L-stable embedded Rosenbrock ODE solver of order (3)4. More...

Inheritance diagram for Rosenbrock34:

Collaboration diagram for Rosenbrock34:

[legend]

Public Member Functions
	TypeName ("Rosenbrock34")
	Runtime type information. More...

	Rosenbrock34 (const ODESystem &ode, const dictionary &dict)
	Construct from ODE. More...

scalar	solve (const scalar x0, const scalarField &y0, const scalarField &dydx0, const scalar dx, scalarField &y) const
	Solve a single step dx and return the error. More...

void	solve (scalar &x, scalarField &y, scalar &dxTry) const
	Solve the ODE system and the update the state. More...

virtual void	solve (scalar &x, scalarField &y, scalar &dxTry) const
	Inherit solve from ODESolver. More...

virtual void	solve (scalar &x, scalarField &y, stepState &step) const
	Inherit solve from ODESolver. More...

virtual void	solve (const scalar xStart, const scalar xEnd, scalarField &y, scalar &dxEst) const
	Inherit solve from ODESolver. More...

Public Member Functions inherited from ODESolver
	TypeName ("ODESolver")
	Runtime type information. More...

	declareRunTimeSelectionTable (autoPtr, ODESolver, dictionary,(const ODESystem &ode, const dictionary &dict),(ode, dict))

	ODESolver (const ODESystem &ode, const dictionary &dict)
	Construct for given ODESystem. More...

	ODESolver (const ODESystem &ode, const scalarField &absTol, const scalarField &relTol)
	Construct for given ODESystem specifying tolerances. More...

virtual	~ODESolver ()
	Destructor. More...

scalarField &	absTol ()

scalarField &	relTol ()

virtual void	solve (scalar &x, scalarField &y, stepState &step) const
	Solve the ODE system as far as possible upto dxTry. More...

virtual void	solve (const scalar xStart, const scalar xEnd, scalarField &y, scalar &dxEst) const
	Solve the ODE system from xStart to xEnd, update the state. More...

Public Member Functions inherited from adaptiveSolver
	adaptiveSolver (const ODESystem &ode, const dictionary &dict)
	Construct from ODESystem. More...

virtual	~adaptiveSolver ()
	Destructor. More...

void	solve (const ODESystem &ode, scalar &x, scalarField &y, scalar &dxTry) const
	Solve the ODE system and the update the state. More...

Private Attributes
scalarField	k1_

scalarField	k2_

scalarField	k3_

scalarField	k4_

scalarField	err_

scalarField	dydx_

scalarField	dfdx_

scalarSquareMatrix	dfdy_

scalarSquareMatrix	a_

labelList	pivotIndices_

Static Private Attributes
static const scalar	a21 = 2

static const scalar	a31 = 48.0/25.0

static const scalar	a32 = 6.0/25.0

static const scalar	c21 = -8

static const scalar	c31 = 372.0/25.0

static const scalar	c32 = 12.0/5.0

static const scalar	c41 = -112.0/125.0

static const scalar	c42 = -54.0/125.0

static const scalar	c43 = -2.0/5.0

static const scalar	b1 = 19.0/9.0

static const scalar	b2 = 1.0/2.0

static const scalar	b3 = 25.0/108.0

static const scalar	b4 = 125.0/108.0

static const scalar	e1 = 34.0/108.0

static const scalar	e2 = 7.0/36.0

static const scalar	e3 = 0

static const scalar	e4 = 125.0/108.0

static const scalar	gamma = 1.0/2.0

static const scalar	c2 = 1

static const scalar	c3 = 3.0/5.0

static const scalar	d1 = 1.0/2.0

static const scalar	d2 = -3.0/2.0

static const scalar	d3 = 605.0/250.0

static const scalar	d4 = 29.0/250.0

Additional Inherited Members
Static Public Member Functions inherited from ODESolver
static autoPtr< ODESolver >	New (const ODESystem &ode, const dictionary &dict)
	Select null constructed. More...

Protected Member Functions inherited from ODESolver
scalar	normalizeError (const scalarField &y0, const scalarField &y, const scalarField &err) const
	Return the nomalized scalar error. More...

	ODESolver (const ODESolver &)
	Disallow default bitwise copy construct. More...

void	operator= (const ODESolver &)
	Disallow default bitwise assignment. More...

Protected Attributes inherited from ODESolver
const ODESystem &	odes_
	Reference to ODESystem. More...

label	n_
	Size of the ODESystem. More...

scalarField	absTol_
	Absolute convergence tolerance per step. More...

scalarField	relTol_
	Relative convergence tolerance per step. More...

label	maxSteps_
	The maximum number of sub-steps allowed for the integration step. More...

Detailed Description

L-stable embedded Rosenbrock ODE solver of order (3)4.

    "Solving Ordinary Differential Equations II: Stiff
     and Differential-Algebraic Problems, second edition",
    Hairer, E.,
    Nørsett, S.,
    Wanner, G.,
    Springer-Verlag, Berlin. 1996.

The default constants are from:

    "Implementation of Rosenbrock Methods"
    Shampine, L. F.,
    ACM Transactions on Mathematical Software, vol. 8, 1982, pp. 93–113.

with which the scheme is more accurate than with the L-Stable coefficients for small step-size but less stable for large step-size.

The L-Stable scheme constants are provided commented-out in Rosenbrock34.C

Source files

Definition at line 69 of file Rosenbrock34.H.

Constructor & Destructor Documentation

◆ Rosenbrock34()

Rosenbrock34	(	const ODESystem &	ode,
		const dictionary &	dict
	)

Construct from ODE.

Definition at line 108 of file Rosenbrock34.C.

Member Function Documentation

◆ TypeName()

TypeName ( "Rosenbrock34" )

Runtime type information.

◆ solve() [1/5]

Foam::scalar solve	(	const scalar	x0,
		const scalarField &	y0,
		const scalarField &	dydx0,
		const scalar	dx,
		scalarField &	y
	)		const

virtual

Solve a single step dx and return the error.

Implements adaptiveSolver.

Definition at line 128 of file Rosenbrock34.C.

References Foam::constant::physicoChemical::c2, forAll, Foam::LUBacksubstitute(), Foam::LUDecompose(), y, and Foam::y0().

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◆ solve() [2/5]

void solve	(	scalar &	x,
		scalarField &	y,
		scalar &	dxTry
	)		const

virtual

Solve the ODE system and the update the state.

Reimplemented from ODESolver.

Definition at line 209 of file Rosenbrock34.C.

References adaptiveSolver::solve(), x, and y.

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◆ solve() [3/5]

virtual void solve

inline

Inherit solve from ODESolver.

Definition at line 178 of file ODESolver.H.

◆ solve() [4/5]

void solve

Inherit solve from ODESolver.

Definition at line 86 of file ODESolver.C.

◆ solve() [5/5]

void solve

Inherit solve from ODESolver.

Definition at line 99 of file ODESolver.C.

Field Documentation

◆ k1_

scalarField k1_

mutableprivate

Definition at line 76 of file Rosenbrock34.H.

◆ k2_

scalarField k2_

mutableprivate

Definition at line 77 of file Rosenbrock34.H.

◆ k3_

scalarField k3_

mutableprivate

Definition at line 78 of file Rosenbrock34.H.

◆ k4_

scalarField k4_

mutableprivate

Definition at line 79 of file Rosenbrock34.H.

◆ err_

scalarField err_

mutableprivate

Definition at line 80 of file Rosenbrock34.H.

◆ dydx_

scalarField dydx_

mutableprivate

Definition at line 81 of file Rosenbrock34.H.

◆ dfdx_

scalarField dfdx_

mutableprivate

Definition at line 82 of file Rosenbrock34.H.

◆ dfdy_

scalarSquareMatrix dfdy_

mutableprivate

Definition at line 83 of file Rosenbrock34.H.

◆ a_

scalarSquareMatrix a_

mutableprivate

Definition at line 84 of file Rosenbrock34.H.

◆ pivotIndices_

labelList pivotIndices_

mutableprivate

Definition at line 85 of file Rosenbrock34.H.

◆ a21

const scalar a21 = 2

staticprivate

Definition at line 88 of file Rosenbrock34.H.

◆ a31

const scalar a31 = 48.0/25.0

staticprivate

Definition at line 88 of file Rosenbrock34.H.

◆ a32

const scalar a32 = 6.0/25.0

staticprivate

Definition at line 88 of file Rosenbrock34.H.

◆ c21

const scalar c21 = -8

staticprivate

Definition at line 89 of file Rosenbrock34.H.

◆ c31

const scalar c31 = 372.0/25.0

staticprivate

Definition at line 89 of file Rosenbrock34.H.

◆ c32

const scalar c32 = 12.0/5.0

staticprivate

Definition at line 89 of file Rosenbrock34.H.

◆ c41

const scalar c41 = -112.0/125.0

staticprivate

Definition at line 90 of file Rosenbrock34.H.

◆ c42

const scalar c42 = -54.0/125.0

staticprivate

Definition at line 90 of file Rosenbrock34.H.

◆ c43

const scalar c43 = -2.0/5.0

staticprivate

Definition at line 90 of file Rosenbrock34.H.

◆ b1

const scalar b1 = 19.0/9.0

staticprivate

Definition at line 91 of file Rosenbrock34.H.

◆ b2

const scalar b2 = 1.0/2.0

staticprivate

Definition at line 91 of file Rosenbrock34.H.

◆ b3

const scalar b3 = 25.0/108.0

staticprivate

Definition at line 91 of file Rosenbrock34.H.

◆ b4

const scalar b4 = 125.0/108.0

staticprivate

Definition at line 91 of file Rosenbrock34.H.

◆ e1

const scalar e1 = 34.0/108.0

staticprivate

Definition at line 92 of file Rosenbrock34.H.

◆ e2

const scalar e2 = 7.0/36.0

staticprivate

Definition at line 92 of file Rosenbrock34.H.

◆ e3

const scalar e3 = 0

staticprivate

Definition at line 92 of file Rosenbrock34.H.

◆ e4

const scalar e4 = 125.0/108.0

staticprivate

Definition at line 92 of file Rosenbrock34.H.

◆ gamma

const scalar gamma = 1.0/2.0

staticprivate

Definition at line 93 of file Rosenbrock34.H.

◆ c2

const scalar c2 = 1

staticprivate

Definition at line 94 of file Rosenbrock34.H.

◆ c3

const scalar c3 = 3.0/5.0

staticprivate

Definition at line 94 of file Rosenbrock34.H.

◆ d1

const scalar d1 = 1.0/2.0

staticprivate

Definition at line 95 of file Rosenbrock34.H.

◆ d2

const scalar d2 = -3.0/2.0

staticprivate

Definition at line 95 of file Rosenbrock34.H.

◆ d3

const scalar d3 = 605.0/250.0

staticprivate

Definition at line 95 of file Rosenbrock34.H.

◆ d4

const scalar d4 = 29.0/250.0

staticprivate

Definition at line 95 of file Rosenbrock34.H.

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

src/ODE/ODESolvers/Rosenbrock34/Rosenbrock34.H
src/ODE/ODESolvers/Rosenbrock34/Rosenbrock34.C

Public Member Functions

Private Attributes

Static Private Attributes

Additional Inherited Members

Detailed Description

Constructor & Destructor Documentation

◆ Rosenbrock34()

Member Function Documentation

◆ TypeName()

◆ solve() [1/5]

◆ solve() [2/5]

◆ solve() [3/5]

◆ solve() [4/5]

◆ solve() [5/5]

Field Documentation

◆ k1_

◆ k2_

◆ k3_

◆ k4_

◆ err_

◆ dydx_

◆ dfdx_

◆ dfdy_

◆ a_

◆ pivotIndices_

◆ a21

◆ a31

◆ a32

◆ c21

◆ c31

◆ c32

◆ c41

◆ c42

◆ c43

◆ b1

◆ b2

◆ b3

◆ b4

◆ e1

◆ e2

◆ e3

◆ e4

◆ gamma

◆ c2

◆ c3

◆ d1

◆ d2

◆ d3

◆ d4