Implementation of the locally H(grad)-compatible FEM basis of variable order on the [-1,1] reference line cell, using Lagrange polynomials. More...

#include <Intrepid_HGRAD_LINE_Cn_FEM.hpp>

Inheritance diagram for Intrepid::Basis_HGRAD_LINE_Cn_FEM< Scalar, ArrayScalar >:

Public Member Functions
	~Basis_HGRAD_LINE_Cn_FEM ()
	Destructor.

	Basis_HGRAD_LINE_Cn_FEM (int order, const ArrayScalar &pts)
	Constructor.

	Basis_HGRAD_LINE_Cn_FEM (int order, const EPointType &pointType)
	Constructor. More...

void	getValues (ArrayScalar &outputValues, const ArrayScalar &inputPoints, const EOperator operatorType) const
	Evaluation of a FEM basis on a reference Line cell. More...

void	getValues (ArrayScalar &outputValues, const ArrayScalar &inputPoints, const ArrayScalar &cellVertices, const EOperator operatorType=OPERATOR_VALUE) const
	FVD basis evaluation: invocation of this method throws an exception.

virtual void	getDofCoords (ArrayScalar &DofCoords) const
	implements the dofcoords interface

Public Member Functions inherited from Intrepid::Basis< Scalar, ArrayScalar >
virtual	~Basis ()
	Destructor.

virtual int	getCardinality () const
	Returns cardinality of the basis. More...

virtual int	getDegree () const
	Returns the degree of the basis. More...

virtual const shards::CellTopology	getBaseCellTopology () const
	Returns the base cell topology for which the basis is defined. See Shards documentation http://trilinos.sandia.gov/packages/shards for definition of base cell topology. More...

virtual EBasis	getBasisType () const
	Returns the basis type. More...

virtual ECoordinates	getCoordinateSystem () const
	Returns the type of coordinate system for which the basis is defined. More...

virtual int	getDofOrdinal (const int subcDim, const int subcOrd, const int subcDofOrd)
	DoF tag to ordinal lookup. More...

virtual const std::vector < std::vector< std::vector < int > > > &	getDofOrdinalData ()
	DoF tag to ordinal data structure.

virtual const std::vector< int > &	getDofTag (const int dofOrd)
	DoF ordinal to DoF tag lookup. More...

virtual const std::vector < std::vector< int > > &	getAllDofTags ()
	Retrieves all DoF tags. More...

Public Member Functions inherited from Intrepid::DofCoordsInterface< ArrayScalar >
virtual	~DofCoordsInterface ()=0
	Pure virtual destructor (gives warnings if not included). Following "Effective C++: 3rd Ed." item 7 the implementation is included in the definition file.

Private Member Functions
void	initializeTags ()
	Initializes tagToOrdinal_ and ordinalToTag_ lookup arrays.

Private Attributes
FieldContainer< Scalar >	latticePts_
	Holds the points defining the Lagrange basis.

Basis_HGRAD_LINE_Cn_FEM_JACOBI < Scalar, FieldContainer < Scalar > >	Phis_
	orthogonal basis

FieldContainer< Scalar >	V_
	Generalized Vandermonde matrix V_{ij} = phis_i(x_j)

FieldContainer< Scalar >	Vinv_
	inverse of Generalized Vandermonde matrix, whose columns store the expansion coefficients of the nodal basis in terms of phis_

Additional Inherited Members
Protected Attributes inherited from Intrepid::Basis< Scalar, ArrayScalar >
int	basisCardinality_
	Cardinality of the basis, i.e., the number of basis functions/degrees-of-freedom.

int	basisDegree_
	Degree of the largest complete polynomial space that can be represented by the basis.

shards::CellTopology	basisCellTopology_
	Base topology of the cells for which the basis is defined. See the Shards package http://trilinos.sandia.gov/packages/shards for definition of base cell topology.

EBasis	basisType_
	Type of the basis.

ECoordinates	basisCoordinates_
	The coordinate system for which the basis is defined.

bool	basisTagsAreSet_
	"true" if tagToOrdinal_ and ordinalToTag_ have been initialized

std::vector< std::vector< int > >	ordinalToTag_
	DoF ordinal to tag lookup table. More...

std::vector< std::vector < std::vector< int > > >	tagToOrdinal_
	DoF tag to ordinal lookup table. More...

Detailed Description

template<class Scalar, class ArrayScalar>
class Intrepid::Basis_HGRAD_LINE_Cn_FEM< Scalar, ArrayScalar >

Implementation of the locally H(grad)-compatible FEM basis of variable order on the [-1,1] reference line cell, using Lagrange polynomials.

Implements Lagrange basis of variable order $n$ on the reference [-1,1] line cell. The distribution of the points may be equispaced points with our without the endpoints, the Gauss-Legendre or Gauss-Lobatto points. These points are {x_i}_{i=0}^n. with x_i < x_{i+1}

The basis has cardinality $n+1$ and spans a COMPLETE linear polynomial space. Basis functions are dual to a unisolvent set of degrees of freedom (DoF) n_i( psi ) = psi(x_i). The DoF are ordered by i. The DoF at points -1 and 1 (if included in {x_i} are attached to the vertices, and the rest of the DoF are attached to the edge itself.

Definition at line 78 of file Intrepid_HGRAD_LINE_Cn_FEM.hpp.

Constructor & Destructor Documentation

template<class Scalar , class ArrayScalar >

Intrepid::Basis_HGRAD_LINE_Cn_FEM< Scalar, ArrayScalar >::Basis_HGRAD_LINE_Cn_FEM	(	int	order,
		const EPointType &	pointType
	)

Constructor.

Parameters

int	order: [in] polynomial degree of the basis
int	pointType: [in] type of points, either POINTTYPE_EQUISPACED or POINTTYPE_SPECTRAL

Definition at line 122 of file Intrepid_HGRAD_LINE_Cn_FEMDef.hpp.

Member Function Documentation

template<class Scalar , class ArrayScalar >

void Intrepid::Basis_HGRAD_LINE_Cn_FEM< Scalar, ArrayScalar >::getValues	(	ArrayScalar &	outputValues,
		const ArrayScalar &	inputPoints,
		const EOperator	operatorType
	)		const

virtual

Evaluation of a FEM basis on a reference Line cell.

    Returns values of <var>operatorType</var> acting on FEM basis functions for a set of
    points in the <strong>reference Line</strong> cell. For rank and dimensions of
    I/O array arguments see Section \ref basis_md_array_sec .

Parameters

outputValues	[out] - variable rank array with the basis values
inputPoints	[in] - rank-2 array (P,D) with the evaluation points
operatorType	[in] - the operator acting on the basis functions

Implements Intrepid::Basis< Scalar, ArrayScalar >.

Definition at line 249 of file Intrepid_HGRAD_LINE_Cn_FEMDef.hpp.

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

http://docs.trilinos.org/r13.0/packages/intrepid/src/Discretization/Basis/Intrepid_HGRAD_LINE_Cn_FEM.hpp
http://docs.trilinos.org/r13.0/packages/intrepid/src/Discretization/Basis/Intrepid_HGRAD_LINE_Cn_FEMDef.hpp

Public Member Functions

Private Member Functions

Private Attributes

Additional Inherited Members

Detailed Description

template<class Scalar, class ArrayScalar> class Intrepid::Basis_HGRAD_LINE_Cn_FEM< Scalar, ArrayScalar >

Constructor & Destructor Documentation

Member Function Documentation

template<class Scalar, class ArrayScalar>
class Intrepid::Basis_HGRAD_LINE_Cn_FEM< Scalar, ArrayScalar >