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

#include <dofhandler.hh>

Inheritance diagram for FiniteElement< dim, spacedim >:

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Collaboration diagram for FiniteElement< dim, spacedim >:

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

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

virtual double	basis_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` raw basis function at the point `p` on the reference element. More...

virtual arma::vec::fixed< dim >	basis_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` raw basis function at the point `p` on the reference element. More...

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

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

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 FEInternalData *	initialize (const Quadrature< dim > &q)
	Calculates the data on the reference cell. More...

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

virtual void	fill_fe_values (const Quadrature< dim > &q, FEInternalData &data, FEValuesData< dim, spacedim > &fv_data)
	Computes the shape function values and gradients on the actual cell and fills the FEValues structure. 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...

const 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...

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, spacedim >

class	FEValuesBase< dim, spacedim >

class	FEValues< dim, spacedim >

class	FESideValues< dim, spacedim >

class	FE_P_disc< dim, spacedim >

Detailed Description

template<unsigned int dim, unsigned int spacedim>
class FiniteElement< dim, spacedim >

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 30 of file dofhandler.hh.

Constructor & Destructor Documentation

template<unsigned int dim, unsigned int spacedim>

FiniteElement< dim, spacedim >::FiniteElement ( )

Constructor.

Definition at line 63 of file finite_element.cc.

template<unsigned int dim, unsigned int spacedim>

FiniteElement< dim, spacedim >::~FiniteElement ( )

virtual

Destructor.

Definition at line 268 of file finite_element.cc.

Member Function Documentation

template<unsigned int dim, unsigned int spacedim>

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

virtual

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

Parameters

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

Reimplemented in FESystem< dim, spacedim >.

Definition at line 153 of file finite_element.cc.

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template<unsigned int dim, unsigned int spacedim>

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

virtual

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

Parameters

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

Reimplemented in FESystem< dim, spacedim >.

Definition at line 143 of file finite_element.cc.

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template<unsigned int dim, unsigned int spacedim>

void FiniteElement< dim, spacedim >::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, spacedim >.

Definition at line 87 of file finite_element.cc.

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template<unsigned int dim, unsigned int spacedim>

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

inline

Returns i -th degree of freedom.

Definition at line 316 of file finite_element.hh.

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template<unsigned int dim, unsigned int spacedim>

void FiniteElement< dim, spacedim >::fill_fe_values	(	const Quadrature< dim > &	q,
		FEInternalData &	data,
		FEValuesData< dim, spacedim > &	fv_data
	)

inlineprotectedvirtual

Computes the shape function values and gradients on the actual cell and fills the FEValues structure.

Parameters

q	Quadrature rule.
data	Precomputed finite element data.
fv_data	Data to be computed.

Reimplemented in FESystem< dim, spacedim >.

Definition at line 193 of file finite_element.cc.

template<unsigned int dim, unsigned int spacedim>

const std::vector<bool>& FiniteElement< dim, spacedim >::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 388 of file finite_element.hh.

template<unsigned int dim, unsigned int spacedim>

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

protected

Clears all internal structures.

Definition at line 70 of file finite_element.cc.

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template<unsigned int dim, unsigned int spacedim>

FEInternalData * FiniteElement< dim, spacedim >::initialize ( const Quadrature< dim > & q )

protectedvirtual

Calculates the data on the reference cell.

Parameters

q	Quadrature rule.
flags	Update flags.

Reimplemented in FESystem< dim, spacedim >.

Definition at line 100 of file finite_element.cc.

template<unsigned int dim, unsigned int spacedim>

const bool FiniteElement< dim, spacedim >::is_primitive ( ) const

inlineprotected

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

Definition at line 375 of file finite_element.hh.

template<unsigned int dim, unsigned int spacedim>

virtual unsigned int FiniteElement< dim, spacedim >::n_components ( ) const

inlinevirtual

Returns numer of components of the basis function.

Reimplemented in FESystem< dim, spacedim >.

Definition at line 313 of file finite_element.hh.

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template<unsigned int dim, unsigned int spacedim>

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

inline

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

Definition at line 286 of file finite_element.hh.

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template<unsigned int dim, unsigned int spacedim>

void FiniteElement< dim, spacedim >::setup_components ( )

protected

Initialize vectors with information about components of basis functions.

Definition at line 79 of file finite_element.cc.

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template<unsigned int dim, unsigned int spacedim>

unsigned int FiniteElement< dim, spacedim >::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 381 of file finite_element.hh.

template<unsigned int dim, unsigned int spacedim>

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

inlineprotectedvirtual

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

Parameters

flags Computed update flags.

Reimplemented in FESystem< dim, spacedim >.

Definition at line 164 of file finite_element.cc.

Friends And Related Function Documentation

template<unsigned int dim, unsigned int spacedim>

friend class FE_P_disc< dim, spacedim >

friend

Definition at line 425 of file finite_element.hh.

template<unsigned int dim, unsigned int spacedim>

friend class FESideValues< dim, spacedim >

friend

Definition at line 424 of file finite_element.hh.

template<unsigned int dim, unsigned int spacedim>

friend class FESystem< dim, spacedim >

friend

Definition at line 421 of file finite_element.hh.

template<unsigned int dim, unsigned int spacedim>

friend class FEValues< dim, spacedim >

friend

Definition at line 423 of file finite_element.hh.

template<unsigned int dim, unsigned int spacedim>

friend class FEValuesBase< dim, spacedim >

friend

Definition at line 422 of file finite_element.hh.

Member Data Documentation

template<unsigned int dim, unsigned int spacedim>

std::vector<unsigned int> FiniteElement< dim, spacedim >::component_indices_

protected

Indices of nonzero components of shape functions (for primitive FE).

Definition at line 403 of file finite_element.hh.

template<unsigned int dim, unsigned int spacedim>

std::vector<Dof> FiniteElement< dim, spacedim >::dofs_

protected

Set of degrees of freedom (functionals) defining the FE.

Definition at line 418 of file finite_element.hh.

template<unsigned int dim, unsigned int spacedim>

FunctionSpace* FiniteElement< dim, spacedim >::function_space_

protected

Function space defining the FE.

Definition at line 415 of file finite_element.hh.

template<unsigned int dim, unsigned int spacedim>

bool FiniteElement< dim, spacedim >::is_primitive_

protected

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

Definition at line 400 of file finite_element.hh.

template<unsigned int dim, unsigned int spacedim>

arma::mat FiniteElement< dim, spacedim >::node_matrix

protected

Matrix that determines the coefficients of the raw basis functions from the values at the support points.

Definition at line 412 of file finite_element.hh.

template<unsigned int dim, unsigned int spacedim>

std::vector<std::vector<bool> > FiniteElement< dim, spacedim >::nonzero_components_

protected

Footprints of nonzero components of shape functions.

Definition at line 406 of file finite_element.hh.

template<unsigned int dim, unsigned int spacedim>

FEType FiniteElement< dim, spacedim >::type_

protected

Type of FiniteElement.

Definition at line 394 of file finite_element.hh.

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

/opt/flow123d/flow123d/src/fem/dofhandler.hh
/opt/flow123d/flow123d/src/fem/finite_element.hh
/opt/flow123d/flow123d/src/fem/finite_element.cc

Public Member Functions

Protected Member Functions

Protected Attributes

Friends

Detailed Description

template<unsigned int dim, unsigned int spacedim> class FiniteElement< dim, spacedim >

Constructor & Destructor Documentation

Member Function Documentation

Friends And Related Function Documentation

Member Data Documentation

template<unsigned int dim, unsigned int spacedim>
class FiniteElement< dim, spacedim >