MaterialPropertyLib::SigmoidFunction Class Reference

Detailed Description

Sigmoid function with scalar argument and two constant parameters

The sigmoid function is a smooth step function with the range $[0,1]$ defined by the following formula

$$(1-S_r) \left[1 + \exp(k(T - T_\mathrm{c})) \right]^{-1}$$

where $S_r$ is residual saturation, representing the amount of liquid water remaining after the water-ice phase transition is complete. $T_\mathrm{c}$ is the critical value (e.g. a phase change temperature). The parameter $k$ is proportional to the slope at the characteristic value and controls thus the steepness. Letting $k$ go to infinity, the heaviside step function is obtained.

Definition at line 38 of file SigmoidFunction.h.

#include <SigmoidFunction.h>

Public Member Functions
	SigmoidFunction (double const k, double const T_c, double const S_r)
double	value (double const &T) const
double	dValue (double const &T) const
double	d2Value (double const &T) const

Private Attributes
double const	k_
double const	T_c_
double const	S_r

Constructor & Destructor Documentation

SigmoidFunction()

MaterialPropertyLib::SigmoidFunction::SigmoidFunction	(	double const	k,
		double const	T_c,
		double const	S_r )

Definition at line 17 of file SigmoidFunction.cpp.

    : k_(k), T_c_(T_c), S_r(S_r)
{
}

Member Function Documentation

d2Value()

double MaterialPropertyLib::SigmoidFunction::d2Value

(

double const &

T

)

const

Definition at line 49 of file SigmoidFunction.cpp.

{
    double const fT = dValue(T);
    if (fT == 0)
    {
        return 0;
    }
 
    double const f = value(T);
    return fT * (k_ + 2 * fT / f);
}

References dValue(), k_, and value().

Referenced by MaterialPropertyLib::TemperatureDependentFraction::d2Value().

dValue()

double MaterialPropertyLib::SigmoidFunction::dValue

(

double const &

T

)

const

Definition at line 38 of file SigmoidFunction.cpp.

{
    double const f = value(T);
    if (f * f == 0)
    {
        return 0;
    }
    double const x = k_ * (T - T_c_);
    return -k_ * std::exp(x) * (f * f) / (1. - S_r);
}

References k_, S_r, T_c_, and value().

Referenced by d2Value(), and MaterialPropertyLib::TemperatureDependentFraction::dValue().

value()

double MaterialPropertyLib::SigmoidFunction::value

(

double const &

T

)

const

Definition at line 23 of file SigmoidFunction.cpp.

{
    double const x = k_ * (T - T_c_);
 
    // Cutting off at the last x producing a (non-normal) return value because
    // std::exp(x) produces +infinity beyond this point, approximately 709.78.
    // The reason for using hex representation is that the value is unambiguous.
    if (x > 0x1.62e42fefa39efp+9)
    {
        return 0.;
    }
 
    return (1. - S_r) / (1. + std::exp(x));
}

References k_, S_r, and T_c_.

Referenced by d2Value(), dValue(), and MaterialPropertyLib::TemperatureDependentFraction::value().

Member Data Documentation

k_

double const MaterialPropertyLib::SigmoidFunction::k_

private

Definition at line 50 of file SigmoidFunction.h.

Referenced by d2Value(), dValue(), and value().

S_r

double const MaterialPropertyLib::SigmoidFunction::S_r

private

Definition at line 53 of file SigmoidFunction.h.

Referenced by dValue(), and value().

T_c_

double const MaterialPropertyLib::SigmoidFunction::T_c_

private

Definition at line 51 of file SigmoidFunction.h.

Referenced by dValue(), and value().

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

• MaterialLib/MPL/Utils/SigmoidFunction.h
• MaterialLib/MPL/Utils/SigmoidFunction.cpp