PHiLiP::OPERATOR::metric_operators< real, dim, n_faces > Class Template Reference
Base metric operators class that stores functions used in both the volume and on surface. More...
#include <operators.h>
Inheritance diagram for PHiLiP::OPERATOR::metric_operators< real, dim, n_faces >:
Collaboration diagram for PHiLiP::OPERATOR::metric_operators< real, dim, n_faces >:
Public Member Functions | |
| metric_operators (const int nstate_input, const unsigned int max_degree_input, const unsigned int grid_degree_input, const bool store_vol_flux_nodes_input=false, const bool store_surf_flux_nodes_input=false, const bool store_Jacobian_input=false) | |
| Constructor. | |
| void | transform_physical_to_reference (const dealii::Tensor< 1, dim, real > &phys, const dealii::Tensor< 2, dim, real > &metric_cofactor, dealii::Tensor< 1, dim, real > &ref) |
| Given a physical tensor, return the reference tensor. | |
| void | transform_reference_to_physical (const dealii::Tensor< 1, dim, real > &ref, const dealii::Tensor< 2, dim, real > &metric_cofactor, dealii::Tensor< 1, dim, real > &phys) |
| Given a reference tensor, return the physical tensor. | |
| void | transform_physical_to_reference_vector (const dealii::Tensor< 1, dim, std::vector< real >> &phys, const dealii::Tensor< 2, dim, std::vector< real >> &metric_cofactor, dealii::Tensor< 1, dim, std::vector< real >> &ref) |
| Given a physical tensor of vector of points, return the reference tensor of vector. | |
| void | transform_reference_unit_normal_to_physical_unit_normal (const unsigned int n_quad_pts, const dealii::Tensor< 1, dim, real > &ref, const dealii::Tensor< 2, dim, std::vector< real >> &metric_cofactor, std::vector< dealii::Tensor< 1, dim, real >> &phys) |
| Given a reference tensor, return the physical tensor. | |
| void | build_determinant_volume_metric_Jacobian (const unsigned int n_quad_pts, const unsigned int n_metric_dofs, const std::array< std::vector< real >, dim > &mapping_support_points, mapping_shape_functions< dim, n_faces, real > &mapping_basis) |
| Builds just the determinant of the volume metric determinant. | |
| void | build_volume_metric_operators (const unsigned int n_quad_pts, const unsigned int n_metric_dofs, const std::array< std::vector< real >, dim > &mapping_support_points, mapping_shape_functions< dim, n_faces, real > &mapping_basis, const bool use_invariant_curl_form=false) |
| Builds the volume metric operators. More... | |
| void | build_facet_metric_operators (const unsigned int iface, const unsigned int n_quad_pts, const unsigned int n_metric_dofs, const std::array< std::vector< real >, dim > &mapping_support_points, mapping_shape_functions< dim, n_faces, real > &mapping_basis, const bool use_invariant_curl_form=false) |
| Builds the facet metric operators. 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 | |
| const bool | store_Jacobian |
| Flag if store metric Jacobian at flux nodes. | |
| const bool | store_vol_flux_nodes |
| Flag if store metric Jacobian at flux nodes. | |
| const bool | store_surf_flux_nodes |
| Flag if store metric Jacobian at flux nodes. | |
| dealii::Tensor< 2, dim, std::vector< real > > | metric_cofactor_vol |
| The volume metric cofactor matrix. | |
| dealii::Tensor< 2, dim, std::vector< real > > | metric_cofactor_surf |
| The facet metric cofactor matrix, for ONE face. | |
| std::vector< real > | det_Jac_vol |
| The determinant of the metric Jacobian at volume cubature nodes. | |
| std::vector< real > | det_Jac_surf |
| The determinant of the metric Jacobian at facet cubature nodes. | |
| dealii::Tensor< 2, dim, std::vector< real > > | metric_Jacobian_vol_cubature |
| Stores the metric Jacobian at flux nodes. | |
| dealii::Tensor< 1, dim, std::vector< real > > | flux_nodes_vol |
| Stores the physical volume flux nodes. | |
| std::array< dealii::Tensor< 1, dim, std::vector< real > >, n_faces > | flux_nodes_surf |
| Stores the physical facet flux nodes. | |
| 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. | |
Protected Member Functions | |
| void | build_metric_Jacobian (const unsigned int n_quad_pts, const std::array< std::vector< real >, dim > &mapping_support_points, const dealii::FullMatrix< double > &basis_x_flux_nodes, const dealii::FullMatrix< double > &basis_y_flux_nodes, const dealii::FullMatrix< double > &basis_z_flux_nodes, const dealii::FullMatrix< double > &grad_basis_x_flux_nodes, const dealii::FullMatrix< double > &grad_basis_y_flux_nodes, const dealii::FullMatrix< double > &grad_basis_z_flux_nodes, std::vector< dealii::Tensor< 2, dim, real >> &local_Jac) |
| Builds the metric Jacobian evaluated at a vector of points. More... | |
| void | build_determinant_metric_Jacobian (const unsigned int n_quad_pts, const std::array< std::vector< real >, dim > &mapping_support_points, const dealii::FullMatrix< double > &basis_x_flux_nodes, const dealii::FullMatrix< double > &basis_y_flux_nodes, const dealii::FullMatrix< double > &basis_z_flux_nodes, const dealii::FullMatrix< double > &grad_basis_x_flux_nodes, const dealii::FullMatrix< double > &grad_basis_y_flux_nodes, const dealii::FullMatrix< double > &grad_basis_z_flux_nodes, std::vector< real > &det_metric_Jac) |
| Assembles the determinant of metric Jacobian. More... | |
| void | build_local_metric_cofactor_matrix (const unsigned int n_quad_pts, const unsigned int n_metric_dofs, const std::array< std::vector< real >, dim > &mapping_support_points, const dealii::FullMatrix< double > &basis_x_grid_nodes, const dealii::FullMatrix< double > &basis_y_grid_nodes, const dealii::FullMatrix< double > &basis_z_grid_nodes, const dealii::FullMatrix< double > &basis_x_flux_nodes, const dealii::FullMatrix< double > &basis_y_flux_nodes, const dealii::FullMatrix< double > &basis_z_flux_nodes, const dealii::FullMatrix< double > &grad_basis_x_grid_nodes, const dealii::FullMatrix< double > &grad_basis_y_grid_nodes, const dealii::FullMatrix< double > &grad_basis_z_grid_nodes, const dealii::FullMatrix< double > &grad_basis_x_flux_nodes, const dealii::FullMatrix< double > &grad_basis_y_flux_nodes, const dealii::FullMatrix< double > &grad_basis_z_flux_nodes, dealii::Tensor< 2, dim, std::vector< real >> &metric_cofactor, const bool use_invariant_curl_form=false) |
| Called on the fly and returns the metric cofactor at cubature nodes. | |
| void | compute_local_3D_cofactor (const unsigned int n_metric_dofs, const unsigned int n_quad_pts, const std::array< std::vector< real >, dim > &mapping_support_points, const dealii::FullMatrix< double > &basis_x_grid_nodes, const dealii::FullMatrix< double > &basis_y_grid_nodes, const dealii::FullMatrix< double > &basis_z_grid_nodes, const dealii::FullMatrix< double > &basis_x_flux_nodes, const dealii::FullMatrix< double > &basis_y_flux_nodes, const dealii::FullMatrix< double > &basis_z_flux_nodes, const dealii::FullMatrix< double > &grad_basis_x_grid_nodes, const dealii::FullMatrix< double > &grad_basis_y_grid_nodes, const dealii::FullMatrix< double > &grad_basis_z_grid_nodes, const dealii::FullMatrix< double > &grad_basis_x_flux_nodes, const dealii::FullMatrix< double > &grad_basis_y_flux_nodes, const dealii::FullMatrix< double > &grad_basis_z_flux_nodes, dealii::Tensor< 2, dim, std::vector< real >> &metric_cofactor, const bool use_invariant_curl_form=false) |
| Computes local 3D cofactor matrix. More... | |
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<typename real, int dim, int n_faces>
class PHiLiP::OPERATOR::metric_operators< real, dim, n_faces >
Base metric operators class that stores functions used in both the volume and on surface.
Definition at line 1086 of file operators.h.
Member Function Documentation
◆ build_determinant_metric_Jacobian()
template<typename real , int dim, int n_faces>
|
protected |
Assembles the determinant of metric Jacobian.
\( \|J^\Omega \| = \mathbf{a}_1 \cdot (\mathbf{a}_2 \otimes \mathbf{a}_3)\), where \(\mathbf{a}_i = \mathbf{\nabla}^r x_i \) are the physical vector bases. Pass the 1D mapping shape functions evaluated at flux nodes, and the 1D gradient of mapping shape functions evaluated at flux nodes.
Definition at line 2479 of file operators.cpp.
◆ build_facet_metric_operators()
template<typename real , int dim, int n_faces>
| void PHiLiP::OPERATOR::metric_operators< real, dim, n_faces >::build_facet_metric_operators | ( | const unsigned int | iface, |
| const unsigned int | n_quad_pts, | ||
| const unsigned int | n_metric_dofs, | ||
| const std::array< std::vector< real >, dim > & | mapping_support_points, | ||
| mapping_shape_functions< dim, n_faces, real > & | mapping_basis, | ||
| const bool | use_invariant_curl_form = false |
||
| ) |
Builds the facet metric operators.
Builds and stores facet metric cofactor and determinant of metric Jacobian at the facet cubature nodes (one face). If passed flag to store Jacobian when metric operators is constructed, will also store the JAcobian at flux nodes.
Definition at line 2351 of file operators.cpp.
◆ build_metric_Jacobian()
template<typename real , int dim, int n_faces>
|
protected |
Builds the metric Jacobian evaluated at a vector of points.
\( \mathbf{J} = [\mathbf{a}_1, \mathbf{a}_2, \mathbf{a}_3]^T \) where \(\mathbf{a}_i = \mathbf{\nabla}^r x_i \) are the physical vector bases.
Definition at line 2441 of file operators.cpp.
◆ build_volume_metric_operators()
template<typename real , int dim, int n_faces>
| void PHiLiP::OPERATOR::metric_operators< real, dim, n_faces >::build_volume_metric_operators | ( | const unsigned int | n_quad_pts, |
| const unsigned int | n_metric_dofs, | ||
| const std::array< std::vector< real >, dim > & | mapping_support_points, | ||
| mapping_shape_functions< dim, n_faces, real > & | mapping_basis, | ||
| const bool | use_invariant_curl_form = false |
||
| ) |
Builds the volume metric operators.
Builds and stores volume metric cofactor and determinant of metric Jacobian at the volume cubature nodes. If passed flag to store Jacobian when metric operators is constructed, will also store the JAcobian at flux nodes.
Definition at line 2294 of file operators.cpp.
◆ compute_local_3D_cofactor()
template<typename real , int dim, int n_faces>
|
protected |
Computes local 3D cofactor matrix.
We compute the metric cofactor matrix \(\mathbf{C}_m\) via the conservative curl form of Abe 2014 and Kopriva 2006 by default. Can use invariant curl form by passing flag. To ensure consistent normals, we consider the two cubature sets, grid nodes (mapping-support-points), and flux nodes (quadrature nodes). The metric cofactor matrix is thus:
\[ (\mathbf{C})_{ni} = J(\mathbf{a}^i)_n= -\hat{\mathbf{e}}_i \cdot \nabla^r\times\mathbf{\Theta}(\mathbf{\xi}_{\text{flux nodes}}^r)\Big[ \mathbf{\Theta}(\mathbf{\xi}_{\text{grid nodes}}^r)\hat{\mathbf{x}}_l^{c^T} \nabla^r \mathbf{\Theta}(\mathbf{\xi}_{\text{grid nodes}}^r)\hat{\mathbf{x}}_m^{c^T} \Big] \text{, }\\i=1,2,3\text{, }n=1,2,3\text{ }(n,m,l)\text{ cyclic,} \]
for the conservative curl form, and
\[ (\mathbf{C})_{ni} = J(\mathbf{a}^i)_n= -\frac{1}{2}\hat{\mathbf{e}}_i \cdot \nabla^r\times\mathbf{\Theta}(\mathbf{\xi}_{\text{flux nodes}}^r)\Big[ \mathbf{\Theta}(\mathbf{\xi}_{\text{grid nodes}}^r)\hat{\mathbf{x}}_l^{c^T} \nabla^r \mathbf{\Theta}(\mathbf{\xi}_{\text{grid nodes}}^r)\hat{\mathbf{x}}_m^{c^T} - \mathbf{\Theta}(\mathbf{\xi}_{\text{grid nodes}}^r)\hat{\mathbf{x}}_m^{c^T} \nabla^r \mathbf{\Theta}(\mathbf{\xi}_{\text{grid nodes}}^r)\hat{\mathbf{x}}_l^{c^T}\Big] \text{, }\\i=1,2,3\text{, }n=1,2,3\text{ }(n,m,l)\text{ cyclic,} \]
for the invariant curl form.
We let \(\mathbf{\Theta}(\mathbf{\xi}^r)\) represent the mapping shape functions.
Definition at line 2588 of file operators.cpp.
The documentation for this class was generated from the following files:
- src/operators/operators.h
- src/operators/operators.cpp
