SmoothAbsoluteValue Class Reference

#include <SmoothAbsoluteValue.H>

List of all members.

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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))

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
void	checkAgainstKnown (const Real &a_myAnswer, const IntVect &a_deriv, const RealVect &a_point) const
	if s_knownFunc is set, check against known answer
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
Private Member Functions
	SmoothAbsoluteValue (const SmoothAbsoluteValue &a_inputIF)
	SmoothAbsoluteValue ()
void	operator= (const SmoothAbsoluteValue &a_inputIF)

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Constructor & Destructor Documentation

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.

virtual SmoothAbsoluteValue::~SmoothAbsoluteValue

(

)

[inline, virtual]

SmoothAbsoluteValue::SmoothAbsoluteValue

(

const SmoothAbsoluteValue &

a_inputIF

)

[inline, private]

References MayDay::Abort().

SmoothAbsoluteValue::SmoothAbsoluteValue

(

)

[inline, private]

References MayDay::Abort().

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Member Function Documentation

static void SmoothAbsoluteValue::setKnownFunction

(

int

a_whichfunc

)

[inline, static]

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.

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

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

virtual Real SmoothAbsoluteValue::valueAem

(

const RealVect &

a_point

)

const [protected, virtual]

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();

virtual Real SmoothAbsoluteValue::firstDerivAem	(	const IntVect &	a_deriv,
		const RealVect &	a_point
	)			const [protected, virtual]

virtual Real SmoothAbsoluteValue::secondDerivAem	(	const IntVect &	a_deriv,
		const RealVect &	a_point
	)			const [protected, virtual]

virtual Real SmoothAbsoluteValue::thirdDerivAem	(	const IntVect &	a_deriv,
		const RealVect &	a_point
	)			const [protected, virtual]

virtual Real SmoothAbsoluteValue::fourthDerivAem	(	const IntVect &	a_deriv,
		const RealVect &	a_point
	)			const [protected, virtual]

bool SmoothAbsoluteValue::isBogus

(

const Real &

a_number

)

const [protected]

just checks nan

void SmoothAbsoluteValue::checkAgainstKnown	(	const Real &	a_myAnswer,
		const IntVect &	a_deriv,
		const RealVect &	a_point
	)			const [protected]

if s_knownFunc is set, check against known answer

void SmoothAbsoluteValue::operator=

(

const SmoothAbsoluteValue &

a_inputIF

)

[inline, private]

References MayDay::Abort().

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Member Data Documentation

const BaseIF* SmoothAbsoluteValue::m_f [protected]

Referenced by SmoothAbsoluteValue().

const BaseIF* SmoothAbsoluteValue::m_g [protected]

Referenced by SmoothAbsoluteValue().

Real SmoothAbsoluteValue::m_d [protected]

Referenced by SmoothAbsoluteValue().

Real SmoothAbsoluteValue::m_pi [protected]

Referenced by SmoothAbsoluteValue().

int SmoothAbsoluteValue::s_knownFunc [static, protected]

for debugging against known functions

Referenced by setKnownFunction().

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

• SmoothAbsoluteValue.H