Calculates the shape functions and their derivatives for triangle element. More...

#include <TriangleShapeFunctions.h>

Collaboration diagram for TriangleShapeFunctions:

Public Member Functions
	TriangleShapeFunctions ()
	Default constructor.
	TriangleShapeFunctions (unsigned long MaxPolyOrder)
	Constructor with parameter.
	TriangleShapeFunctions (TriangleShapeFunctions &Instance)
	Copy-initializer constructor.
	~TriangleShapeFunctions ()
	Class destructor.
TriangleShapeFunctions &	operator= (TriangleShapeFunctions &Instance)
	Assigns one Instance to the current object.
void	SetMaxPolyOrder (unsigned long MaxPolyOrder)
	Sets the maximum polynomial order for the shape functions.
LineShapeFunctions &	GetLineShapeFunctions (unsigned long LiDirection=1)
	Returns the reference to LineShapeFunctions. According to LiDirection parameter returns one of the Line attributes of the class TriangleShapeFunctions.
unsigned long	GetMaxPolyOrder ()
	Returns the maximum polynomial order for the shape functions.
long	GetShapeFunctionSetNumber (unsigned long PolyOrder)
	Returns the set number of the shape functions values for the given a polynomial order.
void	GetShapeFunctions (unsigned long PolyOrder, long SFSetNumber, long IPSetNumber, IPCP_E IPCPFlag, unsigned long NumberIndicesNI, double *ShapeFunctions)
	Returns the shape functions given the element shape, polynomial order and integrand order calculated on the integration or collocation points. This method assumes that the values of the shape functions has been already calculated by the method RunShapeFunctions.
double *const	GetShapeFunctions (ElementShape_E EntityShape, long SFSetNumber, long IPSetNumber, IPCP_E IPCPFlag, unsigned long &NumberSFValues, unsigned long LiDirection=1)
	Returns the shape functions given the element shape, polynomial order and integrand order calculated on the integration or collocation points. This method assumes that the values of the shape functions has been already calculated by the method RunShapeFunctions.
double *const	GetShapeFunctions (ElementShape_E EntityShape, long SFSetNumber, long IPSetNumber, IPCP_E IPCPFlag, unsigned long &TotalNumberSFValues, unsigned long &NumberSFValues, unsigned long &NumberPoints, unsigned long LiDirection=1)
	Returns the shape functions given the element shape, polynomial order and integrand order calculated on the integration or collocation points. This method assumes that the values of the shape functions has been already calculated by the method RunShapeFunctions.
double *const	GetdShapeFunctions (ElementShape_E EntityShape, long SFSetNumber, long IPSetNumber, IPCP_E IPCPFlag, unsigned long &NumberSFValues, unsigned long LiDirection=1)
	Returns the derivatives of the shape functions given the shape, the polynomial order and integrand order calculated on the integration or collocation points. This method assumes that the values of the derivatives of the shape functions have been already calculated by the method RunShapeFunctions.
unsigned long *const	GetIndices (unsigned long PolyOrder, unsigned long &NumberIndices)
	Returns the tensorization indices p, q and r for each node/mode.
OneIndexTable< unsigned long > &	GetIndices ()
	Get Indices for tensorization of shape functions.
void	RunShapeFunctions (ElementShape_E EntityShape, ShapeFunctionsAttributes_S SFunctions, NumericalIntegration &NI, collocationPoints &CP, BuiltInArray< unsigned long > &PolyOrder)
	Calculates the shape functions values and their derivatives on the integration and collocation points also calculated for the input element orders given in the PolyOrder argument.
void	RunShapeFunctions (ElementShape_E EntityShape, ShapeFunctionsAttributes_S SFunctions, NumericalIntegration &NI, collocationPoints &CP, TriangleNumericalIntegration &TetraTriNI, TriangleCollocationPoints &TetraTriCP, BuiltInArray< unsigned long > &PolyOrder)
	Calculates the shape functions values and their derivatives on the integration and collocation points also calculated for the input element orders given in the PolyOrder argument, this function is called when running the tetrahedra class when we want to calculate face loads.
void	Print (FILE *File, ElementShape_E ElementShape, BuiltInArray< unsigned long > &PolyOrder)
	: Prints the shape functions attributes and values to the given ascii file.
void	BuildIndices (BuiltInArray< unsigned long > &PolyOrder, ShapeFunctionsAttributes_S SFAttributes)
	Protected function for the calculation of the tensorization indices p, q and r for each polynomial order given in the input argument PolyOrder. The indices are stored in the table Indices. This methods is executed in the RunShapeFunctions method.
Protected Attributes
OneIndexTable< unsigned long >	TensorIndices
	Stores the tensorization indices p, q and r for each node/mode.
LineShapeFunctions	LineSF
	Instance of the line shape functions fot direction L1.
LineShapeFunctions	LineSF1
	Instance of the line shape functions fot direction L1.
LineShapeFunctions	LineSF2
	Instance of the line shape functions fot direction L2.
LineShapeFunctions	LineSF3
	Instance of the line shape functions fot direction L3.
TwoIndexTable< double >	SFIP
	Table that stores the shape functions values for each polynomial order and sets of integration points.
TwoIndexTable< double >	dSFIP
	Table that stores the derivatives of the shape functions for each polynomial order and sets of integration points. The partial derivatives of each function Ni are stored as Ni,L1, Ni,L2 and Ni,L3.
TwoIndexTable< double >	SFCP
	Table that stores the shape functions values for each polynomial order and sets of collocatiion points.
TwoIndexTable< double >	dSFCP
	Table that stores the derivatives of the shape functions for each polynomial order and sets of collocation points. The partial derivatives of each function Ni are stored as Ni,L1, Ni,L2 and Ni,L3.
BuiltInArray< unsigned long >	NumbIntegPoints
	the Number of integration points applied on each shape functions for each polynomial order.
BuiltInArray< unsigned long >	NumbCollocPoints
	the Number of collocation points applied on each shape functions for each polynomial order.
unsigned long	Pmax
	Maximum polynomial order.

Detailed Description

Calculates the shape functions and their derivatives for triangle element.

Author:: Marco Lucio Bittencourt/ Fabiano Fernandes Bargos

Date:: March/15/2011

Constructor & Destructor Documentation

TriangleShapeFunctions::TriangleShapeFunctions ( unsigned long MaxPolyOrder )

Constructor with parameter.

Parameters:

[in] MaxPolyOrder - maximum polynomial order for the triangle shape functions

TriangleShapeFunctions::TriangleShapeFunctions ( TriangleShapeFunctions & Instance )

Copy-initializer constructor.

Returns:: Reference for instance of the TriangleShapeFunctions class

Member Function Documentation

void TriangleShapeFunctions::BuildIndices	(	BuiltInArray< unsigned long > &	PolyOrder,
		ShapeFunctionsAttributes_S	SFAttributes
	)

Protected function for the calculation of the tensorization indices p, q and r for each polynomial order given in the input argument PolyOrder. The indices are stored in the table Indices. This methods is executed in the RunShapeFunctions method.

Parameters:

[in]	PolyOrder	- element orders for a p-nonuniform mesh in a increasing sequence. For a p-uniform, thsi array stores only one value.
[in]	SFAttributes,:	attributes for the shape functions using the ShapeFunctionsAttributes_S struct.

Auxiliary variable used in for-loops and also for indexing the pointer pIndTI.

double *const TriangleShapeFunctions::GetdShapeFunctions	(	ElementShape_E	EntityShape,
		long	SFSetNumber,
		long	IPSetNumber,
		IPCP_E	IPCPFlag,
		unsigned long &	NumberSFValues,
		unsigned long	LiDirection = `1`
	)

Returns the derivatives of the shape functions given the shape, the polynomial order and integrand order calculated on the integration or collocation points. This method assumes that the values of the derivatives of the shape functions have been already calculated by the method RunShapeFunctions.

Parameters:

[in]	EntityShape	- if LINE, the edge shape functions are returned; if TRIANGLE, the values of the element shape functions are returned in the vertex, edge and face sequence.
[in]	SFSetNumber	- Set number of the shape functions.
[in]	IPSetNumber	- Set number of the integration points.
[in]	IPCPFlag	- specifies if the shape functions are to be returned on the integration (IP) or collocation (CP) points
[out]	NumberSFValues	- Number of shape functions values.
[in]	LiDirection	- Baricentric direction number.

Returns:: pointer to the double array with the values of the derivatives of the line shape functions

unsigned long *const TriangleShapeFunctions::GetIndices	(	unsigned long	PolyOrder,
		unsigned long &	NumberIndices
	)

Returns the tensorization indices p, q and r for each node/mode.

Parameters:

[in]	PolyOrder	- Polynomial order.
[out]	NumberIndices	- number of tensorization indices.

Returns:: Pointer to the array with the tensorization indices.

OneIndexTable< unsigned long > & TriangleShapeFunctions::GetIndices ( )

Get Indices for tensorization of shape functions.

Returns:: a OneIndexTable that store the tensor indices for each polynomial order.

LineShapeFunctions & TriangleShapeFunctions::GetLineShapeFunctions ( unsigned long LiDirection = 1 )

Returns the reference to LineShapeFunctions. According to LiDirection parameter returns one of the Line attributes of the class TriangleShapeFunctions.

Parameters:

[in] LiDirection - Baricentric direction number.

Returns:: LineShapeFunctions& - reference to the class LineShapeFunctions.

unsigned long TriangleShapeFunctions::GetMaxPolyOrder ( )

Returns the maximum polynomial order for the shape functions.

Returns:: Maximum polynomial order as an unsigned long.

void TriangleShapeFunctions::GetShapeFunctions	(	unsigned long	PolyOrder,
		long	SFSetNumber,
		long	IPSetNumber,
		IPCP_E	IPCPFlag,
		unsigned long	NumberIndicesNI,
		double *	ShapeFunctions
	)

Returns the shape functions given the element shape, polynomial order and integrand order calculated on the integration or collocation points. This method assumes that the values of the shape functions has been already calculated by the method RunShapeFunctions.

Parameters:

[in]	Polyorder	- the polynomial order.
[in]	SFSetNumber	- Set number of the shape functions.
[in]	IPSetNumber	- Set number of the integration points.
[in]	IPCPFlag	- specifies if the shape functions are to be returned on the integration (IP) or collocation (CP) points
[in]	NumberIndicesNI	- Number of tensor indices from the integration points.
[out]	ShapeFunctions	- the triangle shape functions

double *const TriangleShapeFunctions::GetShapeFunctions	(	ElementShape_E	EntityShape,
		long	SFSetNumber,
		long	IPSetNumber,
		IPCP_E	IPCPFlag,
		unsigned long &	NumberSFValues,
		unsigned long	LiDirection = `1`
	)

Returns the shape functions given the element shape, polynomial order and integrand order calculated on the integration or collocation points. This method assumes that the values of the shape functions has been already calculated by the method RunShapeFunctions.

Parameters:

[in]	EntityShape	- if LINE, the edge shape functions are returned; if TRIANGLE, the values of the element shape functions are returned in the vertex, edge and face sequence.
[in]	SFSetNumber	- Set number of the shape functions.
[in]	IPSetNumber	- Set number of the integration points.
[in]	IPCPFlag	- specifies if the shape functions are to be returned on the integration (IP) or collocation (CP) points
[out]	NumberSFValues	- Number of shape functions values.
[in]	LiDirection	- Baricentric direction number.

Returns:: pointer to the double array with the values of the square shape functions stored in the vertex, edge and face sequence.

double *const TriangleShapeFunctions::GetShapeFunctions	(	ElementShape_E	EntityShape,
		long	SFSetNumber,
		long	IPSetNumber,
		IPCP_E	IPCPFlag,
		unsigned long &	TotalNumberSFValues,
		unsigned long &	NumberSFValues,
		unsigned long &	NumberPoints,
		unsigned long	LiDirection = `1`
	)

Returns the shape functions given the element shape, polynomial order and integrand order calculated on the integration or collocation points. This method assumes that the values of the shape functions has been already calculated by the method RunShapeFunctions.

Parameters:

[in]	EntityShape	- if LINE, the edge shape functions are returned; if TRIANGLE, the values of the element shape functions are returned in the vertex, edge and face sequence.
[in]	SFSetNumber	- Set number of the shape functions.
[in]	IPSetNumber	- Set number of the integration points.
[in]	IPCPFlag	- specifies if the shape functions are to be returned on the integration (IP) or collocation (CP) points
[out]	TotalNumberSFValues	- Total number of elements of the shape functions matrix.
[out]	NumberSFValues	- Number of shape functions values.
[out]	NumberPoints	- Number of points of the integration or collocation depending of the IPCPFlag.
[in]	LiDirection	- Baricentric direction number.

Returns:: pointer to the double array with the values of the square shape functions stored in the vertex, edge and face sequence.

long TriangleShapeFunctions::GetShapeFunctionSetNumber ( unsigned long PolyOrder )

Returns the set number of the shape functions values for the given a polynomial order.

Parameters:

[in] PolyOrder - Polynomial order.

Returns:: a long with the set number value.

TriangleShapeFunctions & TriangleShapeFunctions::operator= ( TriangleShapeFunctions & Instance )

Assigns one Instance to the current object.

Returns:: Reference for instance of the TriangleShapeFunctions class

void TriangleShapeFunctions::Print	(	FILE *	File,
		ElementShape_E	ElementShape,
		BuiltInArray< unsigned long > &	PolyOrder
	)

: Prints the shape functions attributes and values to the given ascii file.

Parameters:

[in]	File	- pointer to the ascii file
[in]	ElementShape	- element shape
[in]	PolyOrder	- element orders for a p-nonuniform mesh in a increasing sequence. For a p-uniform, this array stores only one value

void TriangleShapeFunctions::RunShapeFunctions	(	ElementShape_E	EntityShape,
		ShapeFunctionsAttributes_S	SFunctions,
		NumericalIntegration &	NI,
		collocationPoints &	CP,
		BuiltInArray< unsigned long > &	PolyOrder
	)

Calculates the shape functions values and their derivatives on the integration and collocation points also calculated for the input element orders given in the PolyOrder argument.

Parameters:

[in]	EntityShape	- entity shape for which the interpolation functions and derivatives must be calculated. If it is TRIANGLE, the edge and element shape functions and derivatives are calculated; if it is LINE, only the line shape functions and their derivatives are calculated.
[in]	SFunctions	- attributes of the shape functions
[in]	NI	- instance of the NumericalIntegration class
[in]	CP	- instance of the CollocationPoints class
[in]	PolyOrder	- element orders for a p-nonuniform mesh in a increasing sequence. For a p-uniform, thsi array stores only one value

Total number of shape functions (P1+1)(P1+2)/2 + (P2+1)(P2+2)/2 + ... + (Pn+1)(Pn+2)/2.

Number of shape functions on collocation points: (P1+1)(P1+2)/2)*(P1+1)(P1+2)/2) + (P1+1)(P1+2)/2)*((P2+1)(P2+2)/2) + ... + (Pn+1)(Pn+2)/2)*((Pn+1)(Pn+2)/2)^2.

Calculates the total number of integration points. Which is equal to the sum of the squares of the line integrations points: LineIntgPoint_1^2 + LineIntgPoint_2^2 + ... + LineIntgPoint_n^2

Allocates the tables of shape functions values and their derivatives on the integration and collocation points.

Auxiliary pointers for the indices and data of the tables for shape functions values and their derivatives on the integration points.

Auxiliary pointers for the indices and data of the tables for shape functions values and their derivatives. on the collocation points.

For collocation points.

void TriangleShapeFunctions::RunShapeFunctions	(	ElementShape_E	EntityShape,
		ShapeFunctionsAttributes_S	SFunctions,
		NumericalIntegration &	NI,
		collocationPoints &	CP,
		TriangleNumericalIntegration &	TetraTriNI,
		TriangleCollocationPoints &	TetraTriCP,
		BuiltInArray< unsigned long > &	PolyOrder
	)

Calculates the shape functions values and their derivatives on the integration and collocation points also calculated for the input element orders given in the PolyOrder argument, this function is called when running the tetrahedra class when we want to calculate face loads.

Parameters:

[in]	EntityShape	- entity shape for which the interpolation functions and derivatives must be calculated. If it is TRIANGLE, the edge and element shape functions and derivatives are calculated; if it is LINE, only the line shape functions and their derivatives are calculated.
[in]	SFunctions	- attributes of the shape functions
[in]	NI	- instance of the NumericalIntegration class
[in]	CP	- instance of the CollocationPoints class
[in]	TetraTriNI	- instance to the TriangleNumericalIntegration class, inside TetraNI
[in]	TetraTriCP	- instance to the TriangleCollocationPoints class, inside TetraCP
[in]	PolyOrder	- element orders for a p-nonuniform mesh in a increasing sequence. For a p-uniform, thsi array stores only one value

Total number of shape functions (P1+1)(P1+2)/2 + (P2+1)(P2+2)/2 + ... + (Pn+1)(Pn+2)/2.

Number of shape functions on collocation points: (P1+1)(P1+2)/2)*(P1+1)(P1+2)/2) + (P1+1)(P1+2)/2)*((P2+1)(P2+2)/2) + ... + (Pn+1)(Pn+2)/2)*((Pn+1)(Pn+2)/2)^2.

Calculates the total number of integration points. Which is equal to the sum of the squares of the line integrations points: LineIntgPoint_1^2 + LineIntgPoint_2^2 + ... + LineIntgPoint_n^2

Allocates the tables of shape functions values and their derivatives on the integration and collocation points.

Auxiliary pointers for the indices and data of the tables for shape functions values and their derivatives on the integration points.

Auxiliary pointers for the indices and data of the tables for shape functions values and their derivatives. on the collocation points.

For collocation points.

void TriangleShapeFunctions::SetMaxPolyOrder ( unsigned long MaxPolyOrder )

Sets the maximum polynomial order for the shape functions.

Parameters:

[in] MaxOrder - maximum polynomial order.

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

include/interpolation/shapefunctions/TriangleShapeFunctions.h
src/interpolation/shapefunctions/TriangleShapeFunctions.cpp

Public Member Functions

Protected Attributes

Detailed Description

Constructor & Destructor Documentation

Member Function Documentation