A class that represents a tensor basis for a finite element. This class is used to evaluate the basis functions and their derivatives at a set of reference points. More...

#include <tensor_basis.hpp>

Collaboration diagram for serif::discretization::backend::mfem::TensorBasis:

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Classes
struct	Product
	A struct that represents a product of one-dimensional basis functions. More...

Public Member Functions
int	points () const noexcept
	Get the number of quadrature points in the Cartesian rule.

int	dofs () const noexcept
	Get the number of degrees of freedom in the tensor basis.

int	components () const noexcept
	Get the number of canonical output components per point in the tensor basis.

void	apply (const ::mfem::Vector &input, ::mfem::Vector &output, TensorWorkspace &workspace, const bool transpose=false) const
	Evaluate canonical samples, or their coordinate transpose, with caller-owned scratch.

void	apply_many (const ::mfem::Vector &input, ::mfem::Vector &output, const int lanes, TensorWorkspace &workspace, const bool transpose=false) const
	apply() for several coefficient vectors at once, stored lane-interleaved (entry i of lane j at i * lanes + j).

Static Public Member Functions
static std::shared_ptr< const TensorBasis >	make (const ::mfem::FiniteElement &element, const ::mfem::IntegrationRule &rule, const ReferenceOperation operation, const int copies, const ElementReconstruction *reconstruction=nullptr)
	Return no tensor plan unless its factorization agrees with MFEM's canonical basis.

Private Member Functions
bool	agrees_with (const ::mfem::FiniteElement &element, const ::mfem::IntegrationRule &rule, const ReferenceOperation operation, const ElementReconstruction *reconstruction) const
	Verify signed ordering and every requested basis entry before enabling the fast path.

Static Private Member Functions
static void	contract_axis (const ::mfem::DenseMatrix &factor, const int axis, const std::array< int, 3 > &shape, const ::mfem::Vector &input, ::mfem::Vector &output, const bool transpose, const int lanes=1)

Private Attributes
int	m_points {0}
	The number of quadrature points in the Cartesian rule.

int	m_dofs {0}
	The number of degrees of freedom in the tensor basis.

int	m_components {0}
	The number of canonical output components per point in the tensor basis.

std::vector< Product >	m_products
	The products of one-dimensional basis functions for each axis. (TOOD: consider if this should be a heap allocated vector of it this could be put on the stack somehow)

Detailed Description

A class that represents a tensor basis for a finite element. This class is used to evaluate the basis functions and their derivatives at a set of reference points.

Member Function Documentation

◆ agrees_with()

bool serif::discretization::backend::mfem::TensorBasis::agrees_with	(	const ::mfem::FiniteElement &	element,
		const ::mfem::IntegrationRule &	rule,
		const ReferenceOperation	operation,
		const ElementReconstruction *	reconstruction ) const

inlinenodiscardprivate

Verify signed ordering and every requested basis entry before enabling the fast path.

Verify that the signed ordering and every requested basis entry agrees with MFEM's canonical basis.

Parameters

element	The finite element to verify against.
rule	The integration rule to use for evaluating the basis functions.
operation	The reference operation to apply (e.g., value, gradient).

Returns: True if the tensor basis agrees with MFEM's canonical basis, false otherwise.

◆ apply()

void serif::discretization::backend::mfem::TensorBasis::apply	(	const ::mfem::Vector &	input,
		::mfem::Vector &	output,
		TensorWorkspace &	workspace,
		const bool	transpose = false ) const

inline

Evaluate canonical samples, or their coordinate transpose, with caller-owned scratch.

Apply the tensor basis to an input vector and store the results in an output vector. This function performs the tensor contraction of the input vector with the tensor basis.

Parameters

input	The input vector to be contracted with the tensor basis.
output	The output vector to store the result of the contraction. (Owned by the caller)
workspace	The workspace to use for the contraction. (Owned by the caller)
transpose	Whether to transpose the contraction (default is false).

Precondition: The input vector must have a size equal to the number of degrees of freedom in the tensor basis if transpose is false, or equal to the number of points times the number of components if transpose is true.; The output vector must be constructed

Postcondition: The output vector will have a size equal to the number of points times the number of components if transpose is false, or equal to the number of degrees of freedom in the tensor basis if transpose is true.; The output vector will contain the result of the tensor contraction of the input vector with the tensor basis.

◆ apply_many()

void serif::discretization::backend::mfem::TensorBasis::apply_many	(	const ::mfem::Vector &	input,
		::mfem::Vector &	output,
		const int	lanes,
		TensorWorkspace &	workspace,
		const bool	transpose = false ) const

inline

apply() for several coefficient vectors at once, stored lane-interleaved (entry i of lane j at i * lanes + j).

Note: The lanes form the fastest tensor index, so every lane is contracted with exactly the operations and summation order apply() uses for it alone; only the loops are shared.

◆ components()

int serif::discretization::backend::mfem::TensorBasis::components ( ) const

inlinenodiscardnoexcept

Get the number of canonical output components per point in the tensor basis.

Returns: The number of canonical output components per point in the tensor basis.

◆ contract_axis()

static void serif::discretization::backend::mfem::TensorBasis::contract_axis	(	const ::mfem::DenseMatrix &	factor,
		const int	axis,
		const std::array< int, 3 > &	shape,
		const ::mfem::Vector &	input,
		::mfem::Vector &	output,
		const bool	transpose,
		const int	lanes = 1 )

inlinestaticprivate

@breif apply one factor along one tensor axis, teh other two indices will remain unchanged

Parameters

factor	The one-dimensional basis function to apply along the specified axis.
axis	The axis along which to apply the factor (0, 1, or 2).
shape	The shape of the input tensor (number of points along each axis).
input	The input vector to be contracted with the factor.
output	The output vector to store the result of the contraction.
transpose	Whether to transpose the factor matrix before applying it.
lanes	Number of interleaved independent tensors (the fastest index); 1 for a single tensor.

Precondition: The input vector must have a size equal to the product of the dimensions specified in the shape array.

Postcondition: The output vector will have a size equal to the product of the dimensions specified in the next array.; The output vector will contain the result of the contraction of the input vector with the factor along the specified axis.

◆ dofs()

int serif::discretization::backend::mfem::TensorBasis::dofs ( ) const

inlinenodiscardnoexcept

Get the number of degrees of freedom in the tensor basis.

Returns: The number of degrees of freedom in the tensor basis.

◆ make()

static std::shared_ptr< const TensorBasis > serif::discretization::backend::mfem::TensorBasis::make	(	const ::mfem::FiniteElement &	element,
		const ::mfem::IntegrationRule &	rule,
		const ReferenceOperation	operation,
		const int	copies,
		const ElementReconstruction *	reconstruction = nullptr )

inlinestaticnodiscard

Return no tensor plan unless its factorization agrees with MFEM's canonical basis.

Make a tensor basis for a given finite element, integration rule, reference operation, and number of copies. This function returns a shared pointer to a TensorBasis object that can be used to do efficient evaluation of the basis functions and their derivatives at reference points.

Parameters

element	The finite element for which to construct the tensor basis.
rule	The integration rule to use for evaluating the basis functions.
operation	The reference operation to apply (e.g., value, gradient).
copies	The number of copies of the basis functions.

Returns: A shared pointer to a TensorBasis object if the tensor basis can be constructed, or an empty shared pointer if it cannot.

◆ points()

int serif::discretization::backend::mfem::TensorBasis::points ( ) const

inlinenodiscardnoexcept

Get the number of quadrature points in the Cartesian rule.

Returns: The number of quadrature points in the Cartesian rule.

Member Data Documentation

◆ m_components

int serif::discretization::backend::mfem::TensorBasis::m_components {0}

private

The number of canonical output components per point in the tensor basis.

◆ m_dofs

int serif::discretization::backend::mfem::TensorBasis::m_dofs {0}

private

The number of degrees of freedom in the tensor basis.

◆ m_points

int serif::discretization::backend::mfem::TensorBasis::m_points {0}

private

The number of quadrature points in the Cartesian rule.

◆ m_products

std::vector<Product> serif::discretization::backend::mfem::TensorBasis::m_products

private

The products of one-dimensional basis functions for each axis. (TOOD: consider if this should be a heap allocated vector of it this could be put on the stack somehow)

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

src/include/serif/backend/mfem/discretization/tensor_basis.hpp

Classes

Public Member Functions

Static Public Member Functions

Private Member Functions

Static Private Member Functions

Private Attributes

Detailed Description

Member Function Documentation

◆ agrees_with()

◆ apply()

◆ apply_many()

◆ components()

◆ contract_axis()

◆ dofs()

◆ make()

◆ points()

Member Data Documentation

◆ m_components

◆ m_dofs

◆ m_points

◆ m_products