Abstract class for the description of a general finite element on a reference simplex in dim dimensions. More...

#include <finite_element.hh>

Inheritance diagram for FiniteElement< dim >:

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Collaboration diagram for FiniteElement< dim >:

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Public Member Functions
	FiniteElement ()
	Constructor. More...

unsigned int	n_dofs () const
	Returns the number of degrees of freedom needed by the finite element. More...

double	shape_value (const unsigned int i, const arma::vec::fixed< dim > &p, const unsigned int comp=0) const
	Calculates the value of the `comp-th` component of the `i-th` shape function at the point `p` on the reference element. More...

arma::vec::fixed< dim >	shape_grad (const unsigned int i, const arma::vec::fixed< dim > &p, const unsigned int comp=0) const
	Calculates the `comp-th` component of the gradient of the `i-th` shape function at the point `p` on the reference element. More...

unsigned int	n_components () const
	Returns numer of components of the basis function. More...

const Dof &	dof (unsigned int i) const
	Returns `i` -th degree of freedom. More...

unsigned int	n_space_components (unsigned int spacedim)
	Number of components of FE in a mapped space with dimension `spacedim`. More...

virtual std::vector< arma::vec::fixed< dim+1 > >	dof_points () const

virtual	~FiniteElement ()
	Destructor. More...

Protected Member Functions
void	init (bool primitive=true, FEType type=FEScalar)
	Clears all internal structures. More...

void	setup_components ()
	Initialize vectors with information about components of basis functions. More...

virtual UpdateFlags	update_each (UpdateFlags flags)
	Decides which additional quantities have to be computed for each cell. More...

virtual void	compute_node_matrix ()
	Initializes the `node_matrix` for computing the coefficients of the shape functions in the raw basis of `functions_space_`. This is done by evaluating the `dofs_` for the basis function and by inverting the resulting matrix. More...

bool	is_primitive () const
	Indicates whether the basis functions have one or more nonzero components (scalar FE spaces are always primitive). More...

unsigned int	system_to_component_index (unsigned sys_idx) const
	Returns the component index for vector valued finite elements. More...

const std::vector< bool > &	get_nonzero_components (unsigned int sys_idx) const
	Returns the mask of nonzero components for given basis function. More...

Protected Attributes
FEType	type_
	Type of FiniteElement. More...

bool	is_primitive_
	Primitive FE is using componentwise shape functions, i.e. only one component is nonzero for each shape function. More...

std::vector< unsigned int >	component_indices_
	Indices of nonzero components of shape functions (for primitive FE). More...

std::vector< std::vector< bool > >	nonzero_components_
	Footprints of nonzero components of shape functions. More...

arma::mat	node_matrix
	Matrix that determines the coefficients of the raw basis functions from the values at the support points. More...

std::shared_ptr< FunctionSpace >	function_space_
	Function space defining the FE. More...

std::vector< Dof >	dofs_
	Set of degrees of freedom (functionals) defining the FE. More...

Friends
class	FESystem< dim >

class	FEValues< 3 >

class	FE_P_disc< dim >

class	SubDOFHandlerMultiDim

Detailed Description

template<unsigned int dim>
class FiniteElement< dim >

Abstract class for the description of a general finite element on a reference simplex in dim dimensions.

The finite element is determined by a function_space_ and a set of dofs_. Further it must be set whether the finite element is_primitive_, which means that even if the functions in function_space_ are vector-valued, the basis functions have only one nonzero component (this is typical for tensor-product FE, e.g. vector-valued polynomial FE, but not for Raviart-Thomas FE).

Description of dofs:

The reference cell consists of lower dimensional entities (points, lines, triangles). Each dof is associated to one of these entities. If the entity is shared by 2 or more neighbouring cells in the mesh then this dof is shared by the finite elements on all of these cells. If a dof is associated to the cell itself then it is not shared with neighbouring cells.

Shape functions:

Sometimes it is convenient to describe the function space using a basis (called the raw basis) that is different from the set of shape functions for the finite element (the actual basis). For this reason we define the support points which play the role of nodal functionals associated to the particular dofs. To convert between the two bases one can use the node_matrix, which is constructed by the method compute_node_matrix(). In the case of non-Lagrangean finite elements the dofs are not associated to nodal functionals but e.g. to derivatives or averages. For that reason we distinguish between the unit support points which are uniquely associated to the dofs and the generalized support points that are auxiliary for the calculation of the dof functionals.

Definition at line 250 of file finite_element.hh.

Constructor & Destructor Documentation

◆ FiniteElement()

template<unsigned int dim>

FiniteElement< dim >::FiniteElement

Constructor.

Definition at line 74 of file finite_element.cc.

◆ ~FiniteElement()

template<unsigned int dim>

virtual FiniteElement< dim >::~FiniteElement ( )

inlinevirtual

Destructor.

Definition at line 309 of file finite_element.hh.

Member Function Documentation

◆ compute_node_matrix()

template<unsigned int dim>

void FiniteElement< dim >::compute_node_matrix

inlineprotectedvirtual

Initializes the node_matrix for computing the coefficients of the shape functions in the raw basis of functions_space_. This is done by evaluating the dofs_ for the basis function and by inverting the resulting matrix.

Reimplemented in FESystem< dim >.

Definition at line 98 of file finite_element.cc.

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◆ dof()

template<unsigned int dim>

const Dof& FiniteElement< dim >::dof ( unsigned int i ) const

inline

Returns i -th degree of freedom.

Definition at line 296 of file finite_element.hh.

◆ dof_points()

template<unsigned int dim>

vector< arma::vec::fixed< dim+1 > > FiniteElement< dim >::dof_points

virtual

Get barycentric coordinates of the points on the reference element associated with the dofs. Used in BDDC for unknown reason.

Reimplemented in FESystem< dim >.

Definition at line 208 of file finite_element.cc.

◆ get_nonzero_components()

template<unsigned int dim>

const std::vector<bool>& FiniteElement< dim >::get_nonzero_components ( unsigned int sys_idx ) const

inlineprotected

Returns the mask of nonzero components for given basis function.

Parameters

sys_idx Index of basis function.

Definition at line 358 of file finite_element.hh.

◆ init()

template<unsigned int dim>

void FiniteElement< dim >::init	(	bool	primitive = `true`,
		FEType	type = `FEScalar`
	)

protected

Clears all internal structures.

Definition at line 81 of file finite_element.cc.

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◆ is_primitive()

template<unsigned int dim>

bool FiniteElement< dim >::is_primitive ( ) const

inlineprotected

Indicates whether the basis functions have one or more nonzero components (scalar FE spaces are always primitive).

Definition at line 344 of file finite_element.hh.

◆ n_components()

template<unsigned int dim>

unsigned int FiniteElement< dim >::n_components ( ) const

inline

Returns numer of components of the basis function.

Definition at line 292 of file finite_element.hh.

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◆ n_dofs()

template<unsigned int dim>

unsigned int FiniteElement< dim >::n_dofs ( ) const

inline

Returns the number of degrees of freedom needed by the finite element.

Definition at line 262 of file finite_element.hh.

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◆ n_space_components()

template<unsigned int dim>

unsigned int FiniteElement< dim >::n_space_components ( unsigned int spacedim )

Number of components of FE in a mapped space with dimension spacedim.

Definition at line 178 of file finite_element.cc.

◆ setup_components()

template<unsigned int dim>

void FiniteElement< dim >::setup_components

protected

Initialize vectors with information about components of basis functions.

Definition at line 90 of file finite_element.cc.

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◆ shape_grad()

template<unsigned int dim>

arma::vec::fixed< dim > FiniteElement< dim >::shape_grad	(	const unsigned int	i,
		const arma::vec::fixed< dim > &	p,
		const unsigned int	comp = `0`
	)		const

Calculates the comp-th component of the gradient of the i-th shape function at the point p on the reference element.

Parameters

i	Number of the shape function.
p	Point of evaluation.
comp	Number of vector component.

Definition at line 127 of file finite_element.cc.

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◆ shape_value()

template<unsigned int dim>

double FiniteElement< dim >::shape_value	(	const unsigned int	i,
		const arma::vec::fixed< dim > &	p,
		const unsigned int	comp = `0`
	)		const

Calculates the value of the comp-th component of the i-th shape function at the point p on the reference element.

Parameters

i	Number of the shape function.
p	Point of evaluation.
comp	Number of vector component.

Definition at line 112 of file finite_element.cc.

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◆ system_to_component_index()

template<unsigned int dim>

unsigned int FiniteElement< dim >::system_to_component_index ( unsigned sys_idx ) const

inlineprotected

Returns the component index for vector valued finite elements.

Parameters

sys_idx Index of shape function.

Definition at line 351 of file finite_element.hh.

◆ update_each()

template<unsigned int dim>

UpdateFlags FiniteElement< dim >::update_each ( UpdateFlags flags )

inlineprotectedvirtual

Decides which additional quantities have to be computed for each cell.

Parameters

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

/home/runner/work/flow123d/flow123d/src/fem/discrete_space.hh
/home/runner/work/flow123d/flow123d/src/fem/finite_element.hh
/home/runner/work/flow123d/flow123d/src/fem/finite_element.cc

Public Member Functions

Protected Member Functions

Protected Attributes

Friends

Detailed Description

template<unsigned int dim> class FiniteElement< dim >

Constructor & Destructor Documentation

◆ FiniteElement()

◆ ~FiniteElement()

Member Function Documentation

◆ compute_node_matrix()

◆ dof()

◆ dof_points()

◆ get_nonzero_components()

◆ init()

◆ is_primitive()

◆ n_components()

◆ n_dofs()

◆ n_space_components()

◆ setup_components()

◆ shape_grad()

◆ shape_value()

◆ system_to_component_index()

◆ update_each()

Friends And Related Function Documentation

◆ FE_P_disc< dim >

◆ FESystem< dim >

◆ FEValues< 3 >

◆ SubDOFHandlerMultiDim

Member Data Documentation

◆ component_indices_

◆ dofs_

◆ function_space_

◆ is_primitive_

◆ node_matrix

◆ nonzero_components_

◆ type_

template<unsigned int dim>
class FiniteElement< dim >