Classes
struct	FacetData
	data for specifying a faceted weight. More...

Enumerations
enum	Kernel { B4, SQUARE, EPANECHNIKOV, POLYRAMP, INVSQRT, COULOMB, STEP }
	Kernel types. More...

enum	Geometry { ELLIPTIC, TENSOR, FACETED }
	Geometry types. More...

Functions
double	sign (double x)
	scalar sign function. More...

double	unit_step (double x)
	scalar step function More...

double	b4 (double x)
	scalar cubic b-spline. More...

double	db4 (double x)
	scalar cubic b-spline derivative. More...

double	ddb4 (double x)
	scalar cubic b-spline second derivative. More...

double	ib4 (double x)
	scalar cubic b-spline anti-derivative. More...

double	b4lh (double x)
	scalar left half cubic b-spline. More...

double	b4rh (double x)
	scalar right half cubic b-spline. More...

double	epanechnikov (double x)
	scalar epanechnikov kernel. More...

double	depanechnikov (double x)
	scalar epanechnikov kernel derivative. More...

double	ddepanechnikov (double x)
	scalar epanechnikov kernel second derivative. More...

double	square (double x)
	scalar square kernel. More...

double	dsquare (double x)
	scalar square kernel derivative. More...

double	ddsquare (double x)
	scalar square kernel second derivative. More...

double	polyramp (double x)
	scalar smooth ramp for faceted weight. More...

double	dpolyramp (double x)
	scalar smooth ramp for faceted weight derivative. More...

double	ddpolyramp (double x)
	scalar smooth ramp for faceted weight derivative. More...

double	invsqrt (double x)
	inverse square root kernel. More...

double	dinvsqrt (double x)
	derivative of inverse square root kernel. More...

double	ddinvsqrt (double x)
	second derivative of inverse square root kernel. More...

double	coulomb (double x)
	coulomb weight. More...

double	dcoulomb (double x)
	coulomb weight derivative. More...

double	ddcoulomb (double x)
	coulomb weight second derivative. More...

double	step (double x)
	step weight. More...

double	dstep (double x)
	step weight derivative. More...

double	ddstep (double x)
	step weight second derivative. More...

double	kernel (const Kernel kern, double x)
	General kernel function. More...

template<int dim>
double	elliptic (Wonton::Point< dim > const &x, Wonton::Point< dim > const &y, std::array< double, dim > const &h)
	generic elliptically symmetric weight function argument. More...

template<int dim>
std::array< double, dim >	tensor (Wonton::Point< dim > const &x, Wonton::Point< dim > const &y, std::array< double, dim > const &h)
	generic tensor weight function arguments. More...

template<int dim>
double	eval (Geometry const geometry, Kernel const kern, Wonton::Point< dim > const &x, Wonton::Point< dim > const &y, std::array< double, dim > const &h)
	evaluation function for elliptic or tensor product weights. More...

template<int dim>
double	faceted (Kernel const kern, Wonton::Point< dim > const &x, Wonton::Point< dim > const &y, std::vector< FacetData< dim >> const &facets, size_t nsides)
	faceted weight function More...

template<int dim>
double	eval (Geometry const geo, Kernel const kern, Wonton::Point< dim > const &x, Wonton::Point< dim > const &y, std::vector< std::vector< double >> const &vh)
	evaluation function for any weight. More...

Variables
double const	normconst [4] = { 2./3., 1./(.7 * M_PI), 1./M_PI, 1./M_PI }
	normalization constants for cubic B-spline (linear, cylindrical, and spherical). More...

double const	epsilon = std::numeric_limits<double>::epsilon()
	Numerical tolerance. More...

Enumeration Type Documentation

◆ Geometry

enum Portage::Meshfree::Weight::Geometry

Geometry types.

Enumerator
ELLIPTIC
TENSOR
FACETED

◆ Kernel

enum Portage::Meshfree::Weight::Kernel

Kernel types.

Enumerator
B4
SQUARE
EPANECHNIKOV
POLYRAMP
INVSQRT
COULOMB
STEP

Function Documentation

◆ b4()

double Portage::Meshfree::Weight::b4 ( double x )

inline

scalar cubic b-spline.

Parameters

x	given scalar

Returns: its value at x.

◆ b4lh()

double Portage::Meshfree::Weight::b4lh ( double x )

inline

scalar left half cubic b-spline.

Parameters

x	given scalar

Returns: its value at x.

◆ b4rh()

double Portage::Meshfree::Weight::b4rh ( double x )

inline

scalar right half cubic b-spline.

Parameters

x	given scalar

Returns: its value at x.

◆ coulomb()

double Portage::Meshfree::Weight::coulomb ( double x )

inline

coulomb weight.

Parameters

x	given scalar.

Returns: its value at x.

◆ db4()

double Portage::Meshfree::Weight::db4 ( double x )

inline

scalar cubic b-spline derivative.

Parameters

x	given scalar

Returns: its value at x.

◆ dcoulomb()

double Portage::Meshfree::Weight::dcoulomb ( double x )

inline

coulomb weight derivative.

Parameters

x	given scalar.

Returns: its value at x.

◆ ddb4()

double Portage::Meshfree::Weight::ddb4 ( double x )

inline

scalar cubic b-spline second derivative.

Parameters

x	given scalar

Returns: its value at x.

◆ ddcoulomb()

double Portage::Meshfree::Weight::ddcoulomb ( double x )

inline

coulomb weight second derivative.

Parameters

x	given scalar.

Returns: its value at x.

◆ ddepanechnikov()

double Portage::Meshfree::Weight::ddepanechnikov ( double x )

inline

scalar epanechnikov kernel second derivative.

Parameters

x	given scalar.

Returns: its value at x.

◆ ddinvsqrt()

double Portage::Meshfree::Weight::ddinvsqrt ( double x )

inline

second derivative of inverse square root kernel.

Parameters

x	given scalar.

Returns: its value at x.

◆ ddpolyramp()

double Portage::Meshfree::Weight::ddpolyramp ( double x )

inline

scalar smooth ramp for faceted weight derivative.

Parameters

x	given scalar.

Returns: its value at x.

◆ ddsquare()

double Portage::Meshfree::Weight::ddsquare ( double x )

inline

scalar square kernel second derivative.

Parameters

x	given scalar.

Returns: its value at x.

◆ ddstep()

double Portage::Meshfree::Weight::ddstep ( double x )

inline

step weight second derivative.

Parameters

x	given scalar.

Returns: its value at x.

◆ depanechnikov()

double Portage::Meshfree::Weight::depanechnikov ( double x )

inline

scalar epanechnikov kernel derivative.

Parameters

x	given scalar.

Returns: its value at x.

◆ dinvsqrt()

double Portage::Meshfree::Weight::dinvsqrt ( double x )

inline

derivative of inverse square root kernel.

Parameters

x	given scalar.

Returns: its value at x.

◆ dpolyramp()

double Portage::Meshfree::Weight::dpolyramp ( double x )

inline

scalar smooth ramp for faceted weight derivative.

Parameters

x	given scalar.

Returns: its value at x.

◆ dsquare()

double Portage::Meshfree::Weight::dsquare ( double x )

inline

scalar square kernel derivative.

Parameters

x	given scalar.

Returns: its value at x.

◆ dstep()

double Portage::Meshfree::Weight::dstep ( double x )

inline

step weight derivative.

Parameters

x	given scalar.

Returns: its value at x.

◆ elliptic()

template<int dim>

double Portage::Meshfree::Weight::elliptic	(	Wonton::Point< dim > const &	x,
		Wonton::Point< dim > const &	y,
		std::array< double, dim > const &	h
	)

generic elliptically symmetric weight function argument.

Template Parameters

dim	spatial dimension.

Parameters

x	first point
y	second point
h	size metric

Returns: sqrt(sum_i (xi - yi)^2 / hi^2)

◆ epanechnikov()

double Portage::Meshfree::Weight::epanechnikov ( double x )

inline

scalar epanechnikov kernel.

Parameters

x	given scalar

Returns: its value at x.

◆ eval() [1/2]

template<int dim>

double Portage::Meshfree::Weight::eval	(	Geometry const	geometry,
		Kernel const	kern,
		Wonton::Point< dim > const &	x,
		Wonton::Point< dim > const &	y,
		std::array< double, dim > const &	h
	)

evaluation function for elliptic or tensor product weights.

Template Parameters

dim	spatial dimension.

Parameters

geometry	the geometry to consider.
kern	the kernel to consider.
x	first point
y	second point
h	size metric

Returns: evaluated kernel value.

◆ eval() [2/2]

template<int dim>

double Portage::Meshfree::Weight::eval	(	Geometry const	geo,
		Kernel const	kern,
		Wonton::Point< dim > const &	x,
		Wonton::Point< dim > const &	y,
		std::vector< std::vector< double >> const &	vh
	)

evaluation function for any weight.

Template Parameters

dim	spatial dimension.

Parameters

geo	the geometry to consider.
kern	the kernel to consider.
x	first point.
y	second point.
vh	size matrix.

Returns: evaluated kernel value.

◆ faceted()

template<int dim>

double Portage::Meshfree::Weight::faceted	(	Kernel const	kern,
		Wonton::Point< dim > const &	x,
		Wonton::Point< dim > const &	y,
		std::vector< FacetData< dim >> const &	facets,
		size_t	nsides
	)

faceted weight function

Template Parameters

dim	spatial dimension.

Parameters

kern	the kernel to use.
x	first point.
y	second point.
facets	list of facets.
nsides	number of sides.

Returns: evaluated kernel value.

◆ ib4()

double Portage::Meshfree::Weight::ib4 ( double x )

inline

scalar cubic b-spline anti-derivative.

Parameters

x	given scalar

Returns: its value at x.

◆ invsqrt()

double Portage::Meshfree::Weight::invsqrt ( double x )

inline

inverse square root kernel.

Parameters

x	given scalar.

Returns: its value at x.

◆ kernel()

double Portage::Meshfree::Weight::kernel	(	const Kernel	kern,
		double	x
	)

inline

General kernel function.

Parameters

kern	kernel type.
x	given scalar.

Returns: related value.

◆ polyramp()

double Portage::Meshfree::Weight::polyramp ( double x )

inline

scalar smooth ramp for faceted weight.

Parameters

x	given scalar.

Returns: its value at x.

◆ sign()

double Portage::Meshfree::Weight::sign ( double x )

inline

scalar sign function.

Parameters

x	given scalar.

Returns: its sign.

◆ square()

double Portage::Meshfree::Weight::square ( double x )

inline

scalar square kernel.

Parameters

x	given scalar.

Returns: its value at x.

◆ step()

double Portage::Meshfree::Weight::step ( double x )

inline

step weight.

Parameters

x	given scalar.

Returns: its value at x.

◆ tensor()

template<int dim>

std::array<double,dim> Portage::Meshfree::Weight::tensor	(	Wonton::Point< dim > const &	x,
		Wonton::Point< dim > const &	y,
		std::array< double, dim > const &	h
	)

generic tensor weight function arguments.

Template Parameters

dim	spatial dimension.

Parameters

x	first point
y	second point
h	size metric

Returns: [(xi - yi) / hi]_{i=0,dim-1}

◆ unit_step()

double Portage::Meshfree::Weight::unit_step ( double x )

inline

scalar step function

Variable Documentation

◆ epsilon

double const Portage::Meshfree::Weight::epsilon = std::numeric_limits<double>::epsilon()

Numerical tolerance.

◆ normconst

double const Portage::Meshfree::Weight::normconst[4] = { 2./3., 1./(.7 * M_PI), 1./M_PI, 1./M_PI }

normalization constants for cubic B-spline (linear, cylindrical, and spherical).

Classes

Enumerations

Functions

Variables

Enumeration Type Documentation

◆ Geometry

◆ Kernel

Function Documentation

◆ b4()

◆ b4lh()

◆ b4rh()

◆ coulomb()

◆ db4()

◆ dcoulomb()

◆ ddb4()

◆ ddcoulomb()

◆ ddepanechnikov()

◆ ddinvsqrt()

◆ ddpolyramp()

◆ ddsquare()

◆ ddstep()

◆ depanechnikov()

◆ dinvsqrt()

◆ dpolyramp()

◆ dsquare()

◆ dstep()

◆ elliptic()

◆ epanechnikov()

◆ eval() [1/2]

◆ eval() [2/2]

◆ faceted()

◆ ib4()

◆ invsqrt()

◆ kernel()

◆ polyramp()

◆ sign()

◆ square()

◆ step()

◆ tensor()

◆ unit_step()

Variable Documentation

◆ epsilon

◆ normconst