ESFR correction matrix without jac dependence. More...
#include <operators.h>
Public Member Functions | |
| local_Flux_Reconstruction_operator (const int nstate_input, const unsigned int max_degree_input, const unsigned int grid_degree_input, const Parameters::AllParameters::Flux_Reconstruction FR_param_input) | |
| Constructor. | |
| void | get_Huynh_g2_parameter (const unsigned int curr_cell_degree, double &c) |
| Evaluates Huynh's g2 parameter for flux reconstruction. | |
| void | get_spectral_difference_parameter (const unsigned int curr_cell_degree, double &c) |
| Evaluates the spectral difference parameter for flux reconstruction. More... | |
| void | get_c_negative_FR_parameter (const unsigned int curr_cell_degree, double &c) |
| Evaluates the flux reconstruction parameter at the bottom limit where the scheme is unstable. More... | |
| void | get_c_negative_divided_by_two_FR_parameter (const unsigned int curr_cell_degree, double &c) |
| Evaluates the flux reconstruction parameter at the bottom limit where the scheme is unstable, divided by 2. More... | |
| void | get_c_plus_parameter (const unsigned int curr_cell_degree, double &c) |
| Gets the FR correction parameter corresponding to the maximum timestep. More... | |
| void | get_FR_correction_parameter (const unsigned int curr_cell_degree, double &c) |
| Gets the FR correction parameter for the primary equation and stores. More... | |
| void | build_local_Flux_Reconstruction_operator (const dealii::FullMatrix< double > &local_Mass_Matrix, const dealii::FullMatrix< double > &pth_derivative, const unsigned int n_dofs, const double c, dealii::FullMatrix< double > &Flux_Reconstruction_operator) |
| Computes a single local Flux_Reconstruction operator (ESFR correction operator) on the fly for a local element. More... | |
| void | build_1D_volume_operator (const dealii::FESystem< 1, 1 > &finite_element, const dealii::Quadrature< 1 > &quadrature) |
| Assembles the one dimensional operator. | |
| dealii::FullMatrix< double > | build_dim_Flux_Reconstruction_operator (const dealii::FullMatrix< double > &local_Mass_Matrix, const int nstate, const unsigned int n_dofs) |
| Computes the dim sized flux reconstruction operator with simplified tensor product form. More... | |
| dealii::FullMatrix< double > | build_dim_Flux_Reconstruction_operator_directly (const int nstate, const unsigned int n_dofs, dealii::FullMatrix< double > &pth_deriv, dealii::FullMatrix< double > &mass_matrix) |
| Computes the dim sized flux reconstruction operator for general Mass Matrix (needed for curvilinear). More... | |
 Public Member Functions inherited from PHiLiP::OPERATOR::SumFactorizedOperators< dim, n_faces, real > | |
| SumFactorizedOperators (const int nstate_input, const unsigned int max_degree_input, const unsigned int grid_degree_input) | |
| Precompute 1D operator in constructor. | |
| void | matrix_vector_mult (const std::vector< real > &input_vect, std::vector< real > &output_vect, const dealii::FullMatrix< double > &basis_x, const dealii::FullMatrix< double > &basis_y, const dealii::FullMatrix< double > &basis_z, const bool adding=false, const double factor=1.0) override |
| Computes a matrix-vector product using sum-factorization. Pass the one-dimensional basis, where x runs the fastest, then y, and z runs the slowest. Also, assume each one-dimensional basis is the same size. More... | |
| void | divergence_matrix_vector_mult (const dealii::Tensor< 1, dim, std::vector< real >> &input_vect, std::vector< real > &output_vect, const dealii::FullMatrix< double > &basis_x, const dealii::FullMatrix< double > &basis_y, const dealii::FullMatrix< double > &basis_z, const dealii::FullMatrix< double > &gradient_basis_x, const dealii::FullMatrix< double > &gradient_basis_y, const dealii::FullMatrix< double > &gradient_basis_z) |
| Computes the divergence using the sum factorization matrix-vector multiplication. More... | |
| void | divergence_matrix_vector_mult_1D (const dealii::Tensor< 1, dim, std::vector< real >> &input_vect, std::vector< real > &output_vect, const dealii::FullMatrix< double > &basis, const dealii::FullMatrix< double > &gradient_basis) |
| Computes the divergence using sum-factorization where the basis are the same in each direction. | |
| void | gradient_matrix_vector_mult (const std::vector< real > &input_vect, dealii::Tensor< 1, dim, std::vector< real >> &output_vect, const dealii::FullMatrix< double > &basis_x, const dealii::FullMatrix< double > &basis_y, const dealii::FullMatrix< double > &basis_z, const dealii::FullMatrix< double > &gradient_basis_x, const dealii::FullMatrix< double > &gradient_basis_y, const dealii::FullMatrix< double > &gradient_basis_z) |
| Computes the gradient of a scalar using sum-factorization. | |
| void | gradient_matrix_vector_mult_1D (const std::vector< real > &input_vect, dealii::Tensor< 1, dim, std::vector< real >> &output_vect, const dealii::FullMatrix< double > &basis, const dealii::FullMatrix< double > &gradient_basis) |
| Computes the gradient of a scalar using sum-factorization where the basis are the same in each direction. | |
| void | inner_product (const std::vector< real > &input_vect, const std::vector< real > &weight_vect, std::vector< real > &output_vect, const dealii::FullMatrix< double > &basis_x, const dealii::FullMatrix< double > &basis_y, const dealii::FullMatrix< double > &basis_z, const bool adding=false, const double factor=1.0) override |
| Computes the inner product between a matrix and a vector multiplied by some weight function. More... | |
| void | divergence_two_pt_flux_Hadamard_product (const dealii::Tensor< 1, dim, dealii::FullMatrix< real >> &input_mat, std::vector< real > &output_vect, const std::vector< real > &weights, const dealii::FullMatrix< double > &basis, const double scaling=2.0) |
| Computes the divergence of the 2pt flux Hadamard products, then sums the rows. More... | |
| void | surface_two_pt_flux_Hadamard_product (const dealii::FullMatrix< real > &input_mat, std::vector< real > &output_vect_vol, std::vector< real > &output_vect_surf, const std::vector< real > &weights, const std::array< dealii::FullMatrix< double >, 2 > &surf_basis, const unsigned int iface, const unsigned int dim_not_zero, const double scaling=2.0) |
| Computes the surface cross Hadamard products for skew-symmetric form from Eq. (15) in Chan, Jesse. "Skew-symmetric entropy stable modal discontinuous Galerkin formulations." Journal of Scientific Computing 81.1 (2019): 459-485. | |
| void | two_pt_flux_Hadamard_product (const dealii::FullMatrix< real > &input_mat, dealii::FullMatrix< real > &output_mat, const dealii::FullMatrix< double > &basis, const std::vector< real > &weights, const int direction) |
| Computes the Hadamard product ONLY for 2pt flux calculations. More... | |
| void | sum_factorized_Hadamard_sparsity_pattern (const unsigned int rows_size, const unsigned int columns_size, std::vector< std::array< unsigned int, dim >> &rows, std::vector< std::array< unsigned int, dim >> &columns) |
| Computes the rows and columns vectors with non-zero indices for sum-factorized Hadamard products. | |
| void | sum_factorized_Hadamard_basis_assembly (const unsigned int rows_size_1D, const unsigned int columns_size_1D, const std::vector< std::array< unsigned int, dim >> &rows, const std::vector< std::array< unsigned int, dim >> &columns, const dealii::FullMatrix< double > &basis, const std::vector< double > &weights, std::array< dealii::FullMatrix< double >, dim > &basis_sparse) |
| Constructs the \( n^d \times n\) basis operator storing all non-zero entries for a "sum-factorized" Hadamard product. | |
| void | sum_factorized_Hadamard_surface_sparsity_pattern (const unsigned int rows_size, const unsigned int columns_size, std::vector< unsigned int > &rows, std::vector< unsigned int > &columns, const int dim_not_zero) |
| Computes the rows and columns vectors with non-zero indices for surface sum-factorized Hadamard products. | |
| void | sum_factorized_Hadamard_surface_basis_assembly (const unsigned int rows_size, const unsigned int columns_size_1D, const std::vector< unsigned int > &rows, const std::vector< unsigned int > &columns, const dealii::FullMatrix< double > &basis, const std::vector< double > &weights, dealii::FullMatrix< double > &basis_sparse, const int dim_not_zero) |
| Constructs the \( n^{d-1} \times n\) basis operator storing all non-zero entries for a "sum-factorized" surface Hadamard product. | |
| void | matrix_vector_mult_1D (const std::vector< real > &input_vect, std::vector< real > &output_vect, const dealii::FullMatrix< double > &basis_x, const bool adding=false, const double factor=1.0) |
| Apply the matrix vector operation using the 1D operator in each direction. More... | |
| void | inner_product_1D (const std::vector< real > &input_vect, const std::vector< real > &weight_vect, std::vector< real > &output_vect, const dealii::FullMatrix< double > &basis_x, const bool adding=false, const double factor=1.0) |
| Apply the inner product operation using the 1D operator in each direction. | |
| void | matrix_vector_mult_surface_1D (const unsigned int face_number, const std::vector< real > &input_vect, std::vector< real > &output_vect, const std::array< dealii::FullMatrix< double >, 2 > &basis_surf, const dealii::FullMatrix< double > &basis_vol, const bool adding=false, const double factor=1.0) |
| Apply sum-factorization matrix vector multiplication on a surface. More... | |
| void | inner_product_surface_1D (const unsigned int face_number, const std::vector< real > &input_vect, const std::vector< real > &weight_vect, std::vector< real > &output_vect, const std::array< dealii::FullMatrix< double >, 2 > &basis_surf, const dealii::FullMatrix< double > &basis_vol, const bool adding=false, const double factor=1.0) |
| Apply sum-factorization inner product on a surface. | |
| void | Hadamard_product (const dealii::FullMatrix< real > &input_mat1, const dealii::FullMatrix< real > &input_mat2, dealii::FullMatrix< real > &output_mat) |
| Computes a single Hadamard product. More... | |
| Public Member Functions inherited from PHiLiP::OPERATOR::OperatorsBase< dim, n_faces, real > | |
| virtual | ~OperatorsBase ()=default |
| Destructor. | |
| OperatorsBase (const int nstate_input, const unsigned int max_degree_input, const unsigned int grid_degree_input) | |
| Constructor. | |
| dealii::FullMatrix< double > | tensor_product (const dealii::FullMatrix< double > &basis_x, const dealii::FullMatrix< double > &basis_y, const dealii::FullMatrix< double > &basis_z) |
| Returns the tensor product of matrices passed. | |
| dealii::FullMatrix< double > | tensor_product_state (const int nstate, const dealii::FullMatrix< double > &basis_x, const dealii::FullMatrix< double > &basis_y, const dealii::FullMatrix< double > &basis_z) |
| Returns the tensor product of matrices passed, but makes it sparse diagonal by state. More... | |
| double | compute_factorial (double n) |
| Standard function to compute factorial of a number. | |
Public Attributes | |
| unsigned int | current_degree |
| Stores the degree of the current poly degree. | |
| const Parameters::AllParameters::Flux_Reconstruction | FR_param_type |
| Flux reconstruction parameter type. | |
| double | FR_param |
| Flux reconstruction paramater value. | |
| Public Attributes inherited from PHiLiP::OPERATOR::SumFactorizedOperators< dim, n_faces, real > | |
| dealii::FullMatrix< double > | oneD_vol_operator |
| Stores the one dimensional volume operator. | |
| std::array< dealii::FullMatrix< double >, 2 > | oneD_surf_operator |
| Stores the one dimensional surface operator. More... | |
| dealii::FullMatrix< double > | oneD_grad_operator |
| Stores the one dimensional gradient operator. | |
| std::array< dealii::FullMatrix< double >, 2 > | oneD_surf_grad_operator |
| Stores the one dimensional surface gradient operator. | |
| Public Attributes inherited from PHiLiP::OPERATOR::OperatorsBase< dim, n_faces, real > | |
| const unsigned int | max_degree |
| Max polynomial degree. | |
| const unsigned int | max_grid_degree |
| Max grid degree. | |
| const int | nstate |
| Number of states. | |
Additional Inherited Members | |
| Protected Attributes inherited from PHiLiP::OPERATOR::OperatorsBase< dim, n_faces, real > | |
| unsigned int | max_grid_degree_check |
| Check to see if the metrics used are a higher order then the initialized grid. | |
| const MPI_Comm | mpi_communicator |
| MPI communicator. | |
| dealii::ConditionalOStream | pcout |
| Parallel std::cout that only outputs on mpi_rank==0. | |
Detailed Description
template<int dim, int n_faces, typename real>
class PHiLiP::OPERATOR::local_Flux_Reconstruction_operator< dim, n_faces, real >
ESFR correction matrix without jac dependence.
Definition at line 539 of file operators.h.
Member Function Documentation
◆ build_dim_Flux_Reconstruction_operator()
| dealii::FullMatrix< double > PHiLiP::OPERATOR::local_Flux_Reconstruction_operator< dim, n_faces, real >::build_dim_Flux_Reconstruction_operator | ( | const dealii::FullMatrix< double > & | local_Mass_Matrix, |
| const int | nstate, | ||
| const unsigned int | n_dofs | ||
| ) |
Computes the dim sized flux reconstruction operator with simplified tensor product form.
The formula for the dim sized flux reconstruction operator is \( \mathbf{K}_m = \sum_{s,v,w} c_{(s,v,w)} \Big( \mathbf{D}_\xi^s\mathbf{D}_\eta^v\mathbf{D}_\zeta^w \Big)^T \mathbf{M}_m \Big( \mathbf{D}_\xi^s\mathbf{D}_\eta^v\mathbf{D}_\zeta^w \Big) \), where \( c_{(s,v,w)} = c^{\frac{s}{p} + \frac{v}{p} +\frac{w}{p}}\). Please pass the number of dofs for the dim sized operator.
Definition at line 1617 of file operators.cpp.
◆ build_dim_Flux_Reconstruction_operator_directly()
| dealii::FullMatrix< double > PHiLiP::OPERATOR::local_Flux_Reconstruction_operator< dim, n_faces, real >::build_dim_Flux_Reconstruction_operator_directly | ( | const int | nstate, |
| const unsigned int | n_dofs, | ||
| dealii::FullMatrix< double > & | pth_deriv, | ||
| dealii::FullMatrix< double > & | mass_matrix | ||
| ) |
Computes the dim sized flux reconstruction operator for general Mass Matrix (needed for curvilinear).
The formula for the dim sized flux reconstruction operator is \( \mathbf{K}_m = \sum_{s,v,w} c_{(s,v,w)} \Big( \mathbf{D}_\xi^s\mathbf{D}_\eta^v\mathbf{D}_\zeta^w \Big)^T \mathbf{M}_m \Big( \mathbf{D}_\xi^s\mathbf{D}_\eta^v\mathbf{D}_\zeta^w \Big) \), where \( c_{(s,v,w)} = c^{\frac{s}{p} + \frac{v}{p} +\frac{w}{p}}\). Please pass the number of dofs for the dim sized operator. For pth deriv, please pass the 1D operator.
Definition at line 1556 of file operators.cpp.
◆ build_local_Flux_Reconstruction_operator()
| void PHiLiP::OPERATOR::local_Flux_Reconstruction_operator< dim, n_faces, real >::build_local_Flux_Reconstruction_operator | ( | const dealii::FullMatrix< double > & | local_Mass_Matrix, |
| const dealii::FullMatrix< double > & | pth_derivative, | ||
| const unsigned int | n_dofs, | ||
| const double | c, | ||
| dealii::FullMatrix< double > & | Flux_Reconstruction_operator | ||
| ) |
Computes a single local Flux_Reconstruction operator (ESFR correction operator) on the fly for a local element.
Note that this is dependent on the Mass Matrix, so for metric Jacobian dependent \(K_m\), pass the metric Jacobian dependent Mass Matrix \(M_m\).
Definition at line 1522 of file operators.cpp.
◆ get_c_negative_divided_by_two_FR_parameter()
| void PHiLiP::OPERATOR::local_Flux_Reconstruction_operator< dim, n_faces, real >::get_c_negative_divided_by_two_FR_parameter | ( | const unsigned int | curr_cell_degree, |
| double & | c | ||
| ) |
Evaluates the flux reconstruction parameter at the bottom limit where the scheme is unstable, divided by 2.
Value from Allaneau, Y., and Antony Jameson. "Connections between the filtered discontinuous Galerkin method and the flux reconstruction approach to high order discretizations." Computer Methods in Applied Mechanics and Engineering 200.49-52 (2011): 3628-3636. Commonly in the lterature we use this value to show the approach to the bottom limit of stability.
Definition at line 1456 of file operators.cpp.
◆ get_c_negative_FR_parameter()
| void PHiLiP::OPERATOR::local_Flux_Reconstruction_operator< dim, n_faces, real >::get_c_negative_FR_parameter | ( | const unsigned int | curr_cell_degree, |
| double & | c | ||
| ) |
Evaluates the flux reconstruction parameter at the bottom limit where the scheme is unstable.
Value from Allaneau, Y., and Antony Jameson. "Connections between the filtered discontinuous Galerkin method and the flux reconstruction approach to high order discretizations." Computer Methods in Applied Mechanics and Engineering 200.49-52 (2011): 3628-3636.
Definition at line 1445 of file operators.cpp.
◆ get_c_plus_parameter()
| void PHiLiP::OPERATOR::local_Flux_Reconstruction_operator< dim, n_faces, real >::get_c_plus_parameter | ( | const unsigned int | curr_cell_degree, |
| double & | c | ||
| ) |
Gets the FR correction parameter corresponding to the maximum timestep.
Note that this parameter is also a good approximation for when the FR scheme begins to lose an order of accuracy, but the original definition is that it corresponds to the maximum timestep. Value from Table 3.4 in Castonguay, Patrice. High-order energy stable flux reconstruction schemes for fluid flow simulations on unstructured grids. Stanford University, 2012.
Definition at line 1464 of file operators.cpp.
◆ get_FR_correction_parameter()
| void PHiLiP::OPERATOR::local_Flux_Reconstruction_operator< dim, n_faces, real >::get_FR_correction_parameter | ( | const unsigned int | curr_cell_degree, |
| double & | c | ||
| ) |
Gets the FR correction parameter for the primary equation and stores.
These values are name specified in parameters/all_parameters.h, passed through control file/or test and here converts/stores as value. Please note that in all the functions within this that evaluate the parameter, we divide the value in the literature by 2.0 because our basis are contructed by an orthonormal Legendre basis rather than the orthogonal basis in the literature. Also, we have the additional scaling by pow(pow(2.0,curr_cell_degree),2) because our basis functions are defined on a reference element between [0,1], whereas the values in the literature are based on [-1,1]. For further details please refer to Cicchino, Alexander, and Siva Nadarajah. "A new norm and stability condition for tensor product flux reconstruction schemes." Journal of Computational Physics 429 (2021): 110025.
Definition at line 1492 of file operators.cpp.
◆ get_spectral_difference_parameter()
| void PHiLiP::OPERATOR::local_Flux_Reconstruction_operator< dim, n_faces, real >::get_spectral_difference_parameter | ( | const unsigned int | curr_cell_degree, |
| double & | c | ||
| ) |
Evaluates the spectral difference parameter for flux reconstruction.
Value from Allaneau, Y., and Antony Jameson. "Connections between the filtered discontinuous Galerkin method and the flux reconstruction approach to high order discretizations." Computer Methods in Applied Mechanics and Engineering 200.49-52 (2011): 3628-3636.
Definition at line 1434 of file operators.cpp.
The documentation for this class was generated from the following files:
- src/operators/operators.h
- src/operators/operators.cpp
