Calculates the Jacobian of the local residual for finite volume spatial discretizations using a finite difference method. More...

#include <fvbasefdlocallinearizer.hh>

Public Member Functions
	FvBaseFdLocalLinearizer ()

	~FvBaseFdLocalLinearizer ()

void	init (Simulator &simulator)
	Initialize the local Jacobian object. More...

void	linearize (const Element &element)
	Compute an element's local Jacobian matrix and evaluate its residual. More...

void	linearize (ElementContext &elemCtx)
	Compute an element's local Jacobian matrix and evaluate its residual. More...

Scalar	numericEpsilon (const ElementContext &elemCtx, int dofIdx, int pvIdx) const
	Returns the epsilon value which is added and removed from the current solution. More...

LocalResidual &	localResidual ()
	Return reference to the local residual. More...

const LocalResidual &	localResidual () const
	Return reference to the local residual. More...

const MatrixBlock &	jacobian (int domainScvIdx, int rangeScvIdx) const
	Returns the local Jacobian matrix of the residual of a sub-control volume. More...

const MatrixBlock &	jacobianStorage (int dofIdx) const
	Returns the local Jacobian matrix the storage term of a sub-control volume. More...

const VectorBlock &	residual (int dofIdx) const
	Returns the local residual of a sub-control volume. More...

const VectorBlock &	residualStorage (int dofIdx) const
	Returns the local storage term of a sub-control volume. More...

Static Public Member Functions
static void	registerParameters ()
	Register all run-time parameters for the local jacobian. More...

static Scalar	baseEpsilon ()
	Returns the unweighted epsilon value used to calculate the local derivatives. More...

Protected Member Functions
Implementation &	asImp_ ()

const Implementation &	asImp_ () const

const Simulator &	simulator_ () const

const Problem &	problem_ () const

const Model &	model_ () const

void	resize_ (const ElementContext &elemCtx)
	Resize all internal attributes to the size of the element. More...

void	reset_ (const ElementContext &elemCtx)
	Reset the all relevant internal attributes to 0. More...

void	evalPartialDerivative_ (ElementContext &elemCtx, int dofIdx, int pvIdx)
	Compute the partial derivatives of a context's residual functions. More...

void	updateLocalLinearizer_ (const ElementContext &elemCtx, int primaryDofIdx, int pvIdx)
	Updates the current local Jacobian matrix with the partial derivatives of all equations in regard to the primary variable 'pvIdx' at vertex 'dofIdx' . More...

Static Protected Member Functions
static int	numericDifferenceMethod_ ()
	Returns the numeric difference method which is applied. More...

Protected Attributes
Simulator *	simulatorPtr_

Model *	modelPtr_

ElementContext *	internalElemContext_

LocalBlockMatrix	jacobian_

LocalStorageMatrix	jacobianStorage_

LocalBlockVector	residual_

LocalBlockVector	residualStorage_

LocalBlockVector	derivResidual_

LocalBlockVector	derivStorage_

LocalResidual	localResidual_

Detailed Description

template<class TypeTag>
class Ewoms::FvBaseFdLocalLinearizer< TypeTag >

Calculates the Jacobian of the local residual for finite volume spatial discretizations using a finite difference method.

The local Jacobian for a given context is defined as the derivatives of the residuals of all degrees of freedom featured by the stencil with regard to the primary variables of the stencil's "primary" degrees of freedom.

This class implements numeric differentiation using finite difference methods, i.e. forward or backward differences (2nd order), or central differences (3rd order). The method used is determined by the "NumericDifferenceMethod" property:

If the value of this property is smaller than 0, backward differences are used, i.e.:
$\frac{\partial f(x)}{\partial x} \approx \frac{f(x) - f(x - \epsilon)}{\epsilon}$
If the value of this property is 0, central differences are used, i.e.:
$\frac{\partial f(x)}{\partial x} \approx \frac{f(x + \epsilon) - f(x - \epsilon)}{2 \epsilon}$
if the value of this property is larger than 0, forward differences are used, i.e.:
$\frac{\partial f(x)}{\partial x} \approx \frac{f(x + \epsilon) - f(x)}{\epsilon}$

Here, $ f $ is the residual function for all equations, $x$ is the value of a sub-control volume's primary variable at the evaluation point and $\epsilon$ is a small scalar value larger than 0.

Constructor & Destructor Documentation

template<class TypeTag >

Ewoms::FvBaseFdLocalLinearizer< TypeTag >::FvBaseFdLocalLinearizer ( )

inline

template<class TypeTag >

Ewoms::FvBaseFdLocalLinearizer< TypeTag >::~FvBaseFdLocalLinearizer ( )

inline

References Ewoms::FvBaseFdLocalLinearizer< TypeTag >::internalElemContext_.

Member Function Documentation

template<class TypeTag >

Implementation& Ewoms::FvBaseFdLocalLinearizer< TypeTag >::asImp_ ( )

inlineprotected

Referenced by Ewoms::FvBaseFdLocalLinearizer< TypeTag >::evalPartialDerivative_(), and Ewoms::FvBaseFdLocalLinearizer< TypeTag >::linearize().

template<class TypeTag >

const Implementation& Ewoms::FvBaseFdLocalLinearizer< TypeTag >::asImp_ ( ) const

inlineprotected

template<class TypeTag >

static Scalar Ewoms::FvBaseFdLocalLinearizer< TypeTag >::baseEpsilon ( )

inlinestatic

Returns the unweighted epsilon value used to calculate the local derivatives.

References GET_PROP_VALUE.

Referenced by Ewoms::FvBaseFdLocalLinearizer< TypeTag >::numericEpsilon().

template<class TypeTag >

void Ewoms::FvBaseFdLocalLinearizer< TypeTag >::evalPartialDerivative_	(	ElementContext &	elemCtx,
		int	dofIdx,
		int	pvIdx
	)

inlineprotected

Compute the partial derivatives of a context's residual functions.

This method can be overwritten by the implementation if a better scheme than numerical differentiation is available.

The default implementation of this method uses numeric differentiation, i.e. forward or backward differences (2nd order), or central differences (3rd order). The method used is determined by the "NumericDifferenceMethod" property:

If the value of this property is smaller than 0, backward differences are used, i.e.:
$\frac{\partial f(x)}{\partial x} \approx \frac{f(x) - f(x - \epsilon)}{\epsilon}$
If the value of this property is 0, central differences are used, i.e.:
$\frac{\partial f(x)}{\partial x} \approx \frac{f(x + \epsilon) - f(x - \epsilon)}{2 \epsilon}$
if the value of this property is larger than 0, forward differences are used, i.e.:
$\frac{\partial f(x)}{\partial x} \approx \frac{f(x + \epsilon) - f(x)}{\epsilon}$

Here, $ f $ is the residual function for all equations, $x$ is the value of a sub-control volume's primary variable at the evaluation point and $\epsilon$ is a small value larger than 0.

Parameters

elemCtx	The element context for which the local partial derivative ought to be calculated
dofIdx	The sub-control volume index of the current finite element for which the partial derivative ought to be calculated
pvIdx	The index of the primary variable at the dofIdx' sub-control volume of the current finite element for which the partial derivative ought to be calculated

References Ewoms::FvBaseFdLocalLinearizer< TypeTag >::asImp_(), Ewoms::FvBaseFdLocalLinearizer< TypeTag >::derivResidual_, Ewoms::FvBaseFdLocalLinearizer< TypeTag >::derivStorage_, Ewoms::FvBaseFdLocalLinearizer< TypeTag >::localResidual_, Ewoms::FvBaseFdLocalLinearizer< TypeTag >::numericDifferenceMethod_(), Ewoms::FvBaseFdLocalLinearizer< TypeTag >::residual_, and Ewoms::FvBaseFdLocalLinearizer< TypeTag >::residualStorage_.

template<class TypeTag >

void Ewoms::FvBaseFdLocalLinearizer< TypeTag >::init ( Simulator & simulator )

inline

Initialize the local Jacobian object.

At this point we can assume that everything has been allocated, although some objects may not yet be completely initialized.

Parameters

simulator The simulator object of the simulation.

References Ewoms::FvBaseFdLocalLinearizer< TypeTag >::internalElemContext_, and Ewoms::FvBaseFdLocalLinearizer< TypeTag >::simulatorPtr_.

template<class TypeTag >

const MatrixBlock& Ewoms::FvBaseFdLocalLinearizer< TypeTag >::jacobian	(	int	domainScvIdx,
		int	rangeScvIdx
	)		const

inline

Returns the local Jacobian matrix of the residual of a sub-control volume.

Parameters

domainScvIdx	The local index of the sub control volume which contains the independents
rangeScvIdx	The local index of the sub control volume which contains the local residual

References Ewoms::FvBaseFdLocalLinearizer< TypeTag >::jacobian_.

template<class TypeTag >

const MatrixBlock& Ewoms::FvBaseFdLocalLinearizer< TypeTag >::jacobianStorage ( int dofIdx ) const

inline

Returns the local Jacobian matrix the storage term of a sub-control volume.

Parameters

dofIdx The local index of sub control volume

References Ewoms::FvBaseFdLocalLinearizer< TypeTag >::jacobianStorage_.

template<class TypeTag >

void Ewoms::FvBaseFdLocalLinearizer< TypeTag >::linearize ( const Element & element )

inline

Compute an element's local Jacobian matrix and evaluate its residual.

The local Jacobian for a given context is defined as the derivatives of the residuals of all degrees of freedom featured by the stencil with regard to the primary variables of the stencil's "primary" degrees of freedom. Adding the local Jacobians for all elements in the grid will give the global Jacobian 'grad f(x)'.

Parameters

element The grid element for which the local residual and its local Jacobian should be calculated.

References Ewoms::FvBaseFdLocalLinearizer< TypeTag >::internalElemContext_.

template<class TypeTag >

void Ewoms::FvBaseFdLocalLinearizer< TypeTag >::linearize ( ElementContext & elemCtx )

inline

Compute an element's local Jacobian matrix and evaluate its residual.

The local Jacobian for a given context is defined as the derivatives of the residuals of all degrees of freedom featured by the stencil with regard to the primary variables of the stencil's "primary" degrees of freedom. Adding the local Jacobians for all elements in the grid will give the global Jacobian 'grad f(x)'.

After calling this method the ElementContext is in an undefined state, so do not use it anymore!

Parameters

elemCtx The element execution context for which the local residual and its local Jacobian should be calculated.

References Ewoms::FvBaseFdLocalLinearizer< TypeTag >::asImp_(), Ewoms::FvBaseFdLocalLinearizer< TypeTag >::localResidual_, Ewoms::FvBaseFdLocalLinearizer< TypeTag >::model_(), Ewoms::FvBaseFdLocalLinearizer< TypeTag >::reset_(), Ewoms::FvBaseFdLocalLinearizer< TypeTag >::residual_, Ewoms::FvBaseFdLocalLinearizer< TypeTag >::residualStorage_, Ewoms::FvBaseFdLocalLinearizer< TypeTag >::resize_(), and Ewoms::FvBaseFdLocalLinearizer< TypeTag >::updateLocalLinearizer_().

template<class TypeTag >

LocalResidual& Ewoms::FvBaseFdLocalLinearizer< TypeTag >::localResidual ( )

inline

Return reference to the local residual.

References Ewoms::FvBaseFdLocalLinearizer< TypeTag >::localResidual_.

template<class TypeTag >

const LocalResidual& Ewoms::FvBaseFdLocalLinearizer< TypeTag >::localResidual ( ) const

inline

Return reference to the local residual.

References Ewoms::FvBaseFdLocalLinearizer< TypeTag >::localResidual_.

template<class TypeTag >

const Model& Ewoms::FvBaseFdLocalLinearizer< TypeTag >::model_ ( ) const

inlineprotected

References Ewoms::Simulator< TypeTag >::model(), and Ewoms::FvBaseFdLocalLinearizer< TypeTag >::simulatorPtr_.

Referenced by Ewoms::FvBaseFdLocalLinearizer< TypeTag >::linearize().

template<class TypeTag >

static int Ewoms::FvBaseFdLocalLinearizer< TypeTag >::numericDifferenceMethod_ ( )

inlinestaticprotected

Returns the numeric difference method which is applied.

References EWOMS_GET_PARAM.

Referenced by Ewoms::FvBaseFdLocalLinearizer< TypeTag >::evalPartialDerivative_().

template<class TypeTag >

Scalar Ewoms::FvBaseFdLocalLinearizer< TypeTag >::numericEpsilon	(	const ElementContext &	elemCtx,
		int	dofIdx,
		int	pvIdx
	)		const

inline

Returns the epsilon value which is added and removed from the current solution.

Parameters

elemCtx	The element execution context for which the local residual and its gradient should be calculated.
dofIdx	The local index of the element's vertex for which the local derivative ought to be calculated.
pvIdx	The index of the primary variable which gets varied

References Ewoms::FvBaseFdLocalLinearizer< TypeTag >::baseEpsilon().

template<class TypeTag >

const Problem& Ewoms::FvBaseFdLocalLinearizer< TypeTag >::problem_ ( ) const

inlineprotected

References Ewoms::Simulator< TypeTag >::problem(), and Ewoms::FvBaseFdLocalLinearizer< TypeTag >::simulatorPtr_.

template<class TypeTag >

static void Ewoms::FvBaseFdLocalLinearizer< TypeTag >::registerParameters ( )

inlinestatic

Register all run-time parameters for the local jacobian.

References EWOMS_REGISTER_PARAM.

template<class TypeTag >

void Ewoms::FvBaseFdLocalLinearizer< TypeTag >::reset_ ( const ElementContext & elemCtx )

inlineprotected

Reset the all relevant internal attributes to 0.

References Ewoms::FvBaseFdLocalLinearizer< TypeTag >::jacobian_, Ewoms::FvBaseFdLocalLinearizer< TypeTag >::jacobianStorage_, Ewoms::FvBaseFdLocalLinearizer< TypeTag >::residual_, and Ewoms::FvBaseFdLocalLinearizer< TypeTag >::residualStorage_.

Referenced by Ewoms::FvBaseFdLocalLinearizer< TypeTag >::linearize().

template<class TypeTag >

const VectorBlock& Ewoms::FvBaseFdLocalLinearizer< TypeTag >::residual ( int dofIdx ) const

inline

Returns the local residual of a sub-control volume.

Parameters

dofIdx The local index of the sub control volume

References Ewoms::FvBaseFdLocalLinearizer< TypeTag >::residual_.

template<class TypeTag >

const VectorBlock& Ewoms::FvBaseFdLocalLinearizer< TypeTag >::residualStorage ( int dofIdx ) const

inline

Returns the local storage term of a sub-control volume.

Parameters

dofIdx The local index of the sub control volume

References Ewoms::FvBaseFdLocalLinearizer< TypeTag >::residualStorage_.

template<class TypeTag >

void Ewoms::FvBaseFdLocalLinearizer< TypeTag >::resize_ ( const ElementContext & elemCtx )

inlineprotected

Resize all internal attributes to the size of the element.

References Ewoms::FvBaseFdLocalLinearizer< TypeTag >::derivResidual_, Ewoms::FvBaseFdLocalLinearizer< TypeTag >::derivStorage_, Ewoms::FvBaseFdLocalLinearizer< TypeTag >::jacobian_, Ewoms::FvBaseFdLocalLinearizer< TypeTag >::jacobianStorage_, Ewoms::FvBaseFdLocalLinearizer< TypeTag >::residual_, and Ewoms::FvBaseFdLocalLinearizer< TypeTag >::residualStorage_.

Referenced by Ewoms::FvBaseFdLocalLinearizer< TypeTag >::linearize().

template<class TypeTag >

const Simulator& Ewoms::FvBaseFdLocalLinearizer< TypeTag >::simulator_ ( ) const

inlineprotected

References Ewoms::FvBaseFdLocalLinearizer< TypeTag >::simulatorPtr_.

template<class TypeTag >

void Ewoms::FvBaseFdLocalLinearizer< TypeTag >::updateLocalLinearizer_	(	const ElementContext &	elemCtx,
		int	primaryDofIdx,
		int	pvIdx
	)

inlineprotected

Updates the current local Jacobian matrix with the partial derivatives of all equations in regard to the primary variable 'pvIdx' at vertex 'dofIdx' .

References Ewoms::FvBaseFdLocalLinearizer< TypeTag >::derivResidual_, Ewoms::FvBaseFdLocalLinearizer< TypeTag >::derivStorage_, Ewoms::FvBaseFdLocalLinearizer< TypeTag >::jacobian_, and Ewoms::FvBaseFdLocalLinearizer< TypeTag >::jacobianStorage_.

Referenced by Ewoms::FvBaseFdLocalLinearizer< TypeTag >::linearize().