Kratos::RBFShapeFunctionsUtility Class Reference

Radial Basis Functions utility to calculate shape function values This class uses Gaussian raidal basis functions to calculate the shape function values for a given value (i.e. norm of a point) with partition of unity. More...

#include <rbf_shape_functions_utility.h>

Collaboration diagram for Kratos::RBFShapeFunctionsUtility:

Public Types
Type Definitions
using	DenseSpace = UblasSpace< double, Matrix, Vector >
	Dense space definition for the QR decomposition using in the solve. More...
using	DenseQRPointerType = typename DenseQRDecomposition< DenseSpace >::Pointer
	QR decomposition pointer definition. More...
using	KratosCoreQRType = DenseHouseholderQRDecomposition< DenseSpace >
	Kratos core QR decomposition type. More...

Static Public Member Functions
Operations
static double	EvaluateRBF (const double x, const double h)
	Calculate the RBF value This function evaluates the Gaussian RBF for a norm. More...
static void	CalculateShapeFunctions (const Matrix &rPoints, const array_1d< double, 3 > &rX, const double h, Vector &rN, DenseQRPointerType pDenseQR=nullptr)
	Calculates the RBF shape function values This method calculates the RBF shape function values in one point using as support the given cloud of points. More...
static void	CalculateShapeFunctions (const Matrix &rPoints, const array_1d< double, 3 > &rX, Vector &rN, DenseQRPointerType pDenseQR=nullptr)
	Calculates the RBF shape function values This method calculates the RBF shape function values in one point using as support the given cloud of points. More...
static double	CalculateShapeFunctionsAndInterpolation (const Matrix &rPoints, const array_1d< double, 3 > &rX, const double h, Vector &rN, Vector &rY)
	Calculates the RBF shape function values This method calculates the RBF shape function values in one point using as support the given cloud of points. More...

Detailed Description

Radial Basis Functions utility to calculate shape function values This class uses Gaussian raidal basis functions to calculate the shape function values for a given value (i.e. norm of a point) with partition of unity.

Member Typedef Documentation

DenseQRPointerType

using Kratos::RBFShapeFunctionsUtility::DenseQRPointerType = typename DenseQRDecomposition<DenseSpace>::Pointer

QR decomposition pointer definition.

DenseSpace

using Kratos::RBFShapeFunctionsUtility::DenseSpace = UblasSpace<double, Matrix, Vector>

Dense space definition for the QR decomposition using in the solve.

KratosCoreQRType

using Kratos::RBFShapeFunctionsUtility::KratosCoreQRType = DenseHouseholderQRDecomposition<DenseSpace>

Kratos core QR decomposition type.

Member Function Documentation

CalculateShapeFunctions() [1/2]

void Kratos::RBFShapeFunctionsUtility::CalculateShapeFunctions ( const Matrix &  rPoints, const array_1d< double, 3 > &  rX, const double  h, Vector &  rN, DenseQRPointerType  pDenseQR = nullptr  )

static

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

Parameters

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

CalculateShapeFunctions() [2/2]

void Kratos::RBFShapeFunctionsUtility::CalculateShapeFunctions ( const Matrix &  rPoints, const array_1d< double, 3 > &  rX, Vector &  rN, DenseQRPointerType  pDenseQR = nullptr  )

static

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

Parameters

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

CalculateShapeFunctionsAndInterpolation()

double Kratos::RBFShapeFunctionsUtility::CalculateShapeFunctionsAndInterpolation ( const Matrix &  rPoints, const array_1d< double, 3 > &  rX, const double  h, Vector &  rN, Vector &  rY  )

static

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

Parameters

rPoints	Matrix containing the coordinates of the support cloud of points
rX	Coordinates where the shape functions are to be computed
h	RBF shape parameter
rN	Shape functions container
Y	Function to interpolate (if values of RHS are known apriori)

EvaluateRBF()

double Kratos::RBFShapeFunctionsUtility::EvaluateRBF ( const double  x, const double  h  )

static

Calculate the RBF value This function evaluates the Gaussian RBF for a norm.

Parameters

x	Norm of RBF argument (i.e. norm of radial vector)
h	Gaussian radius

Returns

double The RBF value

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

• /home/runner/work/Documentation/Documentation/master/kratos/utilities/rbf_shape_functions_utility.h
• /home/runner/work/Documentation/Documentation/master/kratos/utilities/rbf_shape_functions_utility.cpp