dg::DPolynomialHeaviside Struct Reference

\( f(x) = \begin{cases} 0 \text{ if } x < x_b-a || x > x_b+a \\ (35 (a + x - x_b)^3 (a - x + x_b)^3)/(32 a^7) \text{ if } |x-x_b| < a \end{cases}\) The derivative of PolynomialHeaviside approximates delta(x) More...

Public Member Functions
	DPolynomialHeaviside (double xb, double a, int sign=+1)
	Construct with xb, width and sign. More...
DG_DEVICE double	operator() (double x) const
DG_DEVICE double	operator() (double x, double y) const
DG_DEVICE double	operator() (double x, double y, double z) const

Detailed Description

\( f(x) = \begin{cases} 0 \text{ if } x < x_b-a || x > x_b+a \\ (35 (a + x - x_b)^3 (a - x + x_b)^3)/(32 a^7) \text{ if } |x-x_b| < a \end{cases}\) The derivative of PolynomialHeaviside approximates delta(x)

This function is 2 times continuously differentiable, is symmetric around xb and has a width a on both sides of x0. The integral over this function yields 1.

Constructor & Destructor Documentation

DPolynomialHeaviside()

dg::DPolynomialHeaviside::DPolynomialHeaviside ( double  xb, double  a, int  sign = +1  )

inline

Construct with xb, width and sign.

Parameters

xb	boundary value
a	transition width ( must be !=0)
sign	either +1 (original) or -1 (the function is mirrored at x=x0) (since this function is symmetric this parameter is ignored, it's there to be consistent with PolynomialHeaviside)

Member Function Documentation

operator()() [1/3]

DG_DEVICE double dg::DPolynomialHeaviside::operator() ( double  x ) const

inline

operator()() [2/3]

DG_DEVICE double dg::DPolynomialHeaviside::operator() ( double  x, double  y  ) const

inline

operator()() [3/3]

DG_DEVICE double dg::DPolynomialHeaviside::operator() ( double  x, double  y, double  z  ) const

inline

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

• functors.h