Cubic polynomial transition between two functions of one variable. More...

#include <CubicTransition.h>

Inheritance diagram for CubicTransition:

Public Member Functions
	CubicTransition (const Real &x_center, const Real &transition_width)
	Constructor.

virtual Real	value (const Real &x, const Real &f1, const Real &f2) const override
	Computes the transition value.

Real	derivative (const Real &x, const Real &df1dx, const Real &df2dx) const
	Computes the derivative of the transition value.

void	initialize (const Real &f1_end_value, const Real &f2_end_value, const Real &df1dx_end_value, const Real &df2dx_end_value)
	Initializes the polynomial coefficients.

const Real &	leftEnd () const
	Returns the coordinate of the left end of the transition.

const Real &	rightEnd () const
	Returns the coordinate of the right end of the transition.

Protected Attributes
Real	_A

Real	_B

Real	_C

Real	_D

bool	_initialized
	Flag that transition has been initialized.

const Real	_x_center
	Center point of transition.

const Real	_transition_width
	Width of transition.

const Real	_x1
	Left end point of transition.

const Real	_x2
	Right end point of transition.

Detailed Description

Cubic polynomial transition between two functions of one variable.

Definition at line 17 of file CubicTransition.h.

Constructor & Destructor Documentation

◆ CubicTransition()

CubicTransition::CubicTransition	(	const Real &	x_center,
		const Real &	transition_width
	)

Constructor.

Parameters

[in]	x_center	Center point of transition
[in]	transition_width	Width of transition

Definition at line 16 of file CubicTransition.C.

  : SmoothTransition(x_center, transition_width),
 
    _A(0.0),
    _B(0.0),
    _C(0.0),
    _D(0.0),
 
    _initialized(false)
{
}

Member Function Documentation

◆ derivative()

Real CubicTransition::derivative	(	const Real &	x,
		const Real &	df1dx,
		const Real &	df2dx
	)		const

Computes the derivative of the transition value.

Parameters

[in]	x	Point at which to evaluate transition
[in]	df1dx	First function derivative
[in]	df2dx	Second function derivative

Definition at line 89 of file CubicTransition.C.

{
  mooseAssert(_initialized, "initialize() must be called.");
 
  if (x <= _x1)
    return df1dx;
  else if (x >= _x2)
    return df2dx;
  else
    return 3.0 * _A * std::pow(x, 2) + 2.0 * _B * x + _C;
}

Referenced by SmoothTransitionTestMaterial::computeQpProperties().

◆ initialize()

void CubicTransition::initialize	(	const Real &	f1_end_value,
		const Real &	f2_end_value,
		const Real &	df1dx_end_value,
		const Real &	df2dx_end_value
	)

Initializes the polynomial coefficients.

Parameters

[in]	f1_end_value	Value of left function at left transition end point
[in]	f2_end_value	Value of right function at right transition end point
[in]	df1dx_end_value	Value of left function derivative at left transition end point
[in]	df2dx_end_value	Value of right function derivative at right transition end point

Definition at line 29 of file CubicTransition.C.

{
  // compute cubic polynomial coefficients
 
  DenseMatrix<Real> mat(4, 4);
 
  mat(0, 0) = std::pow(_x1, 3);
  mat(0, 1) = std::pow(_x1, 2);
  mat(0, 2) = _x1;
  mat(0, 3) = 1.0;
 
  mat(1, 0) = std::pow(_x2, 3);
  mat(1, 1) = std::pow(_x2, 2);
  mat(1, 2) = _x2;
  mat(1, 3) = 1.0;
 
  mat(2, 0) = 3.0 * std::pow(_x1, 2);
  mat(2, 1) = 2.0 * _x1;
  mat(2, 2) = 1.0;
  mat(2, 3) = 0.0;
 
  mat(3, 0) = 3.0 * std::pow(_x2, 2);
  mat(3, 1) = 2.0 * _x2;
  mat(3, 2) = 1.0;
  mat(3, 3) = 0.0;
 
  DenseVector<Real> rhs(4);
  rhs(0) = f1_end_value;
  rhs(1) = f2_end_value;
  rhs(2) = df1dx_end_value;
  rhs(3) = df2dx_end_value;
 
  DenseVector<Real> coefs(4);
  mat.lu_solve(rhs, coefs);
 
  _A = coefs(0);
  _B = coefs(1);
  _C = coefs(2);
  _D = coefs(3);
 
  _initialized = true;
}

Referenced by CubicTransitionFunction::CubicTransitionFunction(), and SmoothTransitionTestMaterial::SmoothTransitionTestMaterial().

◆ leftEnd()

const Real & SmoothTransition::leftEnd ( ) const

inlineinherited

Returns the coordinate of the left end of the transition.

Definition at line 40 of file SmoothTransition.h.

40{ return _x1; }

Referenced by CubicTransitionFunction::CubicTransitionFunction(), and SmoothTransitionTestMaterial::SmoothTransitionTestMaterial().

◆ rightEnd()

const Real & SmoothTransition::rightEnd ( ) const

inlineinherited

Returns the coordinate of the right end of the transition.

Definition at line 45 of file SmoothTransition.h.

45{ return _x2; }

Referenced by CubicTransitionFunction::CubicTransitionFunction(), and SmoothTransitionTestMaterial::SmoothTransitionTestMaterial().

◆ value()

Real CubicTransition::value	(	const Real &	x,
		const Real &	f1,
		const Real &	f2
	)		const

overridevirtual

Computes the transition value.

Parameters

[in]	x	Point at which to evaluate function
[in]	f1	Left function
[in]	f2	Right function

Implements SmoothTransition.

Definition at line 76 of file CubicTransition.C.

{
  mooseAssert(_initialized, "initialize() must be called.");
 
  if (x <= _x1)
    return f1;
  else if (x >= _x2)
    return f2;
  else
    return _A * std::pow(x, 3) + _B * std::pow(x, 2) + _C * x + _D;
}