dg_base.hpp.

Member Typedef Documentation

Triangulation

template<int dim, int nspecies, typename real, typename MeshType = dealii::parallel::distributed::Triangulation<dim>>

using PHiLiP::DGBase< dim, nspecies, real, MeshType >::Triangulation = MeshType

Triangulation to store the grid. In 1D, dealii::Triangulation<dim> is used. In 2D, 3D, dealii::parallel::distributed::Triangulation<dim> is used.

Definition at line 89 of file dg_base.hpp.

Constructor & Destructor Documentation

DGBase() [1/2]

template<int dim, int nspecies, typename real , typename MeshType >

PHiLiP::DGBase< dim, nspecies, real, MeshType >::DGBase	(	const int	nstate_input,
		const Parameters::AllParameters *const	parameters_input,
		const unsigned int	degree,
		const unsigned int	max_degree_input,
		const unsigned int	grid_degree_input,
		const std::shared_ptr< Triangulation >	triangulation_input
	)

Principal constructor that will call delegated constructor.

Will initialize mapping, fe_dg, all_parameters, volume_quadrature, and face_quadrature from DGBase. The it will new some FEValues that will be used to retrieve the finite element values at physical locations.

Passes create_collection_tuple() to the delegated constructor.

Definition at line 60 of file dg_base.cpp.

DGBase() [2/2]

template<int dim, int nspecies, typename real , typename MeshType >

PHiLiP::DGBase< dim, nspecies, real, MeshType >::DGBase	(	const int	nstate_input,
		const Parameters::AllParameters *const	parameters_input,
		const unsigned int	degree,
		const unsigned int	max_degree_input,
		const unsigned int	grid_degree_input,
		const std::shared_ptr< Triangulation >	triangulation_input,
		const MassiveCollectionTuple	collection_tuple
	)

Delegated constructor that initializes collections.

Since a function is used to generate multiple different objects, a delegated constructor is used to unwrap the tuple and initialize the collections.

The tuple is built from create_collection_tuple().

Definition at line 71 of file dg_base.cpp.

Member Function Documentation

add_mass_matrices()

template<int dim, int nspecies, typename real , typename MeshType >

void PHiLiP::DGBase< dim, nspecies, real, MeshType >::add_mass_matrices

(

const real

scale

)

Add mass matrices to the system scaled by a factor (likely time-step)

Although straightforward, this has not been tested yet. Will be required for accurate time-stepping or nonlinear problems

Definition at line 4441 of file dg_base.cpp.

add_time_scaled_mass_matrices()

template<int dim, int nspecies, typename real , typename MeshType >

void PHiLiP::DGBase< dim, nspecies, real, MeshType >::add_time_scaled_mass_matrices

(

)

Add time scaled mass matrices to the system.

For pseudotime-stepping where the scaling depends on wavespeed and cell-size.

Definition at line 4446 of file dg_base.cpp.

allocate_artificial_dissipation()

template<int dim, int nspecies, typename real , typename MeshType >

void PHiLiP::DGBase< dim, nspecies, real, MeshType >::allocate_artificial_dissipation ( )

private

Allocates variables of artificial dissipation.

It is called by allocate_system() when artificial dissipation is set to true in the parameters file.

Definition at line 3606 of file dg_base.cpp.

allocate_dRdX()

template<int dim, int nspecies, typename real , typename MeshType >

void PHiLiP::DGBase< dim, nspecies, real, MeshType >::allocate_dRdX ( )

privatevirtual

Allocates the residual derivatives w.r.t the volume nodes.

Is called when assembling the residual's second derivatives, and is currently empty due to being cleared by the allocate_system().

Definition at line 3651 of file dg_base.cpp.

allocate_second_derivatives()

template<int dim, int nspecies, typename real , typename MeshType >

void PHiLiP::DGBase< dim, nspecies, real, MeshType >::allocate_second_derivatives ( )

privatevirtual

Allocates the second derivatives.

Is called when assembling the residual's second derivatives, and is currently empty due to being cleared by the allocate_system().

Definition at line 3625 of file dg_base.cpp.

allocate_system()

template<int dim, int nspecies, typename real , typename MeshType >

void PHiLiP::DGBase< dim, nspecies, real, MeshType >::allocate_system ( const bool  compute_dRdW = true, const bool  compute_dRdX = true, const bool  compute_d2R = true  )

virtual

Allocates the system.

Must be done after setting the mesh and before assembling the system.

Definition at line 3478 of file dg_base.cpp.

apply_global_mass_matrix()

template<int dim, int nspecies, typename real , typename MeshType >

void PHiLiP::DGBase< dim, nspecies, real, MeshType >::apply_global_mass_matrix	(	const dealii::LinearAlgebra::distributed::Vector< double > &	input_vector,
		dealii::LinearAlgebra::distributed::Vector< double > &	output_vector,
		const bool	use_auxiliary_eq = false,
		const bool	use_unmodified_mass_matrix = false
	)

Applies the local metric dependent mass matrices when the global is not stored.

We use matrix-free methods to apply the local mass matrix on-the-fly in each cell using sum-factorization techniques. use_unmodified_mass_matrix flag allows the unmodified mass matrix to be used for FR, i.e., use M rather than M+K. For example, if this function is used for an inner product <a,b>, setting use_unmodified_mass_matrix = true will result in an M norm (L2) inner product, whereas setting use_unmodified_mass_matrix = false will result in an M+K norm (broken Sobolev) inner product.

Definition at line 4263 of file dg_base.cpp.

apply_inverse_global_mass_matrix()

template<int dim, int nspecies, typename real , typename MeshType >

void PHiLiP::DGBase< dim, nspecies, real, MeshType >::apply_inverse_global_mass_matrix	(	const dealii::LinearAlgebra::distributed::Vector< double > &	input_vector,
		dealii::LinearAlgebra::distributed::Vector< double > &	output_vector,
		const bool	use_auxiliary_eq = false
	)

Applies the inverse of the local metric dependent mass matrices when the global is not stored.

We use matrix-free methods to apply the inverse of the local mass matrix on-the-fly in each cell using sum-factorization techniques.

Definition at line 4089 of file dg_base.cpp.

assemble_boundary_codi_taped_derivatives_ad()

template<int dim, int nspecies, typename real , typename MeshType >

template<typename adtype >

std::enable_if<!std::is_same< adtype, double >::value, void >::type PHiLiP::DGBase< dim, nspecies, real, MeshType >::assemble_boundary_codi_taped_derivatives_ad	(	typename dealii::DoFHandler< dim >::active_cell_iterator	cell,
		const dealii::types::global_dof_index	current_cell_index,
		const unsigned int	iface,
		const unsigned int	boundary_id,
		const real	penalty,
		const std::vector< dealii::types::global_dof_index > &	soln_dofs_indices,
		const std::vector< dealii::types::global_dof_index > &	metric_dof_indices,
		const unsigned int	poly_degree,
		const unsigned int	grid_degree,
		OPERATOR::basis_functions< dim, 2 *dim > &	soln_basis,
		OPERATOR::basis_functions< dim, 2 *dim > &	flux_basis,
		OPERATOR::vol_projection_operator< dim, 2 *dim > &	soln_basis_projection_oper_int,
		OPERATOR::metric_operators< adtype, dim, 2 *dim > &	metric_oper,
		OPERATOR::mapping_shape_functions< dim, 2 *dim > &	mapping_basis,
		std::array< std::vector< adtype >, dim > &	mapping_support_points,
		dealii::hp::FEFaceValues< dim, dim > &	fe_values_collection_face_int,
		const dealii::FESystem< dim, dim > &	fe_soln,
		std::vector< real > &	local_rhs_cell,
		dealii::Tensor< 1, dim, std::vector< real >> &	local_auxiliary_RHS,
		const bool	compute_auxiliary_right_hand_side,
		const bool	compute_dRdW,
		const bool	compute_dRdX,
		const bool	compute_d2R
	)

Computes boundary term of the cell if the cell has a face at the boundary and performs automatic differentiation.

AD version.

Definition at line 1246 of file dg_base.cpp.

assemble_cell_residual_and_ad_derivatives()

template<int dim, int nspecies, typename real , typename MeshType >

template<typename adtype >

template void PHiLiP::DGBase< dim, nspecies, real, MeshType >::assemble_cell_residual_and_ad_derivatives< codi_HessianComputationType >	(	const dealii::TriaActiveIterator< dealii::DoFCellAccessor< dim, dim, false >> &	current_cell,
		const dealii::TriaActiveIterator< dealii::DoFCellAccessor< dim, dim, false >> &	current_metric_cell,
		const bool	compute_dRdW,
		const bool	compute_dRdX,
		const bool	compute_d2R,
		dealii::hp::FEValues< dim, dim > &	fe_values_collection_volume,
		dealii::hp::FEFaceValues< dim, dim > &	fe_values_collection_face_int,
		dealii::hp::FEFaceValues< dim, dim > &	fe_values_collection_face_ext,
		dealii::hp::FESubfaceValues< dim, dim > &	fe_values_collection_subface,
		dealii::hp::FEValues< dim, dim > &	fe_values_collection_volume_lagrange,
		OPERATOR::basis_functions< dim, 2 *dim > &	soln_basis_int,
		OPERATOR::basis_functions< dim, 2 *dim > &	soln_basis_ext,
		OPERATOR::basis_functions< dim, 2 *dim > &	flux_basis_int,
		OPERATOR::basis_functions< dim, 2 *dim > &	flux_basis_ext,
		OPERATOR::local_basis_stiffness< dim, 2 *dim > &	flux_basis_stiffness,
		OPERATOR::vol_projection_operator< dim, 2 *dim > &	soln_basis_projection_oper_int,
		OPERATOR::vol_projection_operator< dim, 2 *dim > &	soln_basis_projection_oper_ext,
		OPERATOR::mapping_shape_functions< dim, 2 *dim > &	mapping_basis,
		const bool	compute_auxiliary_right_hand_side,
		dealii::LinearAlgebra::distributed::Vector< double > &	rhs,
		std::array< dealii::LinearAlgebra::distributed::Vector< double >, dim > &	rhs_aux
	)

Used in assemble_residual().

IMPORTANT: This does not fully compute the cell residual since it might not perform the work on all the faces. All the active cells must be traversed to ensure that the right hand side is correct.

Definition at line 453 of file dg_base.cpp.

assemble_residual()

template<int dim, int nspecies, typename real , typename MeshType >

void PHiLiP::DGBase< dim, nspecies, real, MeshType >::assemble_residual	(	const bool	compute_dRdW = false,
		const bool	compute_dRdX = false,
		const bool	compute_d2R = false,
		const double	CFL_mass = 0.0
	)

Main loop of the DG class.

Evaluates the right-hand-side \( \mathbf{R(\mathbf{u}}) \) of the system

\[ \frac{\partial \mathbf{u}}{\partial t} = \mathbf{R(\mathbf{u}}) = - \boldsymbol\nabla \cdot ( \mathbf{F}_{conv}(\mathbf{u}) + \mathbf{F}_{diss}(\mathbf{u},\boldsymbol\nabla\mathbf{u}) ) + \mathbf{q} \]

As well as sets the

\[ \mathbf{\text{system_matrix}} = \frac{\partial \mathbf{R}}{\partial \mathbf{u}} \]

It loops over all the cells, evaluates the volume contributions, then loops over the faces of the current cell. Four scenarios may happen

1. Boundary condition.
2. Current face has children. Therefore, neighbor is finer. In that case, loop over neighbor faces to compute its face contributions.
3. Neighbor has same coarseness. Cell with lower global index will be used to compute the face contribution.
4. Neighbor is coarser. Therefore, the current cell is the finer one. Do nothing since this cell will be taken care of by scenario 2.

< FEValues of volume.

< FEValues of interior face.

< FEValues of exterior face.

< FEValues of subface.

Definition at line 2599 of file dg_base.cpp.

automatic_differentiation_indexing_1()

template<int dim, int nspecies, typename real , typename MeshType >

void PHiLiP::DGBase< dim, nspecies, real, MeshType >::automatic_differentiation_indexing_1	(	const bool	compute_dRdW,
		const bool	compute_dRdX,
		const bool	compute_d2R,
		const unsigned int	n_soln_dofs,
		const unsigned int	n_metric_dofs,
		unsigned int &	w_start,
		unsigned int &	w_end,
		unsigned int &	x_start,
		unsigned int &	x_end
	)

Derivative indexing when only 1 cell is concerned. Derivatives are ordered such that w comes first with index 0, then x. If derivatives with respect to w are not needed, then derivatives with respect to x will start at index 0. This function is for a single cell's DoFs.

Definition at line 2300 of file dg_base.cpp.

automatic_differentiation_indexing_2()

template<int dim, int nspecies, typename real , typename MeshType >

void PHiLiP::DGBase< dim, nspecies, real, MeshType >::automatic_differentiation_indexing_2	(	const bool	compute_dRdW,
		const bool	compute_dRdX,
		const bool	compute_d2R,
		const unsigned int	n_soln_dofs_int,
		const unsigned int	n_soln_dofs_ext,
		const unsigned int	n_metric_dofs,
		unsigned int &	w_int_start,
		unsigned int &	w_int_end,
		unsigned int &	w_ext_start,
		unsigned int &	w_ext_end,
		unsigned int &	x_int_start,
		unsigned int &	x_int_end,
		unsigned int &	x_ext_start,
		unsigned int &	x_ext_end
	)

Derivative indexing when 2 cells are concerned. Derivatives are ordered such that w comes first with index 0, then x. If derivatives with respect to w are not needed, then derivatives with respect to x will start at index 0.

Definition at line 2327 of file dg_base.cpp.

create_collection_tuple()

template<int dim, int nspecies, typename real , typename MeshType >

std::tuple< dealii::hp::FECollection< dim >, dealii::hp::QCollection< dim >, dealii::hp::QCollection< dim-1 >, dealii::hp::FECollection< dim >, dealii::hp::FECollection< 1 >, dealii::hp::FECollection< 1 >, dealii::hp::FECollection< 1 >, dealii::hp::QCollection< 1 > > PHiLiP::DGBase< dim, nspecies, real, MeshType >::create_collection_tuple ( const unsigned int  max_degree, const int  nstate, const Parameters::AllParameters *const  parameters_input  ) const

private

Used in the delegated constructor.

The main reason we use this weird function is because all of the above objects need to be looped with the various p-orders. This function allows us to do this in a single function instead of having like 6 different functions to initialize each of them.

Definition at line 142 of file dg_base.cpp.

current_cell_should_do_the_work()

template<int dim, int nspecies, typename real , typename MeshType >

template<typename DoFCellAccessorType1 , typename DoFCellAccessorType2 >

bool PHiLiP::DGBase< dim, nspecies, real, MeshType >::current_cell_should_do_the_work ( const DoFCellAccessorType1 &  current_cell, const DoFCellAccessorType2 &  neighbor_cell  ) const

private

In the case that two cells have the same coarseness, this function decides if the current cell should perform the work.

In the case the neighbor is a ghost cell, we let the processor with the lower rank do the work on that face. We cannot use the cell->index() because the index is relative to the distributed triangulation. Therefore, the cell index of a ghost cell might be different to the physical cell index even if they refer to the same cell.

For a locally owned neighbor cell, cell with lower index does work or if both cells have same index, then cell at the lower level does the work See https://www.dealii.org/developer/doxygen/deal.II/classTriaAccessorBase.html#a695efcbe84fefef3e4c93ee7bdb446ad

Definition at line 417 of file dg_base.cpp.

discontinuity_sensor()

template<int dim, int nspecies, typename real , typename MeshType >

template<typename real2 >

template RadFadType PHiLiP::DGBase< dim, nspecies, real, MeshType >::discontinuity_sensor< RadFadType >	(	const dealii::Quadrature< dim > &	volume_quadrature,
		const std::vector< real2 > &	soln_coeff_high,
		const dealii::FiniteElement< dim, dim > &	fe_high,
		const std::vector< real2 > &	jac_det
	)

Discontinuity sensor with 4 parameters, based on projecting to p-1.

Definition at line 4571 of file dg_base.cpp.

evaluate_penalty_scaling()

template<int dim, int nspecies, typename real , typename MeshType >

template<typename DoFCellAccessorType >

real PHiLiP::DGBase< dim, nspecies, real, MeshType >::evaluate_penalty_scaling ( const DoFCellAccessorType &  cell, const int  iface, const dealii::hp::FECollection< dim >  fe_collection  ) const

private

Evaluate the average penalty term at the face. For a cell with solution of degree p, and Hausdorff measure h, which represents the element dimension orthogonal to the face, the penalty term is given by p*(p+1)/h .

Definition at line 397 of file dg_base.cpp.

evaluate_time_steps()

template<int dim, int nspecies, typename real, typename MeshType = dealii::parallel::distributed::Triangulation<dim>>

std::vector<real> PHiLiP::DGBase< dim, nspecies, real, MeshType >::evaluate_time_steps

(

const bool

exact_time_stepping

)

Evaluates the maximum stable time step.

If exact_time_stepping = true, use the same time step for the entire solution NOT YET IMPLEMENTED

getValue()

template<int dim, int nspecies, typename real , typename MeshType >

template<typename real2 >

double PHiLiP::DGBase< dim, nspecies, real, MeshType >::getValue

(

const real2 &

x

)

Returns the value from a CoDiPack variable.

The recursive calling allows to retrieve nested CoDiPack types.

Definition at line 2290 of file dg_base.cpp.

reinit()

template<int dim, int nspecies, typename real , typename MeshType >

void PHiLiP::DGBase< dim, nspecies, real, MeshType >::reinit

(

)

Reinitializes the DG object after a change of triangulation.

Calls respective function for high-order-grid and initializes dof_handler again. Also resets all fe_degrees to intial_degree set during constructor.

Definition at line 112 of file dg_base.cpp.

set_all_cells_fe_degree()

template<int dim, int nspecies, typename real , typename MeshType >

void PHiLiP::DGBase< dim, nspecies, real, MeshType >::set_all_cells_fe_degree

(

const unsigned int

degree

)

Refers to a collection Mappings, which represents the high-order grid.

Since we are interested in performing mesh movement for optimization purposes, this is not a constant member variables.

Definition at line 292 of file dg_base.cpp.

set_anisotropic_flags()

template<int dim, int nspecies, typename real, typename MeshType = dealii::parallel::distributed::Triangulation<dim>>

void PHiLiP::DGBase< dim, nspecies, real, MeshType >::set_anisotropic_flags

(

)

Set anisotropic flags based on jump indicator.

Some cells must have already been tagged for refinement through some other indicator

time_scale_solution_update()

template<int dim, int nspecies, typename real , typename MeshType >

void PHiLiP::DGBase< dim, nspecies, real, MeshType >::time_scale_solution_update	(	dealii::LinearAlgebra::distributed::Vector< double > &	solution_update,
		const real	CFL
	)		const

Scales a solution update with the appropriate maximum time step.

Used for steady state solutions using the explicit ODE solver.

Definition at line 264 of file dg_base.cpp.

time_scaled_mass_matrices()

template<int dim, int nspecies, typename real , typename MeshType >

void PHiLiP::DGBase< dim, nspecies, real, MeshType >::time_scaled_mass_matrices

(

const real

scale

)

Evaluate the time_scaled_global_mass_matrix such that the maximum time step cell-wise is taken into account.

Definition at line 4451 of file dg_base.cpp.

update_artificial_dissipation_discontinuity_sensor()

template<int dim, int nspecies, typename real , typename MeshType >

void PHiLiP::DGBase< dim, nspecies, real, MeshType >::update_artificial_dissipation_discontinuity_sensor

(

)

Update discontinuity sensor.

< FEValues of volume.

Definition at line 2369 of file dg_base.cpp.

Member Data Documentation

cell_volume

template<int dim, int nspecies, typename real, typename MeshType = dealii::parallel::distributed::Triangulation<dim>>

dealii::Vector<double> PHiLiP::DGBase< dim, nspecies, real, MeshType >::cell_volume

Time it takes for the maximum wavespeed to cross the cell domain.

Uses evaluate_CFL() which would be defined in the subclasses. This is because DGBase isn't templated on nstate and therefore, can't use the Physics to compute maximum wavespeeds.

Definition at line 454 of file dg_base.hpp.

d2RdWdW

template<int dim, int nspecies, typename real, typename MeshType = dealii::parallel::distributed::Triangulation<dim>>

dealii::TrilinosWrappers::SparseMatrix PHiLiP::DGBase< dim, nspecies, real, MeshType >::d2RdWdW

System matrix corresponding to the second derivatives of the right_hand_side with respect to the solution

Definition at line 360 of file dg_base.hpp.

d2RdWdX

template<int dim, int nspecies, typename real, typename MeshType = dealii::parallel::distributed::Triangulation<dim>>

dealii::TrilinosWrappers::SparseMatrix PHiLiP::DGBase< dim, nspecies, real, MeshType >::d2RdWdX

System matrix corresponding to the mixed second derivatives of the right_hand_side with respect to the solution and the volume volume_nodes

Definition at line 368 of file dg_base.hpp.

d2RdXdX

template<int dim, int nspecies, typename real, typename MeshType = dealii::parallel::distributed::Triangulation<dim>>

dealii::TrilinosWrappers::SparseMatrix PHiLiP::DGBase< dim, nspecies, real, MeshType >::d2RdXdX

System matrix corresponding to the second derivatives of the right_hand_side with respect to the volume volume_nodes

Definition at line 364 of file dg_base.hpp.

dof_handler

template<int dim, int nspecies, typename real, typename MeshType = dealii::parallel::distributed::Triangulation<dim>>

dealii::DoFHandler<dim> PHiLiP::DGBase< dim, nspecies, real, MeshType >::dof_handler

Finite Element Collection to represent the high-order grid.

This is a collection of FESystems. Unfortunately, deal.II doesn't have a working hp Mapping FE field. Therefore, every grid/cell will use the maximal polynomial mapping regardless of the solution order.Degrees of freedom handler

Definition at line 1175 of file dg_base.hpp.

dRdXv

template<int dim, int nspecies, typename real, typename MeshType = dealii::parallel::distributed::Triangulation<dim>>

dealii::TrilinosWrappers::SparseMatrix PHiLiP::DGBase< dim, nspecies, real, MeshType >::dRdXv

System matrix corresponding to the derivative of the right_hand_side with respect to the volume volume_nodes Xv

Definition at line 356 of file dg_base.hpp.

dual

template<int dim, int nspecies, typename real, typename MeshType = dealii::parallel::distributed::Triangulation<dim>>

dealii::LinearAlgebra::distributed::Vector<real> PHiLiP::DGBase< dim, nspecies, real, MeshType >::dual

Current optimization dual variables corresponding to the residual constraints also known as the adjoint.

This is used to evaluate the dot-product between the dual and the 2nd derivatives of the residual since storing the 2nd order partials of the residual is a very large 3rd order tensor.

Definition at line 483 of file dg_base.hpp.

dual_d2R

template<int dim, int nspecies, typename real, typename MeshType = dealii::parallel::distributed::Triangulation<dim>>

dealii::LinearAlgebra::distributed::Vector<double> PHiLiP::DGBase< dim, nspecies, real, MeshType >::dual_d2R

private

Dual variables to compute d2R last Will be used to avoid recomputing d2R.

Definition at line 446 of file dg_base.hpp.

face_update_flags

template<int dim, int nspecies, typename real, typename MeshType = dealii::parallel::distributed::Triangulation<dim>>

const dealii::UpdateFlags PHiLiP::DGBase< dim, nspecies, real, MeshType >::face_update_flags

protected

Initial value:

= dealii::update_values | dealii::update_gradients | dealii::update_quadrature_points | dealii::update_JxW_values | dealii::update_normal_vectors
        | dealii::update_jacobians

Update flags needed at face points.

Definition at line 1215 of file dg_base.hpp.

fe_collection

template<int dim, int nspecies, typename real, typename MeshType = dealii::parallel::distributed::Triangulation<dim>>

const dealii::hp::FECollection<dim> PHiLiP::DGBase< dim, nspecies, real, MeshType >::fe_collection

Finite Element Collection for p-finite-element to represent the solution.

This is a collection of FESystems

Definition at line 1120 of file dg_base.hpp.

fe_collection_lagrange

template<int dim, int nspecies, typename real, typename MeshType = dealii::parallel::distributed::Triangulation<dim>>

const dealii::hp::FECollection<dim> PHiLiP::DGBase< dim, nspecies, real, MeshType >::fe_collection_lagrange

Lagrange basis used in strong form.

This is a collection of scalar Lagrange bases

Definition at line 1137 of file dg_base.hpp.

global_inverse_mass_matrix

template<int dim, int nspecies, typename real, typename MeshType = dealii::parallel::distributed::Triangulation<dim>>

dealii::TrilinosWrappers::SparseMatrix PHiLiP::DGBase< dim, nspecies, real, MeshType >::global_inverse_mass_matrix

Global inverser mass matrix.

Should be block diagonal where each block contains the inverse mass matrix of each cell.

Definition at line 332 of file dg_base.hpp.

global_mass_matrix

template<int dim, int nspecies, typename real, typename MeshType = dealii::parallel::distributed::Triangulation<dim>>

dealii::TrilinosWrappers::SparseMatrix PHiLiP::DGBase< dim, nspecies, real, MeshType >::global_mass_matrix

Global mass matrix.

Should be block diagonal where each block contains the mass matrix of each cell.

Definition at line 329 of file dg_base.hpp.

global_mass_matrix_auxiliary

template<int dim, int nspecies, typename real, typename MeshType = dealii::parallel::distributed::Triangulation<dim>>

dealii::TrilinosWrappers::SparseMatrix PHiLiP::DGBase< dim, nspecies, real, MeshType >::global_mass_matrix_auxiliary

Global auxiliary mass matrix.

Note that it has a mass matrix in each dimension since the auxiliary variable is a tensor of size dim. We use the same matrix in each dim.

Definition at line 336 of file dg_base.hpp.

locally_relevant_dofs_grid

template<int dim, int nspecies, typename real, typename MeshType = dealii::parallel::distributed::Triangulation<dim>>

dealii::IndexSet PHiLiP::DGBase< dim, nspecies, real, MeshType >::locally_relevant_dofs_grid

Union of locally owned degrees of freedom and relevant ghost degrees of freedom for the grid

Definition at line 404 of file dg_base.hpp.

mass_sparsity_pattern

template<int dim, int nspecies, typename real, typename MeshType = dealii::parallel::distributed::Triangulation<dim>>

dealii::SparsityPattern PHiLiP::DGBase< dim, nspecies, real, MeshType >::mass_sparsity_pattern

Sparsity pattern used on the system_matrix.

Not sure we need to store it.

Definition at line 321 of file dg_base.hpp.

max_degree

template<int dim, int nspecies, typename real, typename MeshType = dealii::parallel::distributed::Triangulation<dim>>

const unsigned int PHiLiP::DGBase< dim, nspecies, real, MeshType >::max_degree

Maximum degree used for p-refi1nement.

This is known through the constructor parameters. DGBase cannot use nstate as a compile-time known.

Definition at line 104 of file dg_base.hpp.

max_dt_cell

template<int dim, int nspecies, typename real, typename MeshType = dealii::parallel::distributed::Triangulation<dim>>

dealii::Vector<double> PHiLiP::DGBase< dim, nspecies, real, MeshType >::max_dt_cell

Time it takes for the maximum wavespeed to cross the cell domain.

Uses evaluate_CFL() which would be defined in the subclasses. This is because DGBase isn't templated on nstate and therefore, can't use the Physics to compute maximum wavespeeds.

Definition at line 461 of file dg_base.hpp.

max_grid_degree

template<int dim, int nspecies, typename real, typename MeshType = dealii::parallel::distributed::Triangulation<dim>>

const unsigned int PHiLiP::DGBase< dim, nspecies, real, MeshType >::max_grid_degree

Maximum grid degree used for hp-refi1nement.

This is known through the constructor parameters. DGBase cannot use nstate as a compile-time known.

Definition at line 109 of file dg_base.hpp.

neighbor_face_update_flags

template<int dim, int nspecies, typename real, typename MeshType = dealii::parallel::distributed::Triangulation<dim>>

const dealii::UpdateFlags PHiLiP::DGBase< dim, nspecies, real, MeshType >::neighbor_face_update_flags = dealii::update_values | dealii::update_gradients | dealii::update_quadrature_points | dealii::update_JxW_values

protected

Update flags needed at neighbor' face points.

NOTE: With hp-adaptation, might need to query neighbor's quadrature points depending on the order of the cells.

Definition at line 1219 of file dg_base.hpp.

nstate

template<int dim, int nspecies, typename real, typename MeshType = dealii::parallel::distributed::Triangulation<dim>>

const int PHiLiP::DGBase< dim, nspecies, real, MeshType >::nstate

Number of state variables.

This is known through the constructor parameters. DGBase cannot use nstate as a compile-time known.

Definition at line 96 of file dg_base.hpp.

oneD_fe_collection

template<int dim, int nspecies, typename real, typename MeshType = dealii::parallel::distributed::Triangulation<dim>>

const dealii::hp::FECollection<1> PHiLiP::DGBase< dim, nspecies, real, MeshType >::oneD_fe_collection

1D Finite Element Collection for p-finite-element to represent the solution

This is a collection of FESystems for 1D.

Definition at line 1143 of file dg_base.hpp.

oneD_fe_collection_1state

template<int dim, int nspecies, typename real, typename MeshType = dealii::parallel::distributed::Triangulation<dim>>

const dealii::hp::FECollection<1> PHiLiP::DGBase< dim, nspecies, real, MeshType >::oneD_fe_collection_1state

1D Finite Element Collection for p-finite-element to represent the solution for a single state.

This is a collection of FESystems for 1D. Since each state is represented by the same polynomial degree, for the RHS, we only need to store the 1D basis functions for a single state.

Definition at line 1150 of file dg_base.hpp.

oneD_fe_collection_flux

template<int dim, int nspecies, typename real, typename MeshType = dealii::parallel::distributed::Triangulation<dim>>

const dealii::hp::FECollection<1> PHiLiP::DGBase< dim, nspecies, real, MeshType >::oneD_fe_collection_flux

1D collocated flux basis used in strong form

This is a collection of collocated Lagrange bases for 1D.

Definition at line 1153 of file dg_base.hpp.

right_hand_side

template<int dim, int nspecies, typename real, typename MeshType = dealii::parallel::distributed::Triangulation<dim>>

dealii::LinearAlgebra::distributed::Vector<double> PHiLiP::DGBase< dim, nspecies, real, MeshType >::right_hand_side

Residual of the current solution.

Weak form.

The right-hand side sends all the term to the side of the source term.

Given

\[ \frac{\partial \mathbf{u}}{\partial t} + \boldsymbol\nabla \cdot ( \mathbf{F}_{conv}(\mathbf{u}) + \mathbf{F}_{diss}(\mathbf{u},\boldsymbol\nabla\mathbf{u}) ) = \mathbf{q} \]

The right-hand side is given by

\[ \mathbf{\text{rhs}} = - \boldsymbol\nabla \cdot ( \mathbf{F}_{conv}(\mathbf{u}) + \mathbf{F}_{diss}(\mathbf{u},\boldsymbol\nabla\mathbf{u}) ) + \mathbf{q} \]

It is important to note that the \(\mathbf{F}_{diss}\) is positive in the DG formulation. Therefore, the PhysicsBase class should have a negative when considering stable applications of diffusion.

Definition at line 396 of file dg_base.hpp.

solution

template<int dim, int nspecies, typename real, typename MeshType = dealii::parallel::distributed::Triangulation<dim>>

dealii::LinearAlgebra::distributed::Vector<double> PHiLiP::DGBase< dim, nspecies, real, MeshType >::solution

Current modal coefficients of the solution.

Note that the current processor has read-access to all locally_relevant_dofs and has write-access to all locally_owned_dofs

Definition at line 409 of file dg_base.hpp.

solution_d2R

template<int dim, int nspecies, typename real, typename MeshType = dealii::parallel::distributed::Triangulation<dim>>

dealii::LinearAlgebra::distributed::Vector<double> PHiLiP::DGBase< dim, nspecies, real, MeshType >::solution_d2R

private

Modal coefficients of the solution used to compute d2R last Will be used to avoid recomputing d2R.

Definition at line 440 of file dg_base.hpp.

solution_dRdW

template<int dim, int nspecies, typename real, typename MeshType = dealii::parallel::distributed::Triangulation<dim>>

dealii::LinearAlgebra::distributed::Vector<double> PHiLiP::DGBase< dim, nspecies, real, MeshType >::solution_dRdW

private

Modal coefficients of the solution used to compute dRdW last Will be used to avoid recomputing dRdW.

Definition at line 423 of file dg_base.hpp.

solution_dRdX

template<int dim, int nspecies, typename real, typename MeshType = dealii::parallel::distributed::Triangulation<dim>>

dealii::LinearAlgebra::distributed::Vector<double> PHiLiP::DGBase< dim, nspecies, real, MeshType >::solution_dRdX

private

Modal coefficients of the solution used to compute dRdX last Will be used to avoid recomputing dRdX.

Definition at line 433 of file dg_base.hpp.

sparsity_pattern

template<int dim, int nspecies, typename real, typename MeshType = dealii::parallel::distributed::Triangulation<dim>>

dealii::SparsityPattern PHiLiP::DGBase< dim, nspecies, real, MeshType >::sparsity_pattern

Sparsity pattern used on the system_matrix.

Not sure we need to store it.

Definition at line 317 of file dg_base.hpp.

system_matrix

template<int dim, int nspecies, typename real, typename MeshType = dealii::parallel::distributed::Triangulation<dim>>

dealii::TrilinosWrappers::SparseMatrix PHiLiP::DGBase< dim, nspecies, real, MeshType >::system_matrix

System matrix corresponding to the derivative of the right_hand_side with respect to the solution

Definition at line 343 of file dg_base.hpp.

system_matrix_transpose

template<int dim, int nspecies, typename real, typename MeshType = dealii::parallel::distributed::Triangulation<dim>>

dealii::TrilinosWrappers::SparseMatrix PHiLiP::DGBase< dim, nspecies, real, MeshType >::system_matrix_transpose

System matrix corresponding to the derivative of the right_hand_side with respect to the solution TRANSPOSED.

Definition at line 347 of file dg_base.hpp.

time_scaled_global_mass_matrix

template<int dim, int nspecies, typename real, typename MeshType = dealii::parallel::distributed::Triangulation<dim>>

dealii::TrilinosWrappers::SparseMatrix PHiLiP::DGBase< dim, nspecies, real, MeshType >::time_scaled_global_mass_matrix

Global mass matrix divided by the time scales.

Should be block diagonal where each block contains the scaled mass matrix of each cell.

Definition at line 325 of file dg_base.hpp.

volume_nodes_d2R

template<int dim, int nspecies, typename real, typename MeshType = dealii::parallel::distributed::Triangulation<dim>>

dealii::LinearAlgebra::distributed::Vector<double> PHiLiP::DGBase< dim, nspecies, real, MeshType >::volume_nodes_d2R

private

Modal coefficients of the grid nodes used to compute d2R last Will be used to avoid recomputing d2R.

Definition at line 443 of file dg_base.hpp.

volume_nodes_dRdW

template<int dim, int nspecies, typename real, typename MeshType = dealii::parallel::distributed::Triangulation<dim>>

dealii::LinearAlgebra::distributed::Vector<double> PHiLiP::DGBase< dim, nspecies, real, MeshType >::volume_nodes_dRdW

private

Modal coefficients of the grid nodes used to compute dRdW last Will be used to avoid recomputing dRdW.

Definition at line 426 of file dg_base.hpp.

volume_nodes_dRdX

template<int dim, int nspecies, typename real, typename MeshType = dealii::parallel::distributed::Triangulation<dim>>

dealii::LinearAlgebra::distributed::Vector<double> PHiLiP::DGBase< dim, nspecies, real, MeshType >::volume_nodes_dRdX

private

Modal coefficients of the grid nodes used to compute dRdX last Will be used to avoid recomputing dRdX.

Definition at line 436 of file dg_base.hpp.

volume_quadrature_collection

template<int dim, int nspecies, typename real, typename MeshType = dealii::parallel::distributed::Triangulation<dim>>

dealii::hp::QCollection<dim> PHiLiP::DGBase< dim, nspecies, real, MeshType >::volume_quadrature_collection

Finite Element Collection to represent the high-order grid.

This is a collection of FESystems. Unfortunately, deal.II doesn't have a working hp Mapping FE field. Therefore, every grid/cell will use the maximal polynomial mapping regardless of the solution order.Quadrature used to evaluate volume integrals.

Definition at line 1131 of file dg_base.hpp.

volume_update_flags

template<int dim, int nspecies, typename real, typename MeshType = dealii::parallel::distributed::Triangulation<dim>>

const dealii::UpdateFlags PHiLiP::DGBase< dim, nspecies, real, MeshType >::volume_update_flags

protected

Initial value:

= dealii::update_values | dealii::update_gradients | dealii::update_quadrature_points | dealii::update_JxW_values
        | dealii::update_inverse_jacobians

Update flags needed at volume points.

Definition at line 1212 of file dg_base.hpp.

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The documentation for this class was generated from the following files:

• src/dg/dg_base.hpp
• src/dg/dg_base.cpp
• src/dg/residual_sparsity_patterns.cpp