Moving Least-Squares utility to calculate shape function values This class uses a linear polynomial basis and an exponential kernel to calculate the shape function values and gradients in a given point using a Moving Least-Squares minimization. More...

#include <mls_shape_functions_utility.h>

Collaboration diagram for Kratos::MLSShapeFunctionsUtility:

Static Public Member Functions
static double	CalculateKernel (const array_1d< double, 3 > &rRadVect, const double h)
	Calculate the kernel value This function calculates the exponential kernel value in one point. More...

template<std::size_t TDim>
static void	CalculateKernelDerivative (const array_1d< double, 3 > &rRadVect, const double h, array_1d< double, TDim > &rKernelDerivative)
	Calculate the kernel derivative values This function calculates the exponential kernel derivatives in one point. More...

static void	EvaluatePolynomialBasis (const array_1d< double, 3 > &rX, array_1d< double, 3 > &rBasis)
	Evaluates the linear polynomial basis This method evaluates the 2D linear polynommial basis in one point. More...

static void	EvaluatePolynomialBasis (const array_1d< double, 3 > &rX, array_1d< double, 4 > &rBasis)
	Evaluates the linear polynomial basis This method evaluates the 3D linear polynommial basis in one point. More...

static void	EvaluatePolynomialBasis (const array_1d< double, 3 > &rX, array_1d< double, 6 > &rBasis)
	Evaluates the quadratic polynomial basis This method evaluates the 2D quadratic polynommial basis in one point. More...

static void	EvaluatePolynomialBasis (const array_1d< double, 3 > &rX, array_1d< double, 10 > &rBasis)
	Evaluates the quadratic polynomial basis This method evaluates the 3D quadratic polynommial basis in one point. More...

static void	EvaluatePolynomialBasisDerivatives (const array_1d< double, 3 > &rX, BoundedMatrix< double, 2, 3 > &rBasisDerivatives)
	Evaluates the linear polynomial basis derivatives This method evaluates the 2D linear polynommial basis derivatives in one point. More...

static void	EvaluatePolynomialBasisDerivatives (const array_1d< double, 3 > &rX, BoundedMatrix< double, 3, 4 > &rBasisDerivatives)
	Evaluates the linear polynomial basis derivatives This method evaluates the 3D linear polynommial basis derivatives in one point. More...

static void	EvaluatePolynomialBasisDerivatives (const array_1d< double, 3 > &rX, BoundedMatrix< double, 2, 6 > &rBasisDerivatives)
	Evaluates the quadratic polynomial basis derivatives This method evaluates the 2D quadratic polynommial basis derivatives in one point. More...

static void	EvaluatePolynomialBasisDerivatives (const array_1d< double, 3 > &rX, BoundedMatrix< double, 3, 10 > &rBasisDerivatives)
	Evaluates the quadratic polynomial basis derivatives This method evaluates the 3D quadratic polynommial basis derivatives in one point. More...

template<std::size_t TDim, std::size_t TOrder>
static void	CalculateShapeFunctions (const Matrix &rPoints, const array_1d< double, 3 > &rX, const double h, Vector &rN)
	Calculates the MLS shape function values This method calculates the shape function values in one point using as support the given cloud of points. More...

template<std::size_t TDim, std::size_t TOrder>
static void	CalculateShapeFunctionsAndGradients (const Matrix &rPoints, const array_1d< double, 3 > &rX, const double h, Vector &rN, Matrix &rDNDX)
	Calculates the MLS shape function values This method calculates the shape function values and their gradients in one point using as support the given cloud of points. More...

template<>
void	CalculateShapeFunctionsAndGradients (const Matrix &rPoints, const array_1d< double, 3 > &rX, const double h, Vector &rN, Matrix &rDNDX)

template<>
void	CalculateShapeFunctionsAndGradients (const Matrix &rPoints, const array_1d< double, 3 > &rX, const double h, Vector &rN, Matrix &rDNDX)

template<>
void	CalculateShapeFunctionsAndGradients (const Matrix &rPoints, const array_1d< double, 3 > &rX, const double h, Vector &rN, Matrix &rDNDX)

template<>
void	CalculateShapeFunctionsAndGradients (const Matrix &rPoints, const array_1d< double, 3 > &rX, const double h, Vector &rN, Matrix &rDNDX)

Detailed Description

Moving Least-Squares utility to calculate shape function values This class uses a linear polynomial basis and an exponential kernel to calculate the shape function values and gradients in a given point using a Moving Least-Squares minimization.

Member Function Documentation

◆ CalculateKernel()

double Kratos::MLSShapeFunctionsUtility::CalculateKernel	(	const array_1d< double, 3 > &	rRadVect,
		const double	h
	)

static

Calculate the kernel value This function calculates the exponential kernel value in one point.

Parameters

rRadVect	Vector from the current point to the point of interest
h	Kernel radius

Returns: double The kernel value

◆ CalculateKernelDerivative()

template<std::size_t TDim>

template void Kratos::MLSShapeFunctionsUtility::CalculateKernelDerivative< 3 >	(	const array_1d< double, 3 > &	rRadVect,
		const double	h,
		array_1d< double, TDim > &	rKernelDerivative
	)

static

Calculate the kernel derivative values This function calculates the exponential kernel derivatives in one point.

Template Parameters

TDim	Dimension (2 in 2D and 3 in 3D)

Parameters

rRadVect	Vector from the current point to the point of interest
h	Kernel radius
rKernelDerivative	The kernel derivative value

◆ CalculateShapeFunctions()

template<std::size_t TDim, std::size_t TOrder>

template void Kratos::MLSShapeFunctionsUtility::CalculateShapeFunctions< 3, 2 >	(	const Matrix &	rPoints,
		const array_1d< double, 3 > &	rX,
		const double	h,
		Vector &	rN
	)

static

Calculates the MLS shape function values This method calculates the shape function values in one point using as support the given cloud of points.

Template Parameters

TDim	Dimension (2 in 2D and 3 in 3D)

Parameters

rPoints	Matrix containing the coordinates of the support cloud of points
rX	Coordinates where the shape functions are to be computed
h	Kernel radius
rN	Shape functions container

◆ CalculateShapeFunctionsAndGradients() [1/5]

template<>

void Kratos::MLSShapeFunctionsUtility::CalculateShapeFunctionsAndGradients	(	const Matrix &	rPoints,
		const array_1d< double, 3 > &	rX,
		const double	h,
		Vector &	rN,
		Matrix &	rDNDX
	)

static

◆ CalculateShapeFunctionsAndGradients() [2/5]

template<>

void Kratos::MLSShapeFunctionsUtility::CalculateShapeFunctionsAndGradients	(	const Matrix &	rPoints,
		const array_1d< double, 3 > &	rX,
		const double	h,
		Vector &	rN,
		Matrix &	rDNDX
	)

static

◆ CalculateShapeFunctionsAndGradients() [3/5]

template<>

void Kratos::MLSShapeFunctionsUtility::CalculateShapeFunctionsAndGradients	(	const Matrix &	rPoints,
		const array_1d< double, 3 > &	rX,
		const double	h,
		Vector &	rN,
		Matrix &	rDNDX
	)

static

◆ CalculateShapeFunctionsAndGradients() [4/5]

template<>

void Kratos::MLSShapeFunctionsUtility::CalculateShapeFunctionsAndGradients	(	const Matrix &	rPoints,
		const array_1d< double, 3 > &	rX,
		const double	h,
		Vector &	rN,
		Matrix &	rDNDX
	)

static

◆ CalculateShapeFunctionsAndGradients() [5/5]

template<std::size_t TDim, std::size_t TOrder>

static void Kratos::MLSShapeFunctionsUtility::CalculateShapeFunctionsAndGradients	(	const Matrix &	rPoints,
		const array_1d< double, 3 > &	rX,
		const double	h,
		Vector &	rN,
		Matrix &	rDNDX
	)

static

Calculates the MLS shape function values This method calculates the shape function values and their gradients in one point using as support the given cloud of points.

Template Parameters

TDim	Dimension (2 in 2D and 3 in 3D)

Parameters

rPoints	Matrix containing the coordinates of the support cloud of points
rX	Coordinates where the shape functions are to be computed
h	Kernel radius
rN	Shape functions container
rDNDX	Shape functions gradients container

◆ EvaluatePolynomialBasis() [1/4]

void Kratos::MLSShapeFunctionsUtility::EvaluatePolynomialBasis	(	const array_1d< double, 3 > &	rX,
		array_1d< double, 10 > &	rBasis
	)

static

Evaluates the quadratic polynomial basis This method evaluates the 3D quadratic polynommial basis in one point.

Parameters

rX	Coordinates where the basis is evaluated
rBasis	3D quadratic polynomial basis values

◆ EvaluatePolynomialBasis() [2/4]

void Kratos::MLSShapeFunctionsUtility::EvaluatePolynomialBasis	(	const array_1d< double, 3 > &	rX,
		array_1d< double, 3 > &	rBasis
	)

static

Evaluates the linear polynomial basis This method evaluates the 2D linear polynommial basis in one point.

Parameters

rX	Coordinates where the basis is evaluated
rBasis	2D linear polynomial basis values

◆ EvaluatePolynomialBasis() [3/4]

void Kratos::MLSShapeFunctionsUtility::EvaluatePolynomialBasis	(	const array_1d< double, 3 > &	rX,
		array_1d< double, 4 > &	rBasis
	)

static

Evaluates the linear polynomial basis This method evaluates the 3D linear polynommial basis in one point.

Parameters

rX	Coordinates where the basis is evaluated
rBasis	3D linear polynomial basis values

◆ EvaluatePolynomialBasis() [4/4]

void Kratos::MLSShapeFunctionsUtility::EvaluatePolynomialBasis	(	const array_1d< double, 3 > &	rX,
		array_1d< double, 6 > &	rBasis
	)

static

Evaluates the quadratic polynomial basis This method evaluates the 2D quadratic polynommial basis in one point.

Parameters

rX	Coordinates where the basis is evaluated
rBasis	2D linear polynomial basis values

◆ EvaluatePolynomialBasisDerivatives() [1/4]

void Kratos::MLSShapeFunctionsUtility::EvaluatePolynomialBasisDerivatives	(	const array_1d< double, 3 > &	rX,
		BoundedMatrix< double, 2, 3 > &	rBasisDerivatives
	)

static

Evaluates the linear polynomial basis derivatives This method evaluates the 2D linear polynommial basis derivatives in one point.

Parameters

rX	Coordinates where the basis is evaluated
rBasis	2D linear polynomial basis derivatives values

◆ EvaluatePolynomialBasisDerivatives() [2/4]

void Kratos::MLSShapeFunctionsUtility::EvaluatePolynomialBasisDerivatives	(	const array_1d< double, 3 > &	rX,
		BoundedMatrix< double, 2, 6 > &	rBasisDerivatives
	)

static

Evaluates the quadratic polynomial basis derivatives This method evaluates the 2D quadratic polynommial basis derivatives in one point.

Parameters

rX	Coordinates where the basis is evaluated
rBasis	2D quadratic polynomial basis derivatives values

◆ EvaluatePolynomialBasisDerivatives() [3/4]

void Kratos::MLSShapeFunctionsUtility::EvaluatePolynomialBasisDerivatives	(	const array_1d< double, 3 > &	rX,
		BoundedMatrix< double, 3, 10 > &	rBasisDerivatives
	)

static

Evaluates the quadratic polynomial basis derivatives This method evaluates the 3D quadratic polynommial basis derivatives in one point.

Parameters

rX	Coordinates where the basis is evaluated
rBasis	3D quadratic polynomial basis derivatives values

◆ EvaluatePolynomialBasisDerivatives() [4/4]

void Kratos::MLSShapeFunctionsUtility::EvaluatePolynomialBasisDerivatives	(	const array_1d< double, 3 > &	rX,
		BoundedMatrix< double, 3, 4 > &	rBasisDerivatives
	)

static

Evaluates the linear polynomial basis derivatives This method evaluates the 3D linear polynommial basis derivatives in one point.

Parameters

rX	Coordinates where the basis is evaluated
rBasis	3D linear polynomial basis derivatives values

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

/home/runner/work/Documentation/Documentation/master/kratos/utilities/mls_shape_functions_utility.h
/home/runner/work/Documentation/Documentation/master/kratos/utilities/mls_shape_functions_utility.cpp

Static Public Member Functions

Detailed Description

Member Function Documentation

◆ CalculateKernel()

◆ CalculateKernelDerivative()

◆ CalculateShapeFunctions()

◆ CalculateShapeFunctionsAndGradients() [1/5]

◆ CalculateShapeFunctionsAndGradients() [2/5]

◆ CalculateShapeFunctionsAndGradients() [3/5]

◆ CalculateShapeFunctionsAndGradients() [4/5]

◆ CalculateShapeFunctionsAndGradients() [5/5]

◆ EvaluatePolynomialBasis() [1/4]

◆ EvaluatePolynomialBasis() [2/4]

◆ EvaluatePolynomialBasis() [3/4]

◆ EvaluatePolynomialBasis() [4/4]

◆ EvaluatePolynomialBasisDerivatives() [1/4]

◆ EvaluatePolynomialBasisDerivatives() [2/4]

◆ EvaluatePolynomialBasisDerivatives() [3/4]

◆ EvaluatePolynomialBasisDerivatives() [4/4]