Calculates a number of element properties. More...

#include <ElementProperty.h>

Public Member Functions
	ElementProperty (const real_t x0, const real_t x1, const real_t *x2)

	ElementProperty (const real_t x0, const real_t x1, const real_t x2, const real_t x3)

real_t	area (const real_t x0, const real_t x1, const real_t *x2) const

real_t	volume (const real_t x0, const real_t x1, const real_t x2, const real_t x3) const

template<int dim>
double	length (const real_t x0[], const real_t x1[], const double m[]) const

double	lipnikov (const real_t x0, const real_t x1, const real_t x2, const double m0, const double m1, const double m2)

double	lipnikov (const real_t x0, const real_t x1, const real_t *x2, double m00, double m01, double m11)

void	lipnikov_grad (int moving, const double x0, const double x1, const double x2, const double m0, double *grad)

double	lipnikov (const real_t x0, const real_t x1, const real_t x2, const real_t x3, const double m0, const double m1, const double m2, const double m3)

double	lipnikov (const real_t x0, const real_t x1, const real_t x2, const real_t x3, const double *m0)

void	lipnikov_grad (int moving, const double x0, const double x1, const double x2, const double x3, const double m0, double grad)

real_t	sliver (const real_t x0, const real_t x1, const real_t x2, const real_t x3, const double m0, const double m1, const double m2, const double m3)

double	condition (const real_t x0, const real_t x1, const real_t x2, const double m0, const double m1, const double m2)

double	condition (const real_t x0, const real_t x1, const real_t *x2, double m00, double m01, double m11)

double	condition (const real_t x0, const real_t x1, const real_t x2, const real_t x3, const double m0, const double m1, const double m2, const double m3)

int	getOrientation ()

Static Public Member Functions
static double	length2d (const real_t x0[], const real_t x1[], const double m[])

static double	length3d (const real_t x0[], const real_t x1[], const double m[])

Detailed Description

template<typename real_t>
class ElementProperty< real_t >

Calculates a number of element properties.

The constructor for this class requires a reference element so that the orientation convention can be established. After the orientation has been established a negative area or volume indicated an inverted element. Properties calculated are:

Euclidean area (if 2D element).
Euclidean Volume (if 3D element).
Non-Euclidean edge length.
2D/3D Lipnikov quality functional.
3D sliver functional.

Definition at line 65 of file ElementProperty.h.

Constructor & Destructor Documentation

template<typename real_t>

ElementProperty< real_t >::ElementProperty	(	const real_t *	x0,
		const real_t *	x1,
		const real_t *	x2
	)

inline

Constructor for 2D triangular elements.

Parameters

x0	pointer to 2D position for first point in triangle.
x1	pointer to 2D position for second point in triangle.
x2	pointer to 2D position for third point in triangle.

Definition at line 72 of file ElementProperty.h.

template<typename real_t>

ElementProperty< real_t >::ElementProperty	(	const real_t *	x0,
		const real_t *	x1,
		const real_t *	x2,
		const real_t *	x3
	)

inline

Constructor for 3D tetrahedral elements.

Parameters

x0	pointer to 3D position for first point in triangle.
x1	pointer to 3D position for second point in triangle.
x2	pointer to 3D position for third point in triangle.
x3	pointer to 3D position for forth point in triangle.

Definition at line 86 of file ElementProperty.h.

Member Function Documentation

template<typename real_t>

real_t ElementProperty< real_t >::area	(	const real_t *	x0,
		const real_t *	x1,
		const real_t *	x2
	)		const

inline

Calculate area of 2D triangle.

Parameters

x0	pointer to 2D position for first point in triangle.
x1	pointer to 2D position for second point in triangle.
x2	pointer to 2D position for third point in triangle.

Definition at line 99 of file ElementProperty.h.

template<typename real_t>

double ElementProperty< real_t >::condition	(	const real_t *	x0,
		const real_t *	x1,
		const real_t *	x2,
		const double *	m0,
		const double *	m1,
		const double *	m2
	)

inline

Evaluates the 2D Condition number functional. The description for the functional is taken from: P. Knupp, Achieving finite element mesh quality via optimization, International Journal for Numerical Methods in Engineering, Vol. 48, No. 3, 2000, pp. 401 - 420.

Parameters

x0	pointer to 2D position for first point in triangle.
x1	pointer to 2D position for second point in triangle.
x2	pointer to 2D position for third point in triangle.
m0	2x2 metric tensor for first point.
m1	2x2 metric tensor for second point.
m2	2x2 metric tensor for third point.

Definition at line 540 of file ElementProperty.h.

template<typename real_t>

double ElementProperty< real_t >::condition	(	const real_t *	x0,
		const real_t *	x1,
		const real_t *	x2,
		double	m00,
		double	m01,
		double	m11
	)

inline

Evaluates the 2D Condition number functional. The description for the functional is taken from: P. Knupp, Achieving finite element mesh quality via optimization, International Journal for Numerical Methods in Engineering, Vol. 48, No. 3, 2000, pp. 401 - 420.

Parameters

x0	pointer to 2D position for first point in triangle.
x1	pointer to 2D position for second point in triangle.
x2	pointer to 2D position for third point in triangle.
m00	metric index (0,0)
m01	metric index (0,1)
m11	metric index (1,1)

Definition at line 564 of file ElementProperty.h.

template<typename real_t>

double ElementProperty< real_t >::condition	(	const real_t *	x0,
		const real_t *	x1,
		const real_t *	x2,
		const real_t *	x3,
		const double *	m0,
		const double *	m1,
		const double *	m2,
		const double *	m3
	)

inline

Evaluates the 3D condition number functional. The description for the functional is taken from: L. Freitag, P M Knupp, Tetrahedral mesh improvement via optimization of the element condition number, meshes, Int. J. for Num. Meth. in Eng., Vol. 53, No. 6, pp. 1377-1391 (2002).

Parameters

x0	pointer to 3D position for first point in tetrahedral.
x1	pointer to 3D position for second point in tetrahedral.
x2	pointer to 3D position for third point in tetrahedral.
x3	pointer to 3D position for third point in tetrahedral.
m0	3x3 metric tensor for first point.
m1	3x3 metric tensor for second point.
m2	3x3 metric tensor for third point.
m3	3x3 metric tensor for forth point.

Definition at line 610 of file ElementProperty.h.

template<typename real_t>

int ElementProperty< real_t >::getOrientation ( )

inline

Definition at line 686 of file ElementProperty.h.

template<typename real_t>

template<int dim>

double ElementProperty< real_t >::length	(	const real_t	x0[],
		const real_t	x1[],
		const double	m[]
	)		const

inline

Length of an edge as measured in metric space.

Parameters

x0	coordinate at start of line segment.
x1	coordinate at finish of line segment.
m	metric tensor for first point.

Definition at line 139 of file ElementProperty.h.

template<typename real_t>

static double ElementProperty< real_t >::length2d	(	const real_t	x0[],
		const real_t	x1[],
		const double	m[]
	)

inlinestatic

Length of an edge as measured in metric space.

Parameters

x0	coordinate at start of line segment.
x1	coordinate at finish of line segment.
m	metric tensor for first point.

Definition at line 153 of file ElementProperty.h.

template<typename real_t>

static double ElementProperty< real_t >::length3d	(	const real_t	x0[],
		const real_t	x1[],
		const double	m[]
	)

inlinestatic

Length of an edge as measured in metric space.

Parameters

x0	coordinate at start of line segment.
x1	coordinate at finish of line segment.
m	metric tensor for first point.

Definition at line 168 of file ElementProperty.h.

template<typename real_t>

double ElementProperty< real_t >::lipnikov	(	const real_t *	x0,
		const real_t *	x1,
		const real_t *	x2,
		const double *	m0,
		const double *	m1,
		const double *	m2
	)

inline

Evaluates the 2D Lipnikov functional. The description for the functional is taken from: Yu. V. Vasileskii and K. N. Lipnikov, An Adaptive Algorithm for Quasioptimal Mesh Generation, Computational Mathematics and Mathematical Physics, Vol. 39, No. 9, 1999, pp. 1468 - 1486.

Parameters

x0	pointer to 2D position for first point in triangle.
x1	pointer to 2D position for second point in triangle.
x2	pointer to 2D position for third point in triangle.
m0	2x2 metric tensor for first point.
m1	2x2 metric tensor for second point.
m2	2x2 metric tensor for third point.

Definition at line 195 of file ElementProperty.h.

template<typename real_t>

double ElementProperty< real_t >::lipnikov	(	const real_t *	x0,
		const real_t *	x1,
		const real_t *	x2,
		double	m00,
		double	m01,
		double	m11
	)

inline

Evaluates the 2D Lipnikov functional. The description for the functional is taken from: Yu. V. Vasileskii and K. N. Lipnikov, An Adaptive Algorithm for Quasioptimal Mesh Generation, Computational Mathematics and Mathematical Physics, Vol. 39, No. 9, 1999, pp. 1468 - 1486.

Parameters

x0	pointer to 2D position for first point in triangle.
x1	pointer to 2D position for second point in triangle.
x2	pointer to 2D position for third point in triangle.
m00	metric index (0,0)
m01	metric index (0,1)
m11	metric index (1,1)

Definition at line 218 of file ElementProperty.h.

template<typename real_t>

double ElementProperty< real_t >::lipnikov	(	const real_t *	x0,
		const real_t *	x1,
		const real_t *	x2,
		const real_t *	x3,
		const double *	m0,
		const double *	m1,
		const double *	m2,
		const double *	m3
	)

inline

Evaluates the 3D Lipnikov functional. The description for the functional is taken from: A. Agouzal, K Lipnikov, Yu. Vassilevski, Adaptive generation of quasi-optimal tetrahedral meshes, East-West J. Numer. Math., Vol. 7, No. 4, pp. 223-244 (1999).

Parameters

x0	pointer to 3D position for first point in tetrahedral.
x1	pointer to 3D position for second point in tetrahedral.
x2	pointer to 3D position for third point in tetrahedral.
x3	pointer to 3D position for third point in tetrahedral.
m0	3x3 metric tensor for first point.
m1	3x3 metric tensor for second point.
m2	3x3 metric tensor for third point.
m3	3x3 metric tensor for forth point.

Definition at line 297 of file ElementProperty.h.

template<typename real_t>

double ElementProperty< real_t >::lipnikov	(	const real_t *	x0,
		const real_t *	x1,
		const real_t *	x2,
		const real_t *	x3,
		const double *	m0
	)

inline

Evaluates the 3D Lipnikov functional. The description for the functional is taken from: A. Agouzal, K Lipnikov, Yu. Vassilevski, Adaptive generation of quasi-optimal tetrahedral meshes, East-West J. Numer. Math., Vol. 7, No. 4, pp. 223-244 (1999).

Parameters

x0	pointer to 3D position for first point in tetrahedral.
x1	pointer to 3D position for second point in tetrahedral.
x2	pointer to 3D position for third point in tetrahedral.
x3	pointer to 3D position for third point in tetrahedral.
m0	3x3 metric tensor for first point.

Definition at line 369 of file ElementProperty.h.

template<typename real_t>

void ElementProperty< real_t >::lipnikov_grad	(	int	moving,
		const double *	x0,
		const double *	x1,
		const double *	x2,
		const double *	m0,
		double *	grad
	)

inline

Definition at line 254 of file ElementProperty.h.

template<typename real_t>

void ElementProperty< real_t >::lipnikov_grad	(	int	moving,
		const double *	x0,
		const double *	x1,
		const double *	x2,
		const double *	x3,
		const double *	m0,
		double *	grad
	)

inline

Definition at line 431 of file ElementProperty.h.

template<typename real_t>

real_t ElementProperty< real_t >::sliver	(	const real_t *	x0,
		const real_t *	x1,
		const real_t *	x2,
		const real_t *	x3,
		const double *	m0,
		const double *	m1,
		const double *	m2,
		const double *	m3
	)

inline

Evaluates the sliver functional. Taken from Computer Methods in Applied Mechanics and Engineering Volume 194, Issues 48-49, 15 November 2005, Pages 4915-4950

Parameters

x0	pointer to 3D position for first point in tetrahedral.
x1	pointer to 3D position for second point in tetrahedral.
x2	pointer to 3D position for third point in tetrahedral.
x3	pointer to 3D position for third point in tetrahedral.
m0	3x3 metric tensor for first point.
m1	3x3 metric tensor for second point.
m2	3x3 metric tensor for third point.
m3	3x3 metric tensor for forth point.

Definition at line 472 of file ElementProperty.h.

template<typename real_t>

real_t ElementProperty< real_t >::volume	(	const real_t *	x0,
		const real_t *	x1,
		const real_t *	x2,
		const real_t *	x3
	)		const

inline

Calculate volume of tetrahedron.

Parameters

x0	pointer to 3D position for first point in triangle.
x1	pointer to 3D position for second point in triangle.
x2	pointer to 3D position for third point in triangle.
x3	pointer to 3D position for forth point in triangle.

Definition at line 115 of file ElementProperty.h.

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

include/ElementProperty.h

Public Member Functions

Static Public Member Functions

Detailed Description

template<typename real_t> class ElementProperty< real_t >

Constructor & Destructor Documentation

Member Function Documentation

template<typename real_t>
class ElementProperty< real_t >