An extrapolation-algorithm, based on the linearly implicit Euler method with step size control and order selection. More...

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

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

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

Private Member Functions
bool	seul (const scalar x0, const scalarField &y0, const scalar dxTot, const label k, scalarField &y, const scalarField &scale) const
	Computes the j-th line of the extrapolation table. More...

void	extrapolate (const label k, scalarRectangularMatrix &table, scalarField &y) const
	Polynomial extrpolation. More...

Private Attributes
scalar	jacRedo_

labelField	nSeq_

scalarField	cpu_

scalarSquareMatrix	coeff_

scalar	theta_

label	kTarg_

scalarRectangularMatrix	table_

scalarField	dfdx_

scalarSquareMatrix	dfdy_

scalarSquareMatrix	a_

labelList	pivotIndices_

scalarField	dxOpt_

scalarField	temp_

scalarField	y0_

scalarField	ySequence_

scalarField	scale_

scalarField	dy_

scalarField	yTemp_

scalarField	dydx_

Static Private Attributes
static const label	kMaxx_ = 12

static const label	iMaxx_ = kMaxx_ + 1

static const scalar	stepFactor1_ = 0.6

static const scalar	stepFactor2_ = 0.93

static const scalar	stepFactor3_ = 0.1

static const scalar	stepFactor4_ = 4.0

static const scalar	stepFactor5_ = 0.5

static const scalar	kFactor1_ = 0.7

static const scalar	kFactor2_ = 0.9

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

An extrapolation-algorithm, based on the linearly implicit Euler method with step size control and order selection.

The implementation is based on the SEULEX algorithm in

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

Source files

Definition at line 61 of file seulex.H.

Constructor & Destructor Documentation

◆ seulex()

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

Construct from ODE.

Definition at line 50 of file seulex.C.

References seulex::coeff_, seulex::cpu_, seulex::iMaxx_, k, seulex::kMaxx_, and seulex::nSeq_.

Member Function Documentation

◆ seul()

bool seul	(	const scalar	x0,
		const scalarField &	y0,
		const scalar	dxTot,
		const label	k,
		scalarField &	y,
		const scalarField &	scale
	)		const

private

Computes the j-th line of the extrapolation table.

Definition at line 104 of file seulex.C.

References k, Foam::LUBacksubstitute(), Foam::LUDecompose(), Foam::min(), Foam::sqr(), Foam::sqrt(), y, and Foam::y0().

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◆ extrapolate()

void extrapolate	(	const label	k,
		scalarRectangularMatrix &	table,
		scalarField &	y
	)		const

private

Polynomial extrpolation.

Definition at line 184 of file seulex.C.

References k, and y.

◆ TypeName()

TypeName ( "seulex" )

Runtime type information.

◆ solve()

void solve	(	scalar &	x,
		scalarField &	y,
		stepState &	step
	)		const

virtual

Solve the ODE system and the update the state.

Reimplemented from ODESolver.

Definition at line 207 of file seulex.C.

References ODESolver::stepState::dxDid, ODESolver::stepState::dxTry, Foam::endl(), ODESolver::stepState::first, forAll, ODESolver::stepState::forward, k, ODESolver::stepState::last, Foam::log10(), Foam::mag(), Foam::max(), Foam::min(), Foam::pow(), ODESolver::stepState::prevReject, ODESolver::stepState::reject, Foam::sqr(), Foam::sqrt(), success, WarningInFunction, x, and y.

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Field Documentation

◆ kMaxx_

const label kMaxx_ = 12

staticprivate

Definition at line 69 of file seulex.H.

Referenced by seulex::seulex().

◆ iMaxx_

const label iMaxx_ = kMaxx_ + 1

staticprivate

Definition at line 70 of file seulex.H.

Referenced by seulex::seulex().

◆ stepFactor1_

const scalar stepFactor1_ = 0.6

staticprivate

Definition at line 73 of file seulex.H.

◆ stepFactor2_

const scalar stepFactor2_ = 0.93

staticprivate

Definition at line 73 of file seulex.H.

◆ stepFactor3_

const scalar stepFactor3_ = 0.1

staticprivate

Definition at line 73 of file seulex.H.

◆ stepFactor4_

const scalar stepFactor4_ = 4.0

staticprivate

Definition at line 74 of file seulex.H.

◆ stepFactor5_

const scalar stepFactor5_ = 0.5

staticprivate

Definition at line 74 of file seulex.H.

◆ kFactor1_

const scalar kFactor1_ = 0.7

staticprivate

Definition at line 75 of file seulex.H.

◆ kFactor2_

const scalar kFactor2_ = 0.9

staticprivate

Definition at line 75 of file seulex.H.

◆ jacRedo_

scalar jacRedo_

private

Definition at line 79 of file seulex.H.

◆ nSeq_

labelField nSeq_

private

Definition at line 80 of file seulex.H.

Referenced by seulex::seulex().

◆ cpu_

scalarField cpu_

private

Definition at line 81 of file seulex.H.

Referenced by seulex::seulex().

◆ coeff_

scalarSquareMatrix coeff_

private

Definition at line 82 of file seulex.H.

Referenced by seulex::seulex().

◆ theta_

scalar theta_

mutableprivate

Definition at line 88 of file seulex.H.

◆ kTarg_

label kTarg_

mutableprivate

Definition at line 89 of file seulex.H.

◆ table_

scalarRectangularMatrix table_

mutableprivate

Definition at line 90 of file seulex.H.

◆ dfdx_

scalarField dfdx_

mutableprivate

Definition at line 92 of file seulex.H.

◆ dfdy_

scalarSquareMatrix dfdy_

mutableprivate

Definition at line 93 of file seulex.H.

◆ a_

scalarSquareMatrix a_

mutableprivate

Definition at line 94 of file seulex.H.

◆ pivotIndices_

labelList pivotIndices_

mutableprivate

Definition at line 95 of file seulex.H.

◆ dxOpt_

scalarField dxOpt_

mutableprivate

Definition at line 98 of file seulex.H.

◆ temp_

scalarField temp_

private

Definition at line 98 of file seulex.H.

◆ y0_

scalarField y0_

mutableprivate

Definition at line 99 of file seulex.H.

◆ ySequence_

scalarField ySequence_

private

Definition at line 99 of file seulex.H.

◆ scale_

scalarField scale_

private

Definition at line 99 of file seulex.H.

◆ dy_

scalarField dy_

mutableprivate

Definition at line 102 of file seulex.H.

◆ yTemp_

scalarField yTemp_

private

Definition at line 102 of file seulex.H.

◆ dydx_

scalarField dydx_

private

Definition at line 102 of file seulex.H.

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

src/ODE/ODESolvers/seulex/seulex.H
src/ODE/ODESolvers/seulex/seulex.C

Public Member Functions

Private Member Functions

Private Attributes

Static Private Attributes

Additional Inherited Members

Detailed Description

Constructor & Destructor Documentation

◆ seulex()

Member Function Documentation

◆ seul()

◆ extrapolate()

◆ TypeName()

◆ solve()

Field Documentation

◆ kMaxx_

◆ iMaxx_

◆ stepFactor1_

◆ stepFactor2_

◆ stepFactor3_

◆ stepFactor4_

◆ stepFactor5_

◆ kFactor1_

◆ kFactor2_

◆ jacRedo_

◆ nSeq_

◆ cpu_

◆ coeff_

◆ theta_

◆ kTarg_

◆ table_

◆ dfdx_

◆ dfdy_

◆ a_

◆ pivotIndices_

◆ dxOpt_

◆ temp_

◆ y0_

◆ ySequence_

◆ scale_

◆ dy_

◆ yTemp_

◆ dydx_