dg::PolynomialHeaviside Struct Reference

\( f(x) = \begin{cases} 0 \text{ if } x < x_b-a \\ ((16 a^3 - 29 a^2 (x - x_b) + 20 a (x - x_b)^2 - 5 (x - x_b)^3) (a + x - x_b)^4)/(32 a^7) \text{ if } |x-x_b| < a \\ 1 \text{ if } x > x_b + a \end{cases}\) More...

Public Member Functions
	PolynomialHeaviside (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

\( f(x) = \begin{cases} 0 \text{ if } x < x_b-a \\ ((16 a^3 - 29 a^2 (x - x_b) + 20 a (x - x_b)^2 - 5 (x - x_b)^3) (a + x - x_b)^4)/(32 a^7) \text{ if } |x-x_b| < a \\ 1 \text{ if } x > x_b + a \end{cases}\)

An approximation to Heaviside using polynomials. This function is 3 times continuously differentiable, takes the value 0.5 at xb and has a transition width a on both sides of xb.

Constructor & Destructor Documentation

PolynomialHeaviside()

dg::PolynomialHeaviside::PolynomialHeaviside ( 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 Heaviside) or -1 (the function is mirrored at the x=xb axis: f(2xb-x))

Note

When sign is positive the function leaves the positive and damps the negative and vice versa when sign is negative the function leaves the negative and damps the positive.

Member Function Documentation

operator()() [1/3]

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

inline

operator()() [2/3]

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

inline

operator()() [3/3]

DG_DEVICE double dg::PolynomialHeaviside::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