A representation of finite element variational forms. More...

#include <Form.h>

Public Types
using	scalar_type = T
	Scalar type.

Public Member Functions
	Form (const std::vector< std::shared_ptr< const FunctionSpace< U > > > &V, const std::map< IntegralType, std::vector< std::tuple< int, std::function< void(T , const T , const T , const scalar_value_type_t< T > , const int , const std::uint8_t )>, std::vector< std::int32_t > > > > &integrals, const std::vector< std::shared_ptr< const Function< T, U > > > &coefficients, const std::vector< std::shared_ptr< const Constant< T > > > &constants, bool needs_facet_permutations, std::shared_ptr< const mesh::Mesh< U > > mesh=nullptr)
	Create a finite element form.

	Form (const Form &form)=delete
	Copy constructor.

	Form (Form &&form)=default
	Move constructor.

virtual	~Form ()=default
	Destructor.

int	rank () const
	Rank of the form (bilinear form = 2, linear form = 1, functional = 0, etc)

std::shared_ptr< const mesh::Mesh< U > >	mesh () const
	Extract common mesh for the form.

const std::vector< std::shared_ptr< const FunctionSpace< U > > > &	function_spaces () const
	Return function spaces for all arguments.

std::function< void(T , const T , const T , const scalar_value_type_t< T > , const int , const std::uint8_t )>	kernel (IntegralType type, int i) const
	Get the kernel function for integral i on given domain type.

std::set< IntegralType >	integral_types () const
	Get types of integrals in the form.

int	num_integrals (IntegralType type) const
	Number of integrals on given domain type.

std::vector< int >	integral_ids (IntegralType type) const
	Get the IDs for integrals (kernels) for given integral type. The IDs correspond to the domain IDs which the integrals are defined for in the form. ID=-1 is the default integral over the whole domain.

std::span< const std::int32_t >	domain (IntegralType type, int i) const
	Get the list of cell indices for the ith integral (kernel) for the cell domain type.

const std::vector< std::shared_ptr< const Function< T, U > > > &	coefficients () const
	Access coefficients.

bool	needs_facet_permutations () const
	Get bool indicating whether permutation data needs to be passed into these integrals.

std::vector< int >	coefficient_offsets () const
	Offset for each coefficient expansion array on a cell. Used to pack data for multiple coefficients in a flat array. The last entry is the size required to store all coefficients.

const std::vector< std::shared_ptr< const Constant< T > > > &	constants () const
	Access constants.

Detailed Description

template<dolfinx::scalar T, std::floating_point U = dolfinx::scalar_value_type_t<T>>
class dolfinx::fem::Form< T, U >

A representation of finite element variational forms.

A note on the order of trial and test spaces: FEniCS numbers argument spaces starting with the leading dimension of the corresponding tensor (matrix). In other words, the test space is numbered 0 and the trial space is numbered 1. However, in order to have a notation that agrees with most existing finite element literature, in particular

\[ a = a(u, v) \]

the spaces are numbered from right to left

\[ a: V_1 \times V_0 \rightarrow \mathbb{R} \]

This is reflected in the ordering of the spaces that should be supplied to generated subclasses. In particular, when a bilinear form is initialized, it should be initialized as a(V_1, V_0) = ..., where V_1 is the trial space and V_0 is the test space. However, when a form is initialized by a list of argument spaces (the variable function_spaces in the constructors below), the list of spaces should start with space number 0 (the test space) and then space number 1 (the trial space).

Constructor & Destructor Documentation

◆ Form()

template<dolfinx::scalar T, std::floating_point U = dolfinx::scalar_value_type_t<T>>

Form	(	const std::vector< std::shared_ptr< const FunctionSpace< U > > > &	V,
		const std::map< IntegralType, std::vector< std::tuple< int, std::function< void(T , const T , const T , const scalar_value_type_t< T > , const int , const std::uint8_t )>, std::vector< std::int32_t > > >	,
		&	integrals,
		const std::vector< std::shared_ptr< const Function< T, U > > > &	coefficients,
		const std::vector< std::shared_ptr< const Constant< T > > > &	constants,
		bool	needs_facet_permutations,
		std::shared_ptr< const mesh::Mesh< U > >	mesh = `nullptr`
	)

inline

Create a finite element form.

Note: User applications will normally call a builder function rather using this interface directly.

Parameters

[in]	V	Function spaces for the form arguments
[in]	integrals	Integrals in the form. The first key is the domain type. For each key there is a list of tuples (domain id, integration kernel, entities).
[in]	coefficients
[in]	constants	Constants in the Form
[in]	needs_facet_permutations	Set to true is any of the integration kernels require cell permutation data
[in]	mesh	Mesh of the domain. This is required when there are no argument functions from which the mesh can be extracted, e.g. for functionals.

Member Function Documentation

◆ domain()

template<dolfinx::scalar T, std::floating_point U = dolfinx::scalar_value_type_t<T>>

std::span< const std::int32_t > domain	(	IntegralType	type,
		int	i
	)		const

inline

Get the list of cell indices for the ith integral (kernel) for the cell domain type.

For IntegralType::cell, returns a list of cell indices.

For IntegralType::exterior_facet, returns a list of (cell_index, local_facet_index) pairs. Data is flattened with row-major layout, shape=(num_facets, 2).

For IntegralType::interior_facet, returns list of tuples of the form (cell_index_0, local_facet_index_0, cell_index_1, local_facet_index_1). Data is flattened with row-major layout, shape=(num_facets, 4).

Parameters

[in]	type	Integral domain type
[in]	i	Integral ID, i.e. (sub)domain index

Returns: List of active cell entities for the given integral (kernel)

◆ function_spaces()

template<dolfinx::scalar T, std::floating_point U = dolfinx::scalar_value_type_t<T>>

const std::vector< std::shared_ptr< const FunctionSpace< U > > > & function_spaces ( ) const

inline

Return function spaces for all arguments.

Returns: Function spaces

◆ integral_ids()

template<dolfinx::scalar T, std::floating_point U = dolfinx::scalar_value_type_t<T>>

std::vector< int > integral_ids ( IntegralType type ) const

inline

Get the IDs for integrals (kernels) for given integral type. The IDs correspond to the domain IDs which the integrals are defined for in the form. ID=-1 is the default integral over the whole domain.

Parameters

[in] type Integral type

Returns: List of IDs for given integral type

◆ integral_types()

template<dolfinx::scalar T, std::floating_point U = dolfinx::scalar_value_type_t<T>>

std::set< IntegralType > integral_types ( ) const

inline

Get types of integrals in the form.

Returns: Integrals types.

◆ kernel()

template<dolfinx::scalar T, std::floating_point U = dolfinx::scalar_value_type_t<T>>

std::function< void(T , const T , const T , const scalar_value_type_t< T > , const int , const std::uint8_t )> kernel	(	IntegralType	type,
		int	i
	)		const

inline

Get the kernel function for integral i on given domain type.

Parameters

[in]	type	Integral type
[in]	i	Domain index

Returns: Function to call for tabulate_tensor

◆ mesh()

template<dolfinx::scalar T, std::floating_point U = dolfinx::scalar_value_type_t<T>>

std::shared_ptr< const mesh::Mesh< U > > mesh ( ) const

inline

Extract common mesh for the form.

Returns: The mesh

◆ needs_facet_permutations()

template<dolfinx::scalar T, std::floating_point U = dolfinx::scalar_value_type_t<T>>

bool needs_facet_permutations ( ) const

inline

Get bool indicating whether permutation data needs to be passed into these integrals.

Returns: True if cell permutation data is required

◆ num_integrals()

template<dolfinx::scalar T, std::floating_point U = dolfinx::scalar_value_type_t<T>>

int num_integrals ( IntegralType type ) const

inline

Number of integrals on given domain type.

Parameters

[in] type Integral type.

Returns: Number of integrals.

◆ rank()

template<dolfinx::scalar T, std::floating_point U = dolfinx::scalar_value_type_t<T>>

int rank ( ) const

inline

Rank of the form (bilinear form = 2, linear form = 1, functional = 0, etc)

Returns: The rank of the form

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

/__w/dolfinx/dolfinx/cpp/dolfinx/fem/assembler.h
/__w/dolfinx/dolfinx/cpp/dolfinx/fem/Form.h

Public Types

Public Member Functions

Detailed Description

Constructor & Destructor Documentation

◆ Form()

Member Function Documentation

◆ domain()

◆ function_spaces()

◆ integral_ids()

◆ integral_types()

◆ kernel()

◆ mesh()

◆ needs_facet_permutations()

◆ num_integrals()

◆ rank()