#include <SmoothAbsoluteValue.H>

Public Member Functions
	SmoothAbsoluteValue (const BaseIF a_f, const BaseIF a_g, const Real &a_delta)

virtual	~SmoothAbsoluteValue ()

virtual Real	smoothAbsFMinusG (const IntVect &a_deriv, const RealVect &a_point) const

void	getWCase (int &a_case, Real &a_wval, const RealVect &a_point) const

Static Public Member Functions
static void	setKnownFunction (int a_whichfunc)

Protected Member Functions
virtual Real	valueAem (const RealVect &a_point) const

virtual Real	firstDerivAem (const IntVect &a_deriv, const RealVect &a_point) const

virtual Real	secondDerivAem (const IntVect &a_deriv, const RealVect &a_point) const

virtual Real	thirdDerivAem (const IntVect &a_deriv, const RealVect &a_point) const

virtual Real	fourthDerivAem (const IntVect &a_deriv, const RealVect &a_point) const

bool	isBogus (const Real &a_number) const
	just checks nan More...

void	checkAgainstKnown (const Real &a_myAnswer, const IntVect &a_deriv, const RealVect &a_point) const
	if s_knownFunc is set, check against known answer More...

Protected Attributes
const BaseIF *	m_f

const BaseIF *	m_g

Real	m_d

Real	m_pi

Static Protected Attributes
static int	s_knownFunc
	for debugging against known functions More...

Private Member Functions
	SmoothAbsoluteValue (const SmoothAbsoluteValue &a_inputIF)

	SmoothAbsoluteValue ()

void	operator= (const SmoothAbsoluteValue &a_inputIF)

Detailed Description

Functions to take a smooth absolute value of the difference between two functions A_e(a,b) = |a-b|

max(f, g) = (a + b + |a - b|)/2 We need to make abs(a-b) smooth.

We take the convolution of the absolute value with cos^4(pi w/(2 delta))

Constructor & Destructor Documentation

◆ SmoothAbsoluteValue() [1/3]

SmoothAbsoluteValue::SmoothAbsoluteValue	(	const BaseIF *	a_f,
		const BaseIF *	a_g,
		const Real &	a_delta
	)

inline

References m_d, m_f, m_g, and m_pi.

◆ ~SmoothAbsoluteValue()

virtual SmoothAbsoluteValue::~SmoothAbsoluteValue ( )

inlinevirtual

References checkAgainstKnown(), firstDerivAem(), fourthDerivAem(), getWCase(), isBogus(), secondDerivAem(), smoothAbsFMinusG(), thirdDerivAem(), and valueAem().

◆ SmoothAbsoluteValue() [2/3]

SmoothAbsoluteValue::SmoothAbsoluteValue ( const SmoothAbsoluteValue & a_inputIF )

inlineprivate

References MayDay::Abort().

◆ SmoothAbsoluteValue() [3/3]

SmoothAbsoluteValue::SmoothAbsoluteValue ( )

inlineprivate

References MayDay::Abort().

Member Function Documentation

◆ setKnownFunction()

static void SmoothAbsoluteValue::setKnownFunction ( int a_whichfunc )

inlinestatic

Set a known f and g (from short list I have programmed) to check answer against 1 = double ramp with ramp_normal_0 = 2. 1. 0. ramp_normal_1 = -2. 1. 0. ramp_point_0 = 0. 1. 0. ramp_point_1 = 1. 1. 0.

2 = double sphere with sphere_center_0 = 0 0 0 sphere_center_1 = 1 0 0 sphere_radius_0 = 0.75 sphere_radius_1 = 0.75

References s_knownFunc.

◆ smoothAbsFMinusG()

virtual Real SmoothAbsoluteValue::smoothAbsFMinusG	(	const IntVect &	a_deriv,
		const RealVect &	a_point
	)		const

virtual

Referenced by ~SmoothAbsoluteValue().

◆ getWCase()

void SmoothAbsoluteValue::getWCase	(	int &	a_case,
		Real &	a_wval,
		const RealVect &	a_point
	)		const

returns -1 if w < -delta, 1 if w > delta, 0 otherwise reduces to regular |f-g| unless case == 0

Referenced by ~SmoothAbsoluteValue().

◆ valueAem()

virtual Real SmoothAbsoluteValue::valueAem ( const RealVect & a_point ) const

protectedvirtual

Here is the logic of this stuff. We have three cases that reduce to two cases. w = f(x) - g(x) case 1: (w > delta): -— whole integral is above zero answer = abs(w) case -1: (w < - delta): -— whole integral is below zero answer = abs(w) case 0: (-delta <= w <= delta) — have to split integral into above and below answer = functionAem();

Referenced by DoubleRampExact::~DoubleRampExact(), DoubleSphereExact::~DoubleSphereExact(), OffsetSphereExact::~OffsetSphereExact(), and ~SmoothAbsoluteValue().