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Parallel High-Order Library for PDEs through hp-adaptive Discontinuous Galerkin methods
PHiLiP::OPERATOR::mapping_shape_functions< dim, n_faces, real > Class Template Reference

The mapping shape functions evaluated at the desired nodes (facet set included in volume grid nodes for consistency). More...

#include <operators.h>

Inheritance diagram for PHiLiP::OPERATOR::mapping_shape_functions< dim, n_faces, real >:
Collaboration diagram for PHiLiP::OPERATOR::mapping_shape_functions< dim, n_faces, real >:

Public Member Functions

 mapping_shape_functions (const int nstate_input, const unsigned int max_degree_input, const unsigned int grid_degree_input)
 Constructor.
 
void build_1D_shape_functions_at_grid_nodes (const dealii::FESystem< 1, 1 > &finite_element, const dealii::Quadrature< 1 > &quadrature)
 Constructs the volume operator and gradient operator. More...
 
void build_1D_shape_functions_at_flux_nodes (const dealii::FESystem< 1, 1 > &finite_element, const dealii::Quadrature< 1 > &quadrature, const dealii::Quadrature< 0 > &face_quadrature)
 Constructs the volume, gradient, surface, and surface gradient operator. More...
 
void build_1D_shape_functions_at_volume_flux_nodes (const dealii::FESystem< 1, 1 > &finite_element, const dealii::Quadrature< 1 > &quadrature)
 Constructs the volume and volume gradient operator. 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.
 
unsigned int current_grid_degree
 Stores the degree of the current grid degree.
 
basis_functions< dim, n_faces, real > mapping_shape_functions_grid_nodes
 Object of mapping shape functions evaluated at grid nodes.
 
basis_functions< dim, n_faces, real > mapping_shape_functions_flux_nodes
 Object of mapping shape functions evaluated at 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.
 

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::mapping_shape_functions< dim, n_faces, real >

The mapping shape functions evaluated at the desired nodes (facet set included in volume grid nodes for consistency).

The finite element passed has to be the metric finite element. That is the one collocated on the mapping support points. By default, we use Gauss-Lobatto-Legendre as the mapping support points.

Definition at line 1026 of file operators.h.

Member Function Documentation

◆ build_1D_shape_functions_at_flux_nodes()

template<int dim, int n_faces, typename real >
void PHiLiP::OPERATOR::mapping_shape_functions< dim, n_faces, real >::build_1D_shape_functions_at_flux_nodes ( const dealii::FESystem< 1, 1 > &  finite_element,
const dealii::Quadrature< 1 > &  quadrature,
const dealii::Quadrature< 0 > &  face_quadrature 
)

Constructs the volume, gradient, surface, and surface gradient operator.

Function builds the 1D operators in mapping_shape_functions_flux_nodes.

Definition at line 2164 of file operators.cpp.

◆ build_1D_shape_functions_at_grid_nodes()

template<int dim, int n_faces, typename real >
void PHiLiP::OPERATOR::mapping_shape_functions< dim, n_faces, real >::build_1D_shape_functions_at_grid_nodes ( const dealii::FESystem< 1, 1 > &  finite_element,
const dealii::Quadrature< 1 > &  quadrature 
)

Constructs the volume operator and gradient operator.

This function assures that the shape functions are collocated on the grid nodes. Also, makes for easier function calls. Function builds the 1D operators in mapping_shape_functions_grid_nodes. Note that at grid nodes, we do NOT need any surface information.

Definition at line 2155 of file operators.cpp.

◆ build_1D_shape_functions_at_volume_flux_nodes()

template<int dim, int n_faces, typename real >
void PHiLiP::OPERATOR::mapping_shape_functions< dim, n_faces, real >::build_1D_shape_functions_at_volume_flux_nodes ( const dealii::FESystem< 1, 1 > &  finite_element,
const dealii::Quadrature< 1 > &  quadrature 
)

Constructs the volume and volume gradient operator.

Often times, we only need the values at just the volume flux nodes. Function builds the 1D operators in mapping_shape_functions_flux_nodes.

Definition at line 2176 of file operators.cpp.


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