Implementation of the default H(grad)-compatible Lagrange basis of arbitrary degree on Triangle cell. More...

#include <Intrepid_HGRAD_TRI_Cn_FEM.hpp>

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

Public Member Functions
	Basis_HGRAD_TRI_Cn_FEM (const int n, const EPointType pointType)
	Constructor.

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

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

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

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

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.

virtual EBasis	getBasisType () const
	Returns the basis type.

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

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

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.

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

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

Private Attributes
Basis_HGRAD_TRI_Cn_FEM_ORTH< Scalar, FieldContainer< Scalar > >	Phis
	The orthogonal basis on triangles, out of which the nodal basis is constructed.

FieldContainer< Scalar >	V
	The Vandermonde matrix with V_{ij} = phi_i(x_j), where x_j is the j_th point in the lattice.

FieldContainer< Scalar >	Vinv
	The inverse of V. The columns of Vinv express the Lagrange basis in terms of the orthogonal basis.

FieldContainer< Scalar >	latticePts
	stores the points at which degrees of freedom are located.

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.

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

Detailed Description

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

Implementation of the default H(grad)-compatible Lagrange basis of arbitrary degree on Triangle cell.

    Implements Lagrangian basis of degree n on the reference Triangle cell. The basis has
    cardinality (n+1)(n+2)/2 and spans a COMPLETE polynomial space of degree n.
    Basis functions are dual 
    to a unisolvent set of degrees-of-freedom (DoF) defined on a lattice of order n (see PointTools).
    In particular, the degrees of freedom are point evaluation at
    \li the vertices
    \li (n-1) points on each edge of the triangle
    \li max((n-1)(n-2)/2,0) points on the inside of the triangle.

    The distribution of these points is specified by the pointType argument to the class constructor.
    Currently, either equispaced lattice points or Warburton's warp-blend points are available.

    The dof are enumerated according to the ordering on the lattice (see PointTools).  In particular,
    dof number 0 is at the bottom left vertex (0,0).  The dof increase
    along the lattice with points along the lines of constant
    x adjacent in the enumeration.

Definition at line 84 of file Intrepid_HGRAD_TRI_Cn_FEM.hpp.

Constructor & Destructor Documentation

◆ Basis_HGRAD_TRI_Cn_FEM()

template<class Scalar , class ArrayScalar >

Intrepid::Basis_HGRAD_TRI_Cn_FEM< Scalar, ArrayScalar >::Basis_HGRAD_TRI_Cn_FEM	(	const int	n,
		const EPointType	pointType
	)

Constructor.

Definition at line 54 of file Intrepid_HGRAD_TRI_Cn_FEMDef.hpp.

Member Function Documentation

◆ getValues() [1/2]

template<class Scalar , class ArrayScalar >

void Intrepid::Basis_HGRAD_TRI_Cn_FEM< Scalar, ArrayScalar >::getValues	(	ArrayScalar &	outputValues,
		const ArrayScalar &	inputPoints,
		const ArrayScalar &	cellVertices,
		const EOperator	operatorType = `OPERATOR_VALUE`
	)		const

virtual

FVD basis evaluation: invocation of this method throws an exception.

Implements Intrepid::Basis< Scalar, ArrayScalar >.

Definition at line 286 of file Intrepid_HGRAD_TRI_Cn_FEMDef.hpp.

◆ getValues() [2/2]

template<class Scalar , class ArrayScalar >

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

virtual

Evaluation of a FEM basis on a reference Triangle cell.

    Returns values of <var>operatorType</var> acting on FEM basis functions for a set of
    points in the <strong>reference Triangle</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 190 of file Intrepid_HGRAD_TRI_Cn_FEMDef.hpp.

Referenced by main().

◆ initializeTags()

template<class Scalar , class ArrayScalar >

void Intrepid::Basis_HGRAD_TRI_Cn_FEM< Scalar, ArrayScalar >::initializeTags ( )

privatevirtual

Initializes tagToOrdinal_ and ordinalToTag_ lookup arrays.

Implements Intrepid::Basis< Scalar, ArrayScalar >.

Definition at line 111 of file Intrepid_HGRAD_TRI_Cn_FEMDef.hpp.

Member Data Documentation

◆ latticePts

template<class Scalar , class ArrayScalar >

FieldContainer<Scalar> Intrepid::Basis_HGRAD_TRI_Cn_FEM< Scalar, ArrayScalar >::latticePts

private

stores the points at which degrees of freedom are located.

Definition at line 103 of file Intrepid_HGRAD_TRI_Cn_FEM.hpp.

◆ Phis

template<class Scalar , class ArrayScalar >

Basis_HGRAD_TRI_Cn_FEM_ORTH<Scalar,FieldContainer<Scalar> > Intrepid::Basis_HGRAD_TRI_Cn_FEM< Scalar, ArrayScalar >::Phis

private

The orthogonal basis on triangles, out of which the nodal basis is constructed.

Definition at line 93 of file Intrepid_HGRAD_TRI_Cn_FEM.hpp.

◆ V

template<class Scalar , class ArrayScalar >

FieldContainer<Scalar> Intrepid::Basis_HGRAD_TRI_Cn_FEM< Scalar, ArrayScalar >::V

private

The Vandermonde matrix with V_{ij} = phi_i(x_j), where x_j is the j_th point in the lattice.

Definition at line 96 of file Intrepid_HGRAD_TRI_Cn_FEM.hpp.

◆ Vinv

template<class Scalar , class ArrayScalar >

FieldContainer<Scalar> Intrepid::Basis_HGRAD_TRI_Cn_FEM< Scalar, ArrayScalar >::Vinv

private

The inverse of V. The columns of Vinv express the Lagrange basis in terms of the orthogonal basis.

Definition at line 100 of file Intrepid_HGRAD_TRI_Cn_FEM.hpp.

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

/home/runner/work/trilinos.github.io/trilinos.github.io/Trilinos/packages/intrepid/src/Discretization/Basis/Intrepid_HGRAD_TRI_Cn_FEM.hpp
/home/runner/work/trilinos.github.io/trilinos.github.io/Trilinos/packages/intrepid/src/Discretization/Basis/Intrepid_HGRAD_TRI_Cn_FEMDef.hpp

Public Member Functions

Private Member Functions

Private Attributes

Additional Inherited Members

Detailed Description

Constructor & Destructor Documentation

◆ Basis_HGRAD_TRI_Cn_FEM()

Member Function Documentation

◆ getValues() [1/2]

◆ getValues() [2/2]

◆ initializeTags()

Member Data Documentation

◆ latticePts

◆ Phis

◆ V

◆ Vinv