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 >:

List of all members.

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

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 operatorType acting on FEM basis functions for a set of points in the reference Line cell. For rank and dimensions of I/O array arguments see Section MD array template arguments for basis methods .

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:

/usr/src/RPM/BUILD/trilinos-11.12.1/packages/intrepid/src/Discretization/Basis/Intrepid_HGRAD_LINE_Cn_FEM.hpp
/usr/src/RPM/BUILD/trilinos-11.12.1/packages/intrepid/src/Discretization/Basis/Intrepid_HGRAD_LINE_Cn_FEMDef.hpp

Public Member Functions

Private Member Functions

Private Attributes

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 >