Detailed Description

template<unsigned int TDimension = 3>
class itk::fem::SolverCrankNicolson< TDimension >

FEM Solver for time dependent problems; uses Crank-Nicolson implicit discretization scheme.

This is the main class used for solving FEM time-dependent problems. It solves the following problem:

$( M + \alpha*dt* K )*U_t=(M - (1.- \alpha)*dt* K)* U_{t-1} + dt*(\alpha*f_{n+1} + (1-\alpha)*f_n)$

which is the Crank-Nicolson formulation of the static problem if $\alpha=0.5$ . The static solution is gained if : $\rho = 0.0$ ; $\alpha = 1.0$ ; $dt = 1.0$ ; Practically, it is good to set rho to something small (for the itpack solver). The advantage of choosing $\alpha=0.5$ is that the solution is then stable for any choice of time step, dt. This class inherits and uses most of the Solver class functionality.

Updated: The calls to to AssembleKandM (or AssembleK) and AssembleFforTimeStep (or AssembleF) are now handled internally by calling Update().

FIXME: 1) We should also account for the contribution to the force from essential BCs. Basically there are terms involving $M * (\dot g_b)$ and $ K * g_b $ where $ g_b$ is the essential BC vector.

Definition at line 72 of file itkFEMSolverCrankNicolson.h.

Public Types
typedef SmartPointer< const Self >	ConstPointer

typedef Element::Float	Float

typedef SmartPointer< Self >	Pointer

typedef SolverCrankNicolson	Self

typedef Solver< TDimension >	Superclass

Public Types inherited from itk::fem::Solver< TDimension >
typedef SmartPointer< const Self >	ConstPointer

typedef DataObject::Pointer	DataObjectPointer

typedef Element::ArrayType	ElementArray

typedef FEMObjectType::ConstPointer	FEMObjectConstPointer

typedef FEMObjectType::Pointer	FEMObjectPointer

typedef itk::fem::FEMObject < VDimension >	FEMObjectType

typedef Element::Float	Float

typedef InterpolationGridType::DirectionType	InterpolationGridDirectionType

typedef InterpolationGridType::IndexType	InterpolationGridIndexType

typedef InterpolationGridType::Pointer	InterpolationGridPointerType

typedef InterpolationGridType::PointType	InterpolationGridPointType

typedef InterpolationGridType::RegionType	InterpolationGridRegionType

typedef InterpolationGridType::SizeType	InterpolationGridSizeType

typedef InterpolationGridType::SpacingType	InterpolationGridSpacingType

typedef itk::Image < Element::ConstPointer, VDimension >	InterpolationGridType

typedef Load::ArrayType	LoadArray

typedef Material::ArrayType	MaterialArray

typedef Element::Node::ArrayType	NodeArray

typedef SmartPointer< Self >	Pointer

typedef Solver	Self

typedef ProcessObject	Superclass

typedef Element::VectorType	VectorType

typedef ProcessObject::DataObjectPointerArraySizeType	DataObjectPointerArraySizeType

Public Types inherited from itk::ProcessObject
typedef SmartPointer< const Self >	ConstPointer

typedef DataObject::DataObjectIdentifierType	DataObjectIdentifierType

typedef DataObject::Pointer	DataObjectPointer

typedef std::vector < DataObjectPointer >	DataObjectPointerArray

typedef DataObjectPointerArray::size_type	DataObjectPointerArraySizeType

typedef MultiThreader	MultiThreaderType

typedef std::vector < DataObjectIdentifierType >	NameArray

typedef SmartPointer< Self >	Pointer

typedef ProcessObject	Self

typedef Object	Superclass

Public Types inherited from itk::Object
typedef SmartPointer< const Self >	ConstPointer

typedef SmartPointer< Self >	Pointer

typedef Object	Self

typedef LightObject	Superclass

Public Types inherited from itk::LightObject
typedef SmartPointer< const Self >	ConstPointer

typedef SmartPointer< Self >	Pointer

typedef LightObject	Self

Public Member Functions
void	AddToDisplacements (Float optimum=1.0)

void	AverageLastTwoDisplacements (Float t=0.5)

Float	BrentsMethod (Float tol=0.01, unsigned int MaxIters=25)

Float	EvaluateResidual (Float t=1.0)

void	FindBracketingTriplet (Float a, Float b, Float *c)

Float	GetCurrentMaxSolution ()

Float	GetDeformationEnergy (Float t=1.0)

LinearSystemWrapper *	GetLinearSystem ()

virtual Float	GetTimeStep (void) const ITK_OVERRIDE

Float	GoldenSection (Float tol=0.01, unsigned int MaxIters=25)

Float	GSMax (Float a, Float b)

Float	GSSign (Float a, Float b)

	itkGetConstMacro (Iterations, unsigned int)

	itkGetMacro (TotalSolutionIndex, unsigned int)

	itkGetMacro (SolutionTMinus1Index, unsigned int)

	itkNewMacro (Self)

	itkTypeMacro (SolverCrankNicolson, Solver< TDimension >)

void	PrintDisplacements ()

void	PrintForce ()

void	PrintMinMaxOfSolution ()

void	RecomputeForceVector (unsigned int index)

void	ResetIterations (void)

void	SetEnergyToMin (Float xmin)

virtual void	SetTimeStep (Float dt) ITK_OVERRIDE

void	ZeroVector (int which=0)


	itkSetMacro (UseMassMatrix, bool)

	itkGetMacro (UseMassMatrix, bool)


	itkSetMacro (Alpha, Float)

	itkGetMacro (Alpha, Float)


	itkSetMacro (Rho, Float)

	itkGetMacro (Rho, Float)

Public Member Functions inherited from itk::fem::Solver< TDimension >
virtual ::itk::LightObject::Pointer	CreateAnother () const

Float	GetDeformationEnergy (unsigned int SolutionIndex=0)

const Element *	GetElementAtPoint (const VectorType &pt) const

FEMObjectType *	GetInput ()

FEMObjectType *	GetInput (unsigned int idx)

LinearSystemWrapper::Pointer	GetLinearSystemWrapper ()

virtual const char *	GetNameOfClass () const

Float	GetSolution (unsigned int i, unsigned int which=0)

void	InitializeInterpolationGrid (const InterpolationGridSizeType &size, const InterpolationGridPointType &bb1, const InterpolationGridPointType &bb2)

virtual void	SetInput (FEMObjectType *fem)

virtual void	SetInput (unsigned int, FEMObjectType *fem)

void	SetLinearSystemWrapper (LinearSystemWrapper::Pointer ls)

virtual void	SetOrigin (InterpolationGridPointType _arg)

virtual InterpolationGridPointType	GetOrigin ()

virtual void	SetSpacing (InterpolationGridSpacingType _arg)

virtual InterpolationGridSpacingType	GetSpacing ()

virtual void	SetRegion (InterpolationGridRegionType _arg)

virtual InterpolationGridRegionType	GetRegion ()

virtual void	SetDirection (InterpolationGridDirectionType _arg)

virtual InterpolationGridDirectionType	GetDirection ()

void	InitializeInterpolationGrid (const InterpolationGridSizeType &size)

void	InitializeInterpolationGrid (const InterpolationGridRegionType &region, const InterpolationGridPointType &origin, const InterpolationGridSpacingType &spacing, const InterpolationGridDirectionType &direction)

const InterpolationGridType *	GetInterpolationGrid (void) const

virtual DataObjectPointer	MakeOutput (DataObjectPointerArraySizeType) override

FEMObjectType *	GetOutput ()

FEMObjectType *	GetOutput (unsigned int idx)

Public Member Functions inherited from itk::ProcessObject
virtual void	AbortGenerateDataOff ()

virtual void	AbortGenerateDataOn ()

virtual void	EnlargeOutputRequestedRegion (DataObject *)

virtual const bool &	GetAbortGenerateData () const

DataObjectPointerArray	GetIndexedInputs ()

DataObjectPointerArray	GetIndexedOutputs ()

NameArray	GetInputNames () const

DataObjectPointerArray	GetInputs ()

MultiThreaderType *	GetMultiThreader () const

DataObjectPointerArraySizeType	GetNumberOfIndexedInputs () const

DataObjectPointerArraySizeType	GetNumberOfIndexedOutputs () const

DataObjectPointerArraySizeType	GetNumberOfInputs () const

DataObjectPointerArraySizeType	GetNumberOfOutputs () const

virtual DataObjectPointerArraySizeType	GetNumberOfValidRequiredInputs () const

NameArray	GetOutputNames () const

DataObjectPointerArray	GetOutputs ()

virtual const float &	GetProgress () const

NameArray	GetRequiredInputNames () const

bool	HasInput (const DataObjectIdentifierType &key) const

bool	HasOutput (const DataObjectIdentifierType &key) const

virtual DataObjectPointer	MakeOutput (const DataObjectIdentifierType &)

virtual void	PrepareOutputs ()

virtual void	PropagateRequestedRegion (DataObject *output)

virtual void	ResetPipeline ()

virtual void	SetAbortGenerateData (bool _arg)

virtual void	Update ()

virtual void	UpdateLargestPossibleRegion ()

virtual void	UpdateOutputData (DataObject *output)

virtual void	UpdateOutputInformation ()

void	UpdateProgress (float progress)

void	SetProgress (float progress)

virtual void	SetReleaseDataFlag (bool flag)

virtual bool	GetReleaseDataFlag () const

void	ReleaseDataFlagOn ()

void	ReleaseDataFlagOff ()

virtual void	SetReleaseDataBeforeUpdateFlag (bool _arg)

virtual const bool &	GetReleaseDataBeforeUpdateFlag () const

virtual void	ReleaseDataBeforeUpdateFlagOn ()

virtual void	ReleaseDataBeforeUpdateFlagOff ()

virtual void	SetNumberOfThreads (ThreadIdType _arg)

virtual const ThreadIdType &	GetNumberOfThreads () const

Public Member Functions inherited from itk::Object
unsigned long	AddObserver (const EventObject &event, Command *)

unsigned long	AddObserver (const EventObject &event, Command *) const

virtual void	DebugOff () const

virtual void	DebugOn () const

Command *	GetCommand (unsigned long tag)

bool	GetDebug () const

MetaDataDictionary &	GetMetaDataDictionary ()

const MetaDataDictionary &	GetMetaDataDictionary () const

virtual ModifiedTimeType	GetMTime () const

virtual const TimeStamp &	GetTimeStamp () const

bool	HasObserver (const EventObject &event) const

void	InvokeEvent (const EventObject &)

void	InvokeEvent (const EventObject &) const

virtual void	Modified () const

virtual void	Register () const override

void	RemoveAllObservers ()

void	RemoveObserver (unsigned long tag)

void	SetDebug (bool debugFlag) const

void	SetMetaDataDictionary (const MetaDataDictionary &rhs)

virtual void	SetReferenceCount (int) override

virtual void	UnRegister () const noexceptoverride

virtual void	SetObjectName (std::string _arg)

virtual const std::string &	GetObjectName () const

Public Member Functions inherited from itk::LightObject
virtual void	Delete ()

virtual int	GetReferenceCount () const

	itkCloneMacro (Self)

void	Print (std::ostream &os, Indent indent=0) const

Protected Member Functions
void	AssembleFforTimeStep (int dim=0)

void	AssembleKandM ()

void	GenerateData () ITK_OVERRIDE

void	InitializeForSolution ()

virtual void	RunSolver (void) ITK_OVERRIDE

	SolverCrankNicolson ()

	~SolverCrankNicolson () ITK_OVERRIDE

Protected Member Functions inherited from itk::fem::Solver< TDimension >
	Solver ()

virtual	~Solver () override

virtual void	PrintSelf (std::ostream &os, Indent indent) const override

void	AssembleK ()

virtual void	InitializeMatrixForAssembly (unsigned int N)

virtual void	FinalizeMatrixAfterAssembly (void)

virtual void	AssembleElementMatrix (Element::Pointer e)

virtual void	AssembleLandmarkContribution (Element::ConstPointer e, float)

void	ApplyBC (int dim=0, unsigned int matrix=0)

void	AssembleF (int dim=0)

void	DecomposeK ()

void	UpdateDisplacements ()

void	FillInterpolationGrid ()

virtual void	InitializeLinearSystemWrapper ()

Protected Member Functions inherited from itk::ProcessObject
virtual void	AddInput (DataObject *input)

void	AddOptionalInputName (const DataObjectIdentifierType &)

void	AddOptionalInputName (const DataObjectIdentifierType &, DataObjectPointerArraySizeType idx)

virtual void	AddOutput (DataObject *output)

bool	AddRequiredInputName (const DataObjectIdentifierType &)

bool	AddRequiredInputName (const DataObjectIdentifierType &, DataObjectPointerArraySizeType idx)

virtual void	CacheInputReleaseDataFlags ()

virtual void	GenerateInputRequestedRegion ()

virtual void	GenerateOutputInformation ()

virtual void	GenerateOutputRequestedRegion (DataObject *output)

DataObject *	GetInput (const DataObjectIdentifierType &key)

const DataObject *	GetInput (const DataObjectIdentifierType &key) const

virtual const DataObjectPointerArraySizeType &	GetNumberOfRequiredInputs () const

virtual const DataObjectPointerArraySizeType &	GetNumberOfRequiredOutputs () const

bool	IsIndexedInputName (const DataObjectIdentifierType &) const

bool	IsIndexedOutputName (const DataObjectIdentifierType &) const

bool	IsRequiredInputName (const DataObjectIdentifierType &) const

	itkLegacyMacro (virtual void RemoveOutput(DataObject *output))

	itkLegacyMacro (void SetNumberOfOutputs(DataObjectPointerArraySizeType num))

	itkLegacyMacro (virtual void RemoveInput(DataObject *input))

	itkLegacyMacro (void SetNumberOfInputs(DataObjectPointerArraySizeType num))

DataObjectPointerArraySizeType	MakeIndexFromInputName (const DataObjectIdentifierType &name) const

DataObjectPointerArraySizeType	MakeIndexFromOutputName (const DataObjectIdentifierType &name) const

DataObjectIdentifierType	MakeNameFromInputIndex (DataObjectPointerArraySizeType idx) const

DataObjectIdentifierType	MakeNameFromOutputIndex (DataObjectPointerArraySizeType idx) const

virtual void	PopBackInput ()

virtual void	PopFrontInput ()

	ProcessObject ()

virtual void	PropagateResetPipeline ()

virtual void	PushBackInput (const DataObject *input)

virtual void	PushFrontInput (const DataObject *input)

virtual void	ReleaseInputs ()

virtual void	RemoveInput (const DataObjectIdentifierType &key)

virtual void	RemoveInput (DataObjectPointerArraySizeType)

virtual void	RemoveOutput (const DataObjectIdentifierType &key)

virtual void	RemoveOutput (DataObjectPointerArraySizeType idx)

bool	RemoveRequiredInputName (const DataObjectIdentifierType &)

virtual void	RestoreInputReleaseDataFlags ()

virtual void	SetInput (const DataObjectIdentifierType &key, DataObject *input)

virtual void	SetNthInput (DataObjectPointerArraySizeType num, DataObject *input)

virtual void	SetNthOutput (DataObjectPointerArraySizeType num, DataObject *output)

void	SetNumberOfIndexedInputs (DataObjectPointerArraySizeType num)

void	SetNumberOfIndexedOutputs (DataObjectPointerArraySizeType num)

virtual void	SetNumberOfRequiredInputs (DataObjectPointerArraySizeType)

virtual void	SetNumberOfRequiredOutputs (DataObjectPointerArraySizeType _arg)

virtual void	SetOutput (const DataObjectIdentifierType &key, DataObject *output)

virtual void	SetPrimaryInput (DataObject *input)

virtual void	SetPrimaryOutput (DataObject *output)

void	SetRequiredInputNames (const NameArray &)

virtual void	VerifyInputInformation ()

virtual void	VerifyPreconditions ()

	~ProcessObject () override

DataObject *	GetInput (DataObjectPointerArraySizeType idx)

const DataObject *	GetInput (DataObjectPointerArraySizeType idx) const

DataObject *	GetPrimaryInput ()

const DataObject *	GetPrimaryInput () const

virtual void	SetPrimaryInputName (const DataObjectIdentifierType &key)

virtual const char *	GetPrimaryInputName (void) const

DataObject *	GetOutput (const DataObjectIdentifierType &key)

const DataObject *	GetOutput (const DataObjectIdentifierType &key) const

virtual void	SetPrimaryOutputName (const DataObjectIdentifierType &key)

virtual const char *	GetPrimaryOutputName (void) const

DataObject *	GetOutput (DataObjectPointerArraySizeType idx)

const DataObject *	GetOutput (DataObjectPointerArraySizeType idx) const

DataObject *	GetPrimaryOutput ()

const DataObject *	GetPrimaryOutput () const

Protected Member Functions inherited from itk::Object
	Object ()

bool	PrintObservers (std::ostream &os, Indent indent) const

virtual void	SetTimeStamp (const TimeStamp &time)

virtual	~Object () override

Protected Member Functions inherited from itk::LightObject
virtual LightObject::Pointer	InternalClone () const

	LightObject ()

virtual void	PrintHeader (std::ostream &os, Indent indent) const

virtual void	PrintTrailer (std::ostream &os, Indent indent) const

virtual	~LightObject ()

Protected Attributes
Float	m_Alpha

Float	m_CurrentMaxSolution

unsigned int	m_DifferenceMatrixIndex

unsigned int	m_DiffMatrixBySolutionTMinus1Index

unsigned int	m_ForceTIndex

unsigned int	m_ForceTMinus1Index

unsigned int	m_ForceTotalIndex

unsigned int	m_Iterations

Float	m_Rho

unsigned int	m_SolutionTIndex

unsigned int	m_SolutionTMinus1Index

unsigned int	m_SolutionVectorTMinus1Index

unsigned int	m_SumMatrixIndex

Float	m_TimeStep

unsigned int	m_TotalSolutionIndex

bool	m_UseMassMatrix

Protected Attributes inherited from itk::fem::Solver< TDimension >
unsigned int	m_NGFN

unsigned int	m_NMFC

LinearSystemWrapper::Pointer	m_LinearSystem

LinearSystemWrapperVNL	m_LinearSystemVNL

InterpolationGridPointerType	m_InterpolationGrid

FEMObjectPointer	m_FEMObject

Protected Attributes inherited from itk::ProcessObject
TimeStamp	m_OutputInformationMTime

bool	m_Updating

Protected Attributes inherited from itk::LightObject
AtomicInt< int >	m_ReferenceCount

Private Member Functions
	ITK_DISALLOW_COPY_AND_ASSIGN (SolverCrankNicolson)

Additional Inherited Members
Static Public Member Functions inherited from itk::fem::Solver< TDimension >
static Pointer	New ()

Static Public Member Functions inherited from itk::Object
static bool	GetGlobalWarningDisplay ()

static void	GlobalWarningDisplayOff ()

static void	GlobalWarningDisplayOn ()

static Pointer	New ()

static void	SetGlobalWarningDisplay (bool flag)

Static Public Member Functions inherited from itk::LightObject
static void	BreakOnError ()

static Pointer	New ()

Static Public Attributes inherited from itk::fem::Solver< TDimension >
static const unsigned int	FEMDimension

static const unsigned int	MaxDimensions