Compound finite element on dim dimensional simplex. More...

#include <fe_system.hh>

Inheritance diagram for FESystem< dim >:

Collaboration diagram for FESystem< dim >:

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Public Member Functions
	FESystem (std::shared_ptr< FiniteElement< dim > > fe, FEType t)
	Constructor for FEVectorContravariant and FEVectorPiola. More...

	FESystem (const std::shared_ptr< FiniteElement< dim > > &fe, FEType t, unsigned int n)
	Constructor for FEVector, FETensor and FEMixedSystem. If `t` == FEVector then `n` must be the space dimension into which the reference cell will be mapped and that `fe` is scalar. If `t` == FETensor then `n` must be square of the space dimension into which the reference cell will be mapped and that `fe` is scalar. If `t` == FEMixedSystem, then `n` is the number of components. More...

	FESystem (std::vector< std::shared_ptr< FiniteElement< dim > > > fe)
	Constructor. FESystem for mixed elements. More...

std::vector< unsigned int >	get_scalar_components () const

std::vector< unsigned int >	get_vector_components () const

std::vector< unsigned int >	get_tensor_components () const

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

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

const std::vector< std::shared_ptr< FiniteElement< dim > > > &	fe () const

std::vector< unsigned int >	fe_dofs (unsigned int fe_index)
	Return dof indices belonging to given sub-FE. More...

Public Member Functions inherited from FiniteElement< dim >
	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	~FiniteElement ()
	Destructor. More...

Private Member Functions
void	initialize ()
	Initialization of the internal structures from the vector of base FE. More...

void	compute_node_matrix () override
	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...

Private Attributes
std::vector< std::shared_ptr< FiniteElement< dim > > >	fe_
	Pointers to base FE objects. More...

std::vector< unsigned int >	scalar_components_

std::vector< unsigned int >	vector_components_

std::vector< unsigned int >	tensor_components_

Additional Inherited Members
Protected Member Functions inherited from FiniteElement< dim >
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...

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 inherited from FiniteElement< dim >
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...

Detailed Description

template<unsigned int dim>
class FESystem< dim >

Compound finite element on dim dimensional simplex.

This type of FE is used for vector-valued functions and for systems of equations.

Definition at line 101 of file fe_system.hh.

Constructor & Destructor Documentation

template<unsigned int dim>

FESystem< dim >::FESystem	(	std::shared_ptr< FiniteElement< dim > >	fe,
		FEType	t
	)

Constructor for FEVectorContravariant and FEVectorPiola.

Parameters

fe	Base finite element class (must be scalar).
t	Type (must be FEVectorContravariant or FEVectorPiola).

Definition at line 102 of file fe_system.cc.

template<unsigned int dim>

FESystem< dim >::FESystem	(	const std::shared_ptr< FiniteElement< dim > > &	fe,
		FEType	t,
		unsigned int	n
	)

Constructor for FEVector, FETensor and FEMixedSystem. If t == FEVector then n must be the space dimension into which the reference cell will be mapped and that fe is scalar. If t == FETensor then n must be square of the space dimension into which the reference cell will be mapped and that fe is scalar. If t == FEMixedSystem, then n is the number of components.

Parameters

fe	Base finite element class (must be scalar if `t` is FEVector or FETensor).
t	Type of FESystem (must be either FEVector, FETensor or FEMixedSystem).
n	Multiplicity (number of components).

Definition at line 115 of file fe_system.cc.

template<unsigned int dim>

FESystem< dim >::FESystem ( std::vector< std::shared_ptr< FiniteElement< dim > > > fe )

Constructor. FESystem for mixed elements.

Parameters

fe	Base finite element classes.

Definition at line 129 of file fe_system.cc.

Member Function Documentation

template<unsigned int dim>

void FESystem< dim >::compute_node_matrix ( )

overrideprivatevirtual

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 from FiniteElement< dim >.

Definition at line 246 of file fe_system.cc.

template<unsigned int dim>

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

virtual

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

Reimplemented from FiniteElement< dim >.

Definition at line 233 of file fe_system.cc.

template<unsigned int dim>

const std::vector<std::shared_ptr<FiniteElement<dim> > >& FESystem< dim >::fe ( ) const

inline

Definition at line 147 of file fe_system.hh.