Base class for a FEM standard element. More...

#include <fem_standard_element.hpp>

Inheritance diagram for CFEMStandardElementBase:

Public Member Functions
	CFEMStandardElementBase ()=default
	Constructor. Nothing to be done.

virtual	~CFEMStandardElementBase ()=default
	Destructor. Nothing to be done, because the vectors are deleted automatically.

unsigned short	GetVTK_Type (void) const
	Function, which makes available the type of the element.

const su2double *	GetWeightsIntegration (void) const
	Function, which makes available the weights in the integration points.

unsigned short	GetNIntegration (void) const
	Function, which makes available the number of integration points for this standard element.

unsigned short	GetOrderExact (void) const
	Function, which makes available the polynomial order that must be integrated exactly.

void	GradVandermonde1D (unsigned short nDOFs, const vector< su2double > &r, vector< su2double > &VDr)
	Function, which computes the gradient of the Vandermonde matrix for a standard 1D edge.

void	Vandermonde1D (unsigned short nDOFs, const vector< su2double > &r, vector< su2double > &V)
	Function, which computes the Vandermonde matrix for a standard 1D edge.

Static Public Member Functions
static unsigned short	GetNDOFsStatic (unsigned short VTK_Type, unsigned short nPoly, unsigned long typeErrorMessage=0)
	Static function, which makes available the number of DOFs for an element corresponding to the arguments.

static void	InverseMatrix (unsigned short n, vector< su2double > &A)
	Static function, which computes the inverse of the given square matrix.

Protected Member Functions
	CFEMStandardElementBase (unsigned short val_VTK_Type, unsigned short val_nPoly, bool val_constJac, CConfig *config, unsigned short val_orderExact)
	Alternative constructor.

void	CheckSumDerivativesLagrangianBasisFunctions (const unsigned short nPoints, const unsigned short nDOFs, const vector< su2double > &dLagBasisPoints)
	Function, which checks if the sum of the given derivatives of the Lagrangian interpolation functions is 0 in the points.

void	CheckSumLagrangianBasisFunctions (const unsigned short nPoints, const unsigned short nDOFs, vector< su2double > &lagBasisPoints)
	Function, which checks if the sum of the given Lagrangian interpolation functions is 1 in the points.

void	Copy (const CFEMStandardElementBase &other)
	Function, which copies the data of the given object into the current object.

void	DerivativesBasisFunctionsAdjacentElement (unsigned short VTK_TypeElem, unsigned short nPolyElem, const bool swapFaceInElement, unsigned short &nDOFsElem, vector< su2double > &drLagBasisIntegration, vector< su2double > &dsLagBasisIntegration, vector< su2double > &dtLagBasisIntegration)
	Function, which computes the values of the derivatives of the basis functions of the adjacent elements in the integration points of the face.

void	GradVandermonde2D_Triangle (unsigned short nPoly, unsigned short nDOFs, const vector< su2double > &r, const vector< su2double > &s, vector< su2double > &VDr, vector< su2double > &VDs)
	Function, which computes the gradients of the Vandermonde matrix for a standard triangle.

void	GradVandermonde2D_Quadrilateral (unsigned short nPoly, unsigned short nDOFs, const vector< su2double > &r, const vector< su2double > &s, vector< su2double > &VDr, vector< su2double > &VDs)
	Function, which computes the gradients of the Vandermonde matrix for a standard quadrilateral.

void	GradVandermonde3D_Tetrahedron (unsigned short nPoly, unsigned short nDOFs, const vector< su2double > &r, const vector< su2double > &s, const vector< su2double > &t, vector< su2double > &VDr, vector< su2double > &VDs, vector< su2double > &VDt)
	Function, which computes the gradients of the Vandermonde matrix for a standard tetrahedron.

void	GradVandermonde3D_Pyramid (unsigned short nPoly, unsigned short nDOFs, const vector< su2double > &r, const vector< su2double > &s, const vector< su2double > &t, vector< su2double > &VDr, vector< su2double > &VDs, vector< su2double > &VDt)
	Function, which computes the gradients of the Vandermonde matrix for a standard pyramid.

void	GradVandermonde3D_Prism (unsigned short nPoly, unsigned short nDOFs, const vector< su2double > &r, const vector< su2double > &s, const vector< su2double > &t, vector< su2double > &VDr, vector< su2double > &VDs, vector< su2double > &VDt)
	Function, which computes the gradients of the Vandermonde matrix for a standard prism.

void	GradVandermonde3D_Hexahedron (unsigned short nPoly, unsigned short nDOFs, const vector< su2double > &r, const vector< su2double > &s, const vector< su2double > &t, vector< su2double > &VDr, vector< su2double > &VDs, vector< su2double > &VDt)
	Function, which computes the gradients of the Vandermonde matrix for a standard hexahedron.

void	LagrangianBasisFunctionAndDerivativesLine (const unsigned short nPoly, const vector< su2double > &rPoints, unsigned short &nDOFs, vector< su2double > &rDOFs, vector< su2double > &matVandermondeInv, vector< su2double > &lagBasisPoints, vector< su2double > &drLagBasisPoints)
	Function, which determines the values of the Lagrangian interpolation functions and its derivatives in the given set of points for a line.

void	LagrangianBasisFunctionAndDerivativesTriangle (const unsigned short nPoly, const vector< su2double > &rPoints, const vector< su2double > &sPoints, unsigned short &nDOFs, vector< su2double > &rDOFs, vector< su2double > &sDOFs, vector< su2double > &matVandermondeInv, vector< su2double > &lagBasisPoints, vector< su2double > &drLagBasisPoints, vector< su2double > &dsLagBasisPoints)
	Function, which determines the values of the Lagrangian interpolation functions and its derivatives in the given set of points for a triangle.

void	LagrangianBasisFunctionAndDerivativesQuadrilateral (const unsigned short nPoly, const vector< su2double > &rPoints, const vector< su2double > &sPoints, unsigned short &nDOFs, vector< su2double > &rDOFs, vector< su2double > &sDOFs, vector< su2double > &matVandermondeInv, vector< su2double > &lagBasisPoints, vector< su2double > &drLagBasisPoints, vector< su2double > &dsLagBasisPoints)
	Function, which determines the values of the Lagrangian interpolation functions and its derivatives in the given set of points for a quadrilateral.

void	LagrangianBasisFunctionAndDerivativesTetrahedron (const unsigned short nPoly, const vector< su2double > &rPoints, const vector< su2double > &sPoints, const vector< su2double > &tPoints, unsigned short &nDOFs, vector< su2double > &rDOFs, vector< su2double > &sDOFs, vector< su2double > &tDOFs, vector< su2double > &matVandermondeInv, vector< su2double > &lagBasisPoints, vector< su2double > &drLagBasisPoints, vector< su2double > &dsLagBasisPoints, vector< su2double > &dtLagBasisPoints)
	Function, which determines the values of the Lagrangian interpolation functions and its derivatives in the given set of points for a tetrahedron.

void	LagrangianBasisFunctionAndDerivativesPyramid (const unsigned short nPoly, const vector< su2double > &rPoints, const vector< su2double > &sPoints, const vector< su2double > &tPoints, unsigned short &nDOFs, vector< su2double > &rDOFs, vector< su2double > &sDOFs, vector< su2double > &tDOFs, vector< su2double > &matVandermondeInv, vector< su2double > &lagBasisPoints, vector< su2double > &drLagBasisPoints, vector< su2double > &dsLagBasisPoints, vector< su2double > &dtLagBasisPoints)
	Function, which determines the values of the Lagrangian interpolation functions and its derivatives in the given set of points for a pyramid.

void	LagrangianBasisFunctionAndDerivativesPrism (const unsigned short nPoly, const vector< su2double > &rPoints, const vector< su2double > &sPoints, const vector< su2double > &tPoints, unsigned short &nDOFs, vector< su2double > &rDOFs, vector< su2double > &sDOFs, vector< su2double > &tDOFs, vector< su2double > &matVandermondeInv, vector< su2double > &lagBasisPoints, vector< su2double > &drLagBasisPoints, vector< su2double > &dsLagBasisPoints, vector< su2double > &dtLagBasisPoints)
	Function, which determines the values of the Lagrangian interpolation functions and its derivatives in the given set of points for a prism.

void	LagrangianBasisFunctionAndDerivativesHexahedron (const unsigned short nPoly, const vector< su2double > &rPoints, const vector< su2double > &sPoints, const vector< su2double > &tPoints, unsigned short &nDOFs, vector< su2double > &rDOFs, vector< su2double > &sDOFs, vector< su2double > &tDOFs, vector< su2double > &matVandermondeInv, vector< su2double > &lagBasisPoints, vector< su2double > &drLagBasisPoints, vector< su2double > &dsLagBasisPoints, vector< su2double > &dtLagBasisPoints)
	Function, which determines the values of the Lagrangian interpolation functions and its derivatives in the given set of points for a hexahedron.

void	MatMulRowMajor (const unsigned short nDOFs, const unsigned short nPoints, const vector< su2double > &A, const vector< su2double > &B, vector< su2double > &C)
	Function, which carries out a matrix matrix multiplication to obtain data in points and stores the result row major order.

void	SubConnForPlottingLine (const unsigned short nPoly, vector< unsigned short > &subConn)
	Function, which computes the local connectivity of linear subelements of a line, which can be used for plotting.

void	SubConnForPlottingQuadrilateral (const unsigned short nPoly, vector< unsigned short > &subConn)
	Function, which computes the local connectivity of linear subelements of a quadrilateral, which can be used for plotting.

void	SubConnForPlottingTriangle (const unsigned short nPoly, vector< unsigned short > &subConn)
	Function, which computes the local connectivity of linear subelements of a triangle, which can be used for plotting.

void	Vandermonde2D_Triangle (unsigned short nPoly, unsigned short nDOFs, const vector< su2double > &r, const vector< su2double > &s, vector< su2double > &V)
	Function, which computes the Vandermonde matrix for a standard triangle.

void	Vandermonde2D_Quadrilateral (unsigned short nPoly, unsigned short nDOFs, const vector< su2double > &r, const vector< su2double > &s, vector< su2double > &V)
	Function, which computes the Vandermonde matrix for a standard quadrilateral.

void	Vandermonde3D_Tetrahedron (unsigned short nPoly, unsigned short nDOFs, const vector< su2double > &r, const vector< su2double > &s, const vector< su2double > &t, vector< su2double > &V)
	Function, which computes the Vandermonde matrix for a standard tetrahedron.

void	Vandermonde3D_Pyramid (unsigned short nPoly, unsigned short nDOFs, const vector< su2double > &r, const vector< su2double > &s, const vector< su2double > &t, vector< su2double > &V)
	Function, which computes the Vandermonde matrix for a standard pyramid.

void	Vandermonde3D_Prism (unsigned short nPoly, unsigned short nDOFs, const vector< su2double > &r, const vector< su2double > &s, const vector< su2double > &t, vector< su2double > &V)
	Function, which computes the Vandermonde matrix for a standard prism.

void	Vandermonde3D_Hexahedron (unsigned short nPoly, unsigned short nDOFs, const vector< su2double > &r, const vector< su2double > &s, const vector< su2double > &t, vector< su2double > &V)
	Function, which computes the Vandermonde matrix for a standard hexahedron.

su2double	ViscousPenaltyParameter (const unsigned short VTK_TypeElem, const unsigned short nPolyElem) const
	Function, which computes the constant in the penalty terms for a a viscous discretization.

Protected Attributes
unsigned short	VTK_Type
	Element type using the VTK convention.

unsigned short	orderExact
	Polynomial order that must be integrated exactly by the integration rule.

unsigned short	nIntegration
	Number of points used in the numerical integration.

bool	constJacobian
	Whether or not the element has a constant Jacobian.

vector< su2double >	rIntegration
	r-location of the integration points for this standard element.

vector< su2double >	sIntegration
	s-location of the integration points for this standard element, if needed.

vector< su2double >	tIntegration
	t-location of the integration points for this standard element, if needed.

vector< su2double >	wIntegration
	The weights of the integration points for this standard element.

Detailed Description

Base class for a FEM standard element.

Author: E. van der Weide

Version: 8.5.0 "Harrier"

Constructor & Destructor Documentation

◆ CFEMStandardElementBase() [1/2]

CFEMStandardElementBase::CFEMStandardElementBase ( )

default

Constructor. Nothing to be done.

◆ ~CFEMStandardElementBase()

virtual CFEMStandardElementBase::~CFEMStandardElementBase ( )

virtualdefault

Destructor. Nothing to be done, because the vectors are deleted automatically.

◆ CFEMStandardElementBase() [2/2]

CFEMStandardElementBase::CFEMStandardElementBase	(	unsigned short	val_VTK_Type,
		unsigned short	val_nPoly,
		bool	val_constJac,
		CConfig *	config,
		unsigned short	val_orderExact
	)

protected

Alternative constructor.

Parameters

[in]	val_VTK_Type	- Type of the element using the VTK convention.
[in]	val_nPoly	- Polynomial degree of the element.
[in]	val_constJac	- Whether or not the Jacobians are constant.
[in]	config	- Object, which contains the input parameters.
[in]	val_orderExact	- The order of the polynomials that must be integrated exactly by the integration rule. If 0, it will be determined from the polynomial degree and the parameters in config.

Member Function Documentation

◆ CheckSumDerivativesLagrangianBasisFunctions()

void CFEMStandardElementBase::CheckSumDerivativesLagrangianBasisFunctions	(	const unsigned short	nPoints,
		const unsigned short	nDOFs,
		const vector< su2double > &	dLagBasisPoints
	)

protected

Function, which checks if the sum of the given derivatives of the Lagrangian interpolation functions is 0 in the points.

Parameters

[in]	nPoints	- Number of points to be checked.
[in]	nDOFs	- Number of DOFs of the element.
[in]	dLagBasisPoints	- Values of the derivatives of the Lagrangian interpolation functions in the given points.

◆ CheckSumLagrangianBasisFunctions()

void CFEMStandardElementBase::CheckSumLagrangianBasisFunctions	(	const unsigned short	nPoints,
		const unsigned short	nDOFs,
		vector< su2double > &	lagBasisPoints
	)

protected

Function, which checks if the sum of the given Lagrangian interpolation functions is 1 in the points.

Parameters

[in]	nPoints	- Number of points to be checked.
[in]	nDOFs	- Number of DOFs of the element.
[in,out]	lagBasisPoints	- Values of the Lagrangian interpolation functions in the given points.

◆ Copy()

void CFEMStandardElementBase::Copy ( const CFEMStandardElementBase & other )

protected

Function, which copies the data of the given object into the current object.

Parameters

[in] other - Object, whose data is copied.

◆ DerivativesBasisFunctionsAdjacentElement()

void CFEMStandardElementBase::DerivativesBasisFunctionsAdjacentElement	(	unsigned short	VTK_TypeElem,
		unsigned short	nPolyElem,
		const bool	swapFaceInElement,
		unsigned short &	nDOFsElem,
		vector< su2double > &	drLagBasisIntegration,
		vector< su2double > &	dsLagBasisIntegration,
		vector< su2double > &	dtLagBasisIntegration
	)

protected

Function, which computes the values of the derivatives of the basis functions of the adjacent elements in the integration points of the face.

Parameters

[in]	VTK_TypeElem	- Type of the element adjacent to the face using the VTK convention.
[in]	nPolyElem	- Polynomial degree of the element adjacent to the face.
[in]	swapFaceInElement	- Whether or not the connectivity of the face must be swapped to get the desired numbering compared to the numbering used in the corresponding face of the element.
[out]	nDOFsElem	- Number of DOFs of the element adjacent to the face.
[out]	drLagBasisIntegration	- r-derivatives of the basis functions in the integration points of the face.
[out]	dsLagBasisIntegration	- s-derivatives of the basis functions in the integration points of the face.
[out]	dtLagBasisIntegration	- t-derivatives of the basis functions in the integration points of the face.

◆ GetNDOFsStatic()

unsigned short CFEMStandardElementBase::GetNDOFsStatic	(	unsigned short	VTK_Type,
		unsigned short	nPoly,
		unsigned long	typeErrorMessage = `0`
	)

static

Static function, which makes available the number of DOFs for an element corresponding to the arguments.

Parameters

[in]	VTK_Type	- Type of the element using the VTK convention.
[in]	nPoly	- Polynomial degree of the element.
[in]	typeErrorMessage	- Default argument used to write a good error message.

Returns: The number of DOFs

◆ GetNIntegration()

unsigned short CFEMStandardElementBase::GetNIntegration ( void ) const

inline

Function, which makes available the number of integration points for this standard element.

Returns: The number of integration points of this standard element.

◆ GetOrderExact()

unsigned short CFEMStandardElementBase::GetOrderExact ( void ) const

inline

Function, which makes available the polynomial order that must be integrated exactly.

Returns: The polynomial order that must be integrated exactly.

◆ GetVTK_Type()

unsigned short CFEMStandardElementBase::GetVTK_Type ( void ) const

inline

Function, which makes available the type of the element.

Returns: The type of the element using the VTK convention.

◆ GetWeightsIntegration()

const su2double * CFEMStandardElementBase::GetWeightsIntegration ( void ) const

inline

Function, which makes available the weights in the integration points.

Returns: The const pointer to data, which stores the weights in the integration points.

◆ GradVandermonde1D()

void CFEMStandardElementBase::GradVandermonde1D	(	unsigned short	nDOFs,
		const vector< su2double > &	r,
		vector< su2double > &	VDr
	)

Function, which computes the gradient of the Vandermonde matrix for a standard 1D edge.

Parameters

[in]	nDOFs	- Number of DOFs, which in 1D is the polynomial degree + 1.
[in]	r	- Parametric coordinates for which the gradient of the Vandermonde matrix must be computed.
[out]	VDr	- Matrix to store the gradient of the Vandermonde matrix in all r-locations.

◆ GradVandermonde2D_Quadrilateral()

void CFEMStandardElementBase::GradVandermonde2D_Quadrilateral	(	unsigned short	nPoly,
		unsigned short	nDOFs,
		const vector< su2double > &	r,
		const vector< su2double > &	s,
		vector< su2double > &	VDr,
		vector< su2double > &	VDs
	)

protected

Function, which computes the gradients of the Vandermonde matrix for a standard quadrilateral.

Parameters

[in]	nPoly	- Polynomial degree of the quadrilateral.
[in]	nDOFs	- Number of DOFs of the quadrilateral.
[in]	r	- Parametric coordinate in r-direction for which the gradient of the Vandermonde matrix must be computed.
[in]	s	- Parametric coordinate in s-direction for which the gradient of the Vandermonde matrix must be computed.
[out]	VDr	- Matrix to store the gradient in r-direction of the Vandermonde matrix in all r- and s-locations.
[out]	VDs	- Matrix to store the gradient in s-direction of the Vandermonde matrix in all r- and s-locations.

◆ GradVandermonde2D_Triangle()

void CFEMStandardElementBase::GradVandermonde2D_Triangle	(	unsigned short	nPoly,
		unsigned short	nDOFs,
		const vector< su2double > &	r,
		const vector< su2double > &	s,
		vector< su2double > &	VDr,
		vector< su2double > &	VDs
	)

protected

Function, which computes the gradients of the Vandermonde matrix for a standard triangle.

Parameters

[in]	nPoly	- Polynomial degree of the triangle.
[in]	nDOFs	- Number of DOFs of the triangle.
[in]	r	- Parametric coordinate in r-direction for which the gradient of the Vandermonde matrix must be computed.
[in]	s	- Parametric coordinate in s-direction for which the gradient of the Vandermonde matrix must be computed.
[out]	VDr	- Matrix to store the gradient in r-direction of the Vandermonde matrix in all r- and s-locations.
[out]	VDs	- Matrix to store the gradient in s-direction of the Vandermonde matrix in all r- and s-locations.

◆ GradVandermonde3D_Hexahedron()

void CFEMStandardElementBase::GradVandermonde3D_Hexahedron	(	unsigned short	nPoly,
		unsigned short	nDOFs,
		const vector< su2double > &	r,
		const vector< su2double > &	s,
		const vector< su2double > &	t,
		vector< su2double > &	VDr,
		vector< su2double > &	VDs,
		vector< su2double > &	VDt
	)

protected

Function, which computes the gradients of the Vandermonde matrix for a standard hexahedron.

Parameters

[in]	nPoly	- Polynomial degree of the hexahedron.
[in]	nDOFs	- Number of DOFs of the hexahedron.
[in]	r	- Parametric coordinate in r-direction for which the gradient of the Vandermonde matrix must be computed.
[in]	s	- Parametric coordinate in s-direction for which the gradient of the Vandermonde matrix must be computed.
[in]	t	- Parametric coordinate in t-direction for which the gradient of the Vandermonde matrix must be computed.
[out]	VDr	- Matrix to store the gradient in r-direction of the Vandermonde matrix in all r-, s- and t-locations.
[out]	VDs	- Matrix to store the gradient in s-direction of the Vandermonde matrix in all r-, s- and t-locations.
[out]	VDt	- Matrix to store the gradient in t-direction of the Vandermonde matrix in all r-, s- and t-locations.

◆ GradVandermonde3D_Prism()

void CFEMStandardElementBase::GradVandermonde3D_Prism	(	unsigned short	nPoly,
		unsigned short	nDOFs,
		const vector< su2double > &	r,
		const vector< su2double > &	s,
		const vector< su2double > &	t,
		vector< su2double > &	VDr,
		vector< su2double > &	VDs,
		vector< su2double > &	VDt
	)

protected

Function, which computes the gradients of the Vandermonde matrix for a standard prism.

Parameters

[in]	nPoly	- Polynomial degree of the prism.
[in]	nDOFs	- Number of DOFs of the prism.
[in]	r	- Parametric coordinate in r-direction for which the gradient of the Vandermonde matrix must be computed.
[in]	s	- Parametric coordinate in s-direction for which the gradient of the Vandermonde matrix must be computed.
[in]	t	- Parametric coordinate in t-direction for which the gradient of the Vandermonde matrix must be computed.
[out]	VDr	- Matrix to store the gradient in r-direction of the Vandermonde matrix in all r-, s- and t-locations.
[out]	VDs	- Matrix to store the gradient in s-direction of the Vandermonde matrix in all r-, s- and t-locations.
[out]	VDt	- Matrix to store the gradient in t-direction of the Vandermonde matrix in all r-, s- and t-locations.

◆ GradVandermonde3D_Pyramid()

void CFEMStandardElementBase::GradVandermonde3D_Pyramid	(	unsigned short	nPoly,
		unsigned short	nDOFs,
		const vector< su2double > &	r,
		const vector< su2double > &	s,
		const vector< su2double > &	t,
		vector< su2double > &	VDr,
		vector< su2double > &	VDs,
		vector< su2double > &	VDt
	)

protected

Function, which computes the gradients of the Vandermonde matrix for a standard pyramid.

Parameters

[in]	nPoly	- Polynomial degree of the pyramid.
[in]	nDOFs	- Number of DOFs of the pyramid.
[in]	r	- Parametric coordinate in r-direction for which the gradient of the Vandermonde matrix must be computed.
[in]	s	- Parametric coordinate in s-direction for which the gradient of the Vandermonde matrix must be computed.
[in]	t	- Parametric coordinate in t-direction for which the gradient of the Vandermonde matrix must be computed.
[out]	VDr	- Matrix to store the gradient in r-direction of the Vandermonde matrix in all r-, s- and t-locations.
[out]	VDs	- Matrix to store the gradient in s-direction of the Vandermonde matrix in all r-, s- and t-locations.
[out]	VDt	- Matrix to store the gradient in t-direction of the Vandermonde matrix in all r-, s- and t-locations.

◆ GradVandermonde3D_Tetrahedron()

void CFEMStandardElementBase::GradVandermonde3D_Tetrahedron	(	unsigned short	nPoly,
		unsigned short	nDOFs,
		const vector< su2double > &	r,
		const vector< su2double > &	s,
		const vector< su2double > &	t,
		vector< su2double > &	VDr,
		vector< su2double > &	VDs,
		vector< su2double > &	VDt
	)

protected

Function, which computes the gradients of the Vandermonde matrix for a standard tetrahedron.

Parameters

[in]	nPoly	- Polynomial degree of the tetrahedron.
[in]	nDOFs	- Number of DOFs of the tetrahedron.
[in]	r	- Parametric coordinate in r-direction for which the gradient of the Vandermonde matrix must be computed.
[in]	s	- Parametric coordinate in s-direction for which the gradient of the Vandermonde matrix must be computed.
[in]	t	- Parametric coordinate in t-direction for which the gradient of the Vandermonde matrix must be computed.
[out]	VDr	- Matrix to store the gradient in r-direction of the Vandermonde matrix in all r-, s- and t-locations.
[out]	VDs	- Matrix to store the gradient in s-direction of the Vandermonde matrix in all r-, s- and t-locations.
[out]	VDt	- Matrix to store the gradient in t-direction of the Vandermonde matrix in all r-, s- and t-locations.

◆ InverseMatrix()

void CFEMStandardElementBase::InverseMatrix	(	unsigned short	n,
		vector< su2double > &	A
	)

static

Static function, which computes the inverse of the given square matrix.

Parameters

[in]	n	- Number of rows/columns of the square matrix A.
[in,out]	A	- On input the square matrix to be inverted. On output the inverse.

◆ LagrangianBasisFunctionAndDerivativesHexahedron()

void CFEMStandardElementBase::LagrangianBasisFunctionAndDerivativesHexahedron	(	const unsigned short	nPoly,
		const vector< su2double > &	rPoints,
		const vector< su2double > &	sPoints,
		const vector< su2double > &	tPoints,
		unsigned short &	nDOFs,
		vector< su2double > &	rDOFs,
		vector< su2double > &	sDOFs,
		vector< su2double > &	tDOFs,
		vector< su2double > &	matVandermondeInv,
		vector< su2double > &	lagBasisPoints,
		vector< su2double > &	drLagBasisPoints,
		vector< su2double > &	dsLagBasisPoints,
		vector< su2double > &	dtLagBasisPoints
	)

protected

Function, which determines the values of the Lagrangian interpolation functions and its derivatives in the given set of points for a hexahedron.

Parameters

[in]	nPoly	- Polynomial degree of the interpolation functions.
[in]	rPoints	- r-coordinates of the points where the interpolation functions must be evaluated.
[in]	sPoints	- s-coordinates of the points where the interpolation functions must be evaluated.
[in]	tPoints	- t-coordinates of the points where the interpolation functions must be evaluated.
[out]	nDOFs	- Number of DOFs of the quadrilateral.
[out]	rDOFs	- r-coordinates of the DOFs of the hexahedron.
[out]	sDOFs	- s-coordinates of the DOFs of the hexahedron.
[out]	tDOFs	- t-coordinates of the DOFs of the hexahedron.
[out]	matVandermondeInv-	Values of the inverse matrix of Vandermonde matrix
[out]	lagBasisPoints	- Values of the Lagrangian interpolation functions in the given points.
[out]	drLagBasisPoints	- Values of the r-derivatives of the Lagrangian interpolation functions in the given points.
[out]	dsLagBasisPoints	- Values of the s-derivatives of the Lagrangian interpolation functions in the given points.
[out]	dtLagBasisPoints	- Values of the t-derivatives of the Lagrangian interpolation functions in the given points.

◆ LagrangianBasisFunctionAndDerivativesLine()

void CFEMStandardElementBase::LagrangianBasisFunctionAndDerivativesLine	(	const unsigned short	nPoly,
		const vector< su2double > &	rPoints,
		unsigned short &	nDOFs,
		vector< su2double > &	rDOFs,
		vector< su2double > &	matVandermondeInv,
		vector< su2double > &	lagBasisPoints,
		vector< su2double > &	drLagBasisPoints
	)

protected

Function, which determines the values of the Lagrangian interpolation functions and its derivatives in the given set of points for a line.

Parameters

[in]	nPoly	- Polynomial degree of the interpolation functions.
[in]	rPoints	- r-coordinates of the points where the interpolation functions must be evaluated.
[out]	nDOFs	- Number of DOFs of the line element.
[out]	rDOFs	- r-coordinates of the DOFs of the line element.
[out]	matVandermondeInv-	Values of the inverse matrix of Vandermonde matrix
[out]	lagBasisPoints	- Values of the Lagrangian interpolation functions in the given points.
[out]	drLagBasisPoints	- Values of the r-derivatives of the Lagrangian interpolation functions in the given points.

◆ LagrangianBasisFunctionAndDerivativesPrism()

void CFEMStandardElementBase::LagrangianBasisFunctionAndDerivativesPrism	(	const unsigned short	nPoly,
		const vector< su2double > &	rPoints,
		const vector< su2double > &	sPoints,
		const vector< su2double > &	tPoints,
		unsigned short &	nDOFs,
		vector< su2double > &	rDOFs,
		vector< su2double > &	sDOFs,
		vector< su2double > &	tDOFs,
		vector< su2double > &	matVandermondeInv,
		vector< su2double > &	lagBasisPoints,
		vector< su2double > &	drLagBasisPoints,
		vector< su2double > &	dsLagBasisPoints,
		vector< su2double > &	dtLagBasisPoints
	)

protected

Function, which determines the values of the Lagrangian interpolation functions and its derivatives in the given set of points for a prism.

Parameters

[in]	nPoly	- Polynomial degree of the interpolation functions.
[in]	rPoints	- r-coordinates of the points where the interpolation functions must be evaluated.
[in]	sPoints	- s-coordinates of the points where the interpolation functions must be evaluated.
[in]	tPoints	- t-coordinates of the points where the interpolation functions must be evaluated.
[out]	nDOFs	- Number of DOFs of the quadrilateral.
[out]	rDOFs	- r-coordinates of the DOFs of the prism.
[out]	sDOFs	- s-coordinates of the DOFs of the prism.
[out]	tDOFs	- t-coordinates of the DOFs of the prism.
[out]	matVandermondeInv-	Values of the inverse matrix of Vandermonde matrix
[out]	lagBasisPoints	- Values of the Lagrangian interpolation functions in the given points.
[out]	drLagBasisPoints	- Values of the r-derivatives of the Lagrangian interpolation functions in the given points.
[out]	dsLagBasisPoints	- Values of the s-derivatives of the Lagrangian interpolation functions in the given points.
[out]	dtLagBasisPoints	- Values of the t-derivatives of the Lagrangian interpolation functions in the given points.

◆ LagrangianBasisFunctionAndDerivativesPyramid()

void CFEMStandardElementBase::LagrangianBasisFunctionAndDerivativesPyramid	(	const unsigned short	nPoly,
		const vector< su2double > &	rPoints,
		const vector< su2double > &	sPoints,
		const vector< su2double > &	tPoints,
		unsigned short &	nDOFs,
		vector< su2double > &	rDOFs,
		vector< su2double > &	sDOFs,
		vector< su2double > &	tDOFs,
		vector< su2double > &	matVandermondeInv,
		vector< su2double > &	lagBasisPoints,
		vector< su2double > &	drLagBasisPoints,
		vector< su2double > &	dsLagBasisPoints,
		vector< su2double > &	dtLagBasisPoints
	)

protected

Function, which determines the values of the Lagrangian interpolation functions and its derivatives in the given set of points for a pyramid.

Parameters

[in]	nPoly	- Polynomial degree of the interpolation functions.
[in]	rPoints	- r-coordinates of the points where the interpolation functions must be evaluated.
[in]	sPoints	- s-coordinates of the points where the interpolation functions must be evaluated.
[in]	tPoints	- t-coordinates of the points where the interpolation functions must be evaluated.
[out]	nDOFs	- Number of DOFs of the quadrilateral.
[out]	rDOFs	- r-coordinates of the DOFs of the pyramid.
[out]	sDOFs	- s-coordinates of the DOFs of the pyramid.
[out]	tDOFs	- t-coordinates of the DOFs of the pyramid.
[out]	matVandermondeInv-	Values of the inverse matrix of Vandermonde matrix
[out]	lagBasisPoints	- Values of the Lagrangian interpolation functions in the given points.
[out]	drLagBasisPoints	- Values of the r-derivatives of the Lagrangian interpolation functions in the given points.
[out]	dsLagBasisPoints	- Values of the s-derivatives of the Lagrangian interpolation functions in the given points.
[out]	dtLagBasisPoints	- Values of the t-derivatives of the Lagrangian interpolation functions in the given points.

◆ LagrangianBasisFunctionAndDerivativesQuadrilateral()

void CFEMStandardElementBase::LagrangianBasisFunctionAndDerivativesQuadrilateral	(	const unsigned short	nPoly,
		const vector< su2double > &	rPoints,
		const vector< su2double > &	sPoints,
		unsigned short &	nDOFs,
		vector< su2double > &	rDOFs,
		vector< su2double > &	sDOFs,
		vector< su2double > &	matVandermondeInv,
		vector< su2double > &	lagBasisPoints,
		vector< su2double > &	drLagBasisPoints,
		vector< su2double > &	dsLagBasisPoints
	)

protected

Function, which determines the values of the Lagrangian interpolation functions and its derivatives in the given set of points for a quadrilateral.

Parameters

[in]	nPoly	- Polynomial degree of the interpolation functions.
[in]	rPoints	- r-coordinates of the points where the interpolation functions must be evaluated.
[in]	sPoints	- s-coordinates of the points where the interpolation functions must be evaluated.
[out]	nDOFs	- Number of DOFs of the quadrilateral.
[out]	rDOFs	- r-coordinates of the DOFs of the quadrilateral.
[out]	sDOFs	- s-coordinates of the DOFs of the quadrilateral.
[out]	matVandermondeInv-	Values of the inverse matrix of Vandermonde matrix
[out]	lagBasisPoints	- Values of the Lagrangian interpolation functions in the given points.
[out]	drLagBasisPoints	- Values of the r-derivatives of the Lagrangian interpolation functions in the given points.
[out]	dsLagBasisPoints	- Values of the s-derivatives of the Lagrangian interpolation functions in the given points.

◆ LagrangianBasisFunctionAndDerivativesTetrahedron()

void CFEMStandardElementBase::LagrangianBasisFunctionAndDerivativesTetrahedron	(	const unsigned short	nPoly,
		const vector< su2double > &	rPoints,
		const vector< su2double > &	sPoints,
		const vector< su2double > &	tPoints,
		unsigned short &	nDOFs,
		vector< su2double > &	rDOFs,
		vector< su2double > &	sDOFs,
		vector< su2double > &	tDOFs,
		vector< su2double > &	matVandermondeInv,
		vector< su2double > &	lagBasisPoints,
		vector< su2double > &	drLagBasisPoints,
		vector< su2double > &	dsLagBasisPoints,
		vector< su2double > &	dtLagBasisPoints
	)

protected

Function, which determines the values of the Lagrangian interpolation functions and its derivatives in the given set of points for a tetrahedron.

Parameters

[in]	nPoly	- Polynomial degree of the interpolation functions.
[in]	rPoints	- r-coordinates of the points where the interpolation functions must be evaluated.
[in]	sPoints	- s-coordinates of the points where the interpolation functions must be evaluated.
[in]	tPoints	- t-coordinates of the points where the interpolation functions must be evaluated.
[out]	nDOFs	- Number of DOFs of the quadrilateral.
[out]	rDOFs	- r-coordinates of the DOFs of the tetrahedron.
[out]	sDOFs	- s-coordinates of the DOFs of the tetrahedron.
[out]	tDOFs	- t-coordinates of the DOFs of the tetrahedron.
[out]	matVandermondeInv-	Values of the inverse matrix of Vandermonde matrix
[out]	lagBasisPoints	- Values of the Lagrangian interpolation functions in the given points.
[out]	drLagBasisPoints	- Values of the r-derivatives of the Lagrangian interpolation functions in the given points.
[out]	dsLagBasisPoints	- Values of the s-derivatives of the Lagrangian interpolation functions in the given points.
[out]	dtLagBasisPoints	- Values of the t-derivatives of the Lagrangian interpolation functions in the given points.

◆ LagrangianBasisFunctionAndDerivativesTriangle()

void CFEMStandardElementBase::LagrangianBasisFunctionAndDerivativesTriangle	(	const unsigned short	nPoly,
		const vector< su2double > &	rPoints,
		const vector< su2double > &	sPoints,
		unsigned short &	nDOFs,
		vector< su2double > &	rDOFs,
		vector< su2double > &	sDOFs,
		vector< su2double > &	matVandermondeInv,
		vector< su2double > &	lagBasisPoints,
		vector< su2double > &	drLagBasisPoints,
		vector< su2double > &	dsLagBasisPoints
	)

protected

Function, which determines the values of the Lagrangian interpolation functions and its derivatives in the given set of points for a triangle.

Parameters

[in]	nPoly	- Polynomial degree of the interpolation functions.
[in]	rPoints	- r-coordinates of the points where the interpolation functions must be evaluated.
[in]	sPoints	- s-coordinates of the points where the interpolation functions must be evaluated.
[out]	nDOFs	- Number of DOFs of the triangle.
[out]	rDOFs	- r-coordinates of the DOFs of the triangle.
[out]	sDOFs	- s-coordinates of the DOFs of the triangle.
[out]	matVandermondeInv-	Values of the inverse matrix of Vandermonde matrix
[out]	lagBasisPoints	- Values of the Lagrangian interpolation functions in the given points.
[out]	drLagBasisPoints	- Values of the r-derivatives of the Lagrangian interpolation functions in the given points.
[out]	dsLagBasisPoints	- Values of the s-derivatives of the Lagrangian interpolation functions in the given points.

◆ MatMulRowMajor()

void CFEMStandardElementBase::MatMulRowMajor	(	const unsigned short	nDOFs,
		const unsigned short	nPoints,
		const vector< su2double > &	A,
		const vector< su2double > &	B,
		vector< su2double > &	C
	)

protected

Function, which carries out a matrix matrix multiplication to obtain data in points and stores the result row major order.

Parameters

[in]	nDOFs	- Dimension of the matrices. This typically corresponds to the number of DOFs that are considered.
[in]	nPoints	- Dimension of the matrices. This typically corresponds to the number of integration points used.
[in]	A	- First matrix in the matrix matrix product A*B, dimension nPoints X nDOFs. A is stored in column major order.
[in]	B	- Second matrix in the matrix matrix product A*B, dimension nDOFs X nDOFs. B is stored in column major order.
[out]	C	- Result of A*B, dimension nPoints X nDOFs. The result is stored in row major order

◆ SubConnForPlottingLine()

void CFEMStandardElementBase::SubConnForPlottingLine	(	const unsigned short	nPoly,
		vector< unsigned short > &	subConn
	)

protected

Function, which computes the local connectivity of linear subelements of a line, which can be used for plotting.

Parameters

[in]	nPoly	- Polynomial degree of the line.
[out]	subConn	- The local subconnectivity of a line element.

◆ SubConnForPlottingQuadrilateral()

void CFEMStandardElementBase::SubConnForPlottingQuadrilateral	(	const unsigned short	nPoly,
		vector< unsigned short > &	subConn
	)

protected

Function, which computes the local connectivity of linear subelements of a quadrilateral, which can be used for plotting.

Parameters

[in]	nPoly	- Polynomial degree of the quadrilateral.
[out]	subConn	- The local subconnectivity of a triangle element.

◆ SubConnForPlottingTriangle()

void CFEMStandardElementBase::SubConnForPlottingTriangle	(	const unsigned short	nPoly,
		vector< unsigned short > &	subConn
	)

protected

Function, which computes the local connectivity of linear subelements of a triangle, which can be used for plotting.

Parameters

[in]	nPoly	- Polynomial degree of the triangle.
[out]	subConn	- The local subconnectivity of a triangle element.

◆ Vandermonde1D()

void CFEMStandardElementBase::Vandermonde1D	(	unsigned short	nDOFs,
		const vector< su2double > &	r,
		vector< su2double > &	V
	)

Function, which computes the Vandermonde matrix for a standard 1D edge.

Parameters

[in]	nDOFs	- Number of DOFs, which in 1D is the polynomial degree + 1.
[in]	r	- Parametric coordinates for which the Vandermonde matrix must be computed.
[out]	V	- Matrix to store the Vandermonde matrix in all r-locations.

◆ Vandermonde2D_Quadrilateral()

void CFEMStandardElementBase::Vandermonde2D_Quadrilateral	(	unsigned short	nPoly,
		unsigned short	nDOFs,
		const vector< su2double > &	r,
		const vector< su2double > &	s,
		vector< su2double > &	V
	)

protected

Function, which computes the Vandermonde matrix for a standard quadrilateral.

Parameters

[in]	nPoly	- Polynomial degree of the quadrilateral.
[in]	nDOFs	- Number of DOFs of the quadrilateral.
[in]	r	- Parametric coordinates in r-direction for which the Vandermonde matrix must be computed.
[in]	s	- Parametric coordinates in s-direction for which the Vandermonde matrix must be computed.
[out]	V	- Matrix to store the Vandermonde matrix in all r- and s-locations.

◆ Vandermonde2D_Triangle()

void CFEMStandardElementBase::Vandermonde2D_Triangle	(	unsigned short	nPoly,
		unsigned short	nDOFs,
		const vector< su2double > &	r,
		const vector< su2double > &	s,
		vector< su2double > &	V
	)

protected

Function, which computes the Vandermonde matrix for a standard triangle.

Parameters

[in]	nPoly	- Polynomial degree of the triangle.
[in]	nDOFs	- Number of DOFs of the triangle.
[in]	r	- Parametric coordinates in r-direction for which the Vandermonde matrix must be computed.
[in]	s	- Parametric coordinates in s-direction for which the Vandermonde matrix must be computed.
[out]	V	- Matrix to store the Vandermonde matrix in all r- and s-locations.

◆ Vandermonde3D_Hexahedron()

void CFEMStandardElementBase::Vandermonde3D_Hexahedron	(	unsigned short	nPoly,
		unsigned short	nDOFs,
		const vector< su2double > &	r,
		const vector< su2double > &	s,
		const vector< su2double > &	t,
		vector< su2double > &	V
	)

protected

Function, which computes the Vandermonde matrix for a standard hexahedron.

Parameters

[in]	nPoly	- Polynomial degree of the hexahedron.
[in]	nDOFs	- Number of DOFs of the hexahedron.
[in]	r	- Parametric coordinates in r-direction for which the Vandermonde matrix must be computed.
[in]	s	- Parametric coordinates in s-direction for which the Vandermonde matrix must be computed.
[in]	t	- Parametric coordinates in t-direction for which the Vandermonde matrix must be computed.
[out]	V	- Matrix to store the Vandermonde matrix in all r-, s- and t-locations.

◆ Vandermonde3D_Prism()

void CFEMStandardElementBase::Vandermonde3D_Prism	(	unsigned short	nPoly,
		unsigned short	nDOFs,
		const vector< su2double > &	r,
		const vector< su2double > &	s,
		const vector< su2double > &	t,
		vector< su2double > &	V
	)

protected

Function, which computes the Vandermonde matrix for a standard prism.

Parameters

[in]	nPoly	- Polynomial degree of the prism.
[in]	nDOFs	- Number of DOFs of the prism.
[in]	r	- Parametric coordinates in r-direction for which the Vandermonde matrix must be computed.
[in]	s	- Parametric coordinates in s-direction for which the Vandermonde matrix must be computed.
[in]	t	- Parametric coordinates in t-direction for which the Vandermonde matrix must be computed.
[out]	V	- Matrix to store the Vandermonde matrix in all r-, s- and t-locations.

◆ Vandermonde3D_Pyramid()

void CFEMStandardElementBase::Vandermonde3D_Pyramid	(	unsigned short	nPoly,
		unsigned short	nDOFs,
		const vector< su2double > &	r,
		const vector< su2double > &	s,
		const vector< su2double > &	t,
		vector< su2double > &	V
	)

protected

Function, which computes the Vandermonde matrix for a standard pyramid.

Parameters

[in]	nPoly	- Polynomial degree of the pyramid.
[in]	nDOFs	- Number of DOFs of the pyramid.
[in]	r	- Parametric coordinates in r-direction for which the Vandermonde matrix must be computed.
[in]	s	- Parametric coordinates in s-direction for which the Vandermonde matrix must be computed.
[in]	t	- Parametric coordinates in t-direction for which the Vandermonde matrix must be computed.
[out]	V	- Matrix to store the Vandermonde matrix in all r-, s- and t-locations.

◆ Vandermonde3D_Tetrahedron()

void CFEMStandardElementBase::Vandermonde3D_Tetrahedron	(	unsigned short	nPoly,
		unsigned short	nDOFs,
		const vector< su2double > &	r,
		const vector< su2double > &	s,
		const vector< su2double > &	t,
		vector< su2double > &	V
	)

protected

Function, which computes the Vandermonde matrix for a standard tetrahedron.

Parameters

[in]	nPoly	- Polynomial degree of the tetrahedron.
[in]	nDOFs	- Number of DOFs of the tetrahedron.
[in]	r	- Parametric coordinates in r-direction for which the Vandermonde matrix must be computed.
[in]	s	- Parametric coordinates in s-direction for which the Vandermonde matrix must be computed.
[in]	t	- Parametric coordinates in t-direction for which the Vandermonde matrix must be computed.
[out]	V	- Matrix to store the Vandermonde matrix in all r-, s- and t-locations.

◆ ViscousPenaltyParameter()

su2double CFEMStandardElementBase::ViscousPenaltyParameter	(	const unsigned short	VTK_TypeElem,
		const unsigned short	nPolyElem
	)		const

protected

Function, which computes the constant in the penalty terms for a a viscous discretization.

Parameters

[in]	VTK_TypeElem	- The element type, using the VTK convention, adjacent to the face.
[in]	nPolyElem	- The polynomial degree of the adjacent element.

Returns: The value of the viscous penalty parameter.

Member Data Documentation

◆ constJacobian

bool CFEMStandardElementBase::constJacobian

protected

Whether or not the element has a constant Jacobian.

◆ nIntegration

unsigned short CFEMStandardElementBase::nIntegration

protected

Number of points used in the numerical integration.

◆ orderExact

unsigned short CFEMStandardElementBase::orderExact

protected

Polynomial order that must be integrated exactly by the integration rule.

◆ rIntegration

vector<su2double> CFEMStandardElementBase::rIntegration

protected

r-location of the integration points for this standard element.

◆ sIntegration

vector<su2double> CFEMStandardElementBase::sIntegration

protected

s-location of the integration points for this standard element, if needed.

◆ tIntegration

vector<su2double> CFEMStandardElementBase::tIntegration

protected

t-location of the integration points for this standard element, if needed.

◆ VTK_Type

unsigned short CFEMStandardElementBase::VTK_Type

protected

Element type using the VTK convention.

◆ wIntegration

vector<su2double> CFEMStandardElementBase::wIntegration

protected

The weights of the integration points for this standard element.

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

Common/include/fem/fem_standard_element.hpp
Common/src/fem/fem_integration_rules.cpp
Common/src/fem/fem_standard_element.cpp

Public Member Functions

Static Public Member Functions

Protected Member Functions

Protected Attributes

Detailed Description

Constructor & Destructor Documentation

◆ CFEMStandardElementBase() [1/2]

◆ ~CFEMStandardElementBase()

◆ CFEMStandardElementBase() [2/2]

Member Function Documentation

◆ CheckSumDerivativesLagrangianBasisFunctions()

◆ CheckSumLagrangianBasisFunctions()

◆ Copy()

◆ DerivativesBasisFunctionsAdjacentElement()

◆ GetNDOFsStatic()

◆ GetNIntegration()

◆ GetOrderExact()

◆ GetVTK_Type()

◆ GetWeightsIntegration()

◆ GradVandermonde1D()

◆ GradVandermonde2D_Quadrilateral()

◆ GradVandermonde2D_Triangle()

◆ GradVandermonde3D_Hexahedron()

◆ GradVandermonde3D_Prism()

◆ GradVandermonde3D_Pyramid()

◆ GradVandermonde3D_Tetrahedron()

◆ InverseMatrix()

◆ LagrangianBasisFunctionAndDerivativesHexahedron()

◆ LagrangianBasisFunctionAndDerivativesLine()

◆ LagrangianBasisFunctionAndDerivativesPrism()

◆ LagrangianBasisFunctionAndDerivativesPyramid()

◆ LagrangianBasisFunctionAndDerivativesQuadrilateral()

◆ LagrangianBasisFunctionAndDerivativesTetrahedron()

◆ LagrangianBasisFunctionAndDerivativesTriangle()

◆ MatMulRowMajor()

◆ SubConnForPlottingLine()

◆ SubConnForPlottingQuadrilateral()

◆ SubConnForPlottingTriangle()

◆ Vandermonde1D()

◆ Vandermonde2D_Quadrilateral()

◆ Vandermonde2D_Triangle()

◆ Vandermonde3D_Hexahedron()

◆ Vandermonde3D_Prism()

◆ Vandermonde3D_Pyramid()

◆ Vandermonde3D_Tetrahedron()

◆ ViscousPenaltyParameter()

Member Data Documentation

◆ constJacobian

◆ nIntegration

◆ orderExact

◆ rIntegration

◆ sIntegration

◆ tIntegration

◆ VTK_Type

◆ wIntegration