#include <itkFEMSolverCrankNicolson.h>

Inheritance diagram for itk::fem::SolverCrankNicolson< TDimension >:

Collaboration diagram for itk::fem::SolverCrankNicolson< TDimension >:

Public Types
typedef SmartPointer< const Self >	ConstPointer
typedef Element::Float	Float
typedef SmartPointer< Self >	Pointer
typedef SolverCrankNicolson	Self
typedef Solver< TDimension >	Superclass
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 *	GetLS ()
virtual Float	GetTimeStep (void) const
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)
void	ZeroVector (int which=0)

	itkSetMacro (UseMassMatrix, bool)
	itkGetMacro (UseMassMatrix, bool)

	itkSetMacro (Alpha, Float)
	itkGetMacro (Alpha, Float)

	itkSetMacro (Rho, Float)
	itkGetMacro (Rho, Float)
Protected Member Functions
void	AssembleFforTimeStep (int dim=0)
void	AssembleKandM ()
void	GenerateData ()
void	InitializeForSolution ()
virtual void	RunSolver (void)
	SolverCrankNicolson ()
	~SolverCrankNicolson ()
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
Private Member Functions
void	operator= (const Self &)
	SolverCrankNicolson (const Self &)

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.

Member Typedef Documentation

template<unsigned int TDimension = 3>

typedef SmartPointer<const Self> itk::fem::SolverCrankNicolson< TDimension >::ConstPointer

Reimplemented from itk::fem::Solver< TDimension >.

Definition at line 78 of file itkFEMSolverCrankNicolson.h.

template<unsigned int TDimension = 3>

typedef Element::Float itk::fem::SolverCrankNicolson< TDimension >::Float

Some convenient typedefs.

Reimplemented from itk::fem::Solver< TDimension >.

Definition at line 86 of file itkFEMSolverCrankNicolson.h.

template<unsigned int TDimension = 3>

typedef SmartPointer<Self> itk::fem::SolverCrankNicolson< TDimension >::Pointer

Reimplemented from itk::fem::Solver< TDimension >.

Definition at line 77 of file itkFEMSolverCrankNicolson.h.

template<unsigned int TDimension = 3>

typedef SolverCrankNicolson itk::fem::SolverCrankNicolson< TDimension >::Self

Standard class typedefs.

Reimplemented from itk::fem::Solver< TDimension >.

Definition at line 75 of file itkFEMSolverCrankNicolson.h.

template<unsigned int TDimension = 3>

typedef Solver<TDimension> itk::fem::SolverCrankNicolson< TDimension >::Superclass

Reimplemented from itk::fem::Solver< TDimension >.

Definition at line 76 of file itkFEMSolverCrankNicolson.h.

Constructor & Destructor Documentation

template<unsigned int TDimension = 3>

itk::fem::SolverCrankNicolson< TDimension >::SolverCrankNicolson ( ) [protected]

template<unsigned int TDimension = 3>

itk::fem::SolverCrankNicolson< TDimension >::~SolverCrankNicolson ( ) [inline, protected]

Definition at line 207 of file itkFEMSolverCrankNicolson.h.

template<unsigned int TDimension = 3>

itk::fem::SolverCrankNicolson< TDimension >::SolverCrankNicolson ( const Self & ) [private]

Member Function Documentation

template<unsigned int TDimension = 3>

void itk::fem::SolverCrankNicolson< TDimension >::AddToDisplacements ( Float optimum = 1.0 )

Add solution vector u to the corresponding nodal values, which are stored in node objects). This is standard post processing of the solution

template<unsigned int TDimension = 3>

void itk::fem::SolverCrankNicolson< TDimension >::AssembleFforTimeStep ( int dim = 0 ) [protected]

Assemble the master force vector at a given time.

Parameters:

dim	This is a parameter that can be passed to the function and is normally used with isotropic elements to specify the dimension for which the master force vector should be assembled.

template<unsigned int TDimension = 3>

void itk::fem::SolverCrankNicolson< TDimension >::AssembleKandM ( ) [protected]

Assemble the master stiffness and mass matrix. We actually assemble the right hand side and left hand side of the implicit scheme equation.

template<unsigned int TDimension = 3>

void itk::fem::SolverCrankNicolson< TDimension >::AverageLastTwoDisplacements ( Float t = 0.5 )

template<unsigned int TDimension = 3>

Float itk::fem::SolverCrankNicolson< TDimension >::BrentsMethod	(	Float	tol = `0.01`,
		unsigned int	MaxIters = `25`
	)

template<unsigned int TDimension = 3>

Float itk::fem::SolverCrankNicolson< TDimension >::EvaluateResidual ( Float t = 1.0 )

template<unsigned int TDimension = 3>

void itk::fem::SolverCrankNicolson< TDimension >::FindBracketingTriplet	(	Float *	a,
		Float *	b,
		Float *	c
	)

template<unsigned int TDimension = 3>

void itk::fem::SolverCrankNicolson< TDimension >::GenerateData ( ) [protected, virtual]

Method invoked by the pipeline in order to trigger the computation of the registration.

Reimplemented from itk::fem::Solver< TDimension >.

template<unsigned int TDimension = 3>

Float itk::fem::SolverCrankNicolson< TDimension >::GetCurrentMaxSolution ( ) [inline]

Definition at line 195 of file itkFEMSolverCrankNicolson.h.

References itk::fem::SolverCrankNicolson< TDimension >::m_CurrentMaxSolution.

template<unsigned int TDimension = 3>

Float itk::fem::SolverCrankNicolson< TDimension >::GetDeformationEnergy ( Float t = 1.0 )

template<unsigned int TDimension = 3>

LinearSystemWrapper* itk::fem::SolverCrankNicolson< TDimension >::GetLS ( ) [inline]

Definition at line 190 of file itkFEMSolverCrankNicolson.h.

References itk::fem::Solver< TDimension >::m_ls.

template<unsigned int TDimension = 3>

virtual Float itk::fem::SolverCrankNicolson< TDimension >::GetTimeStep ( void ) const [inline, virtual]

Returns the time step used for dynamic problems.

Reimplemented from itk::fem::Solver< TDimension >.

Definition at line 142 of file itkFEMSolverCrankNicolson.h.

References itk::fem::SolverCrankNicolson< TDimension >::m_TimeStep.

template<unsigned int TDimension = 3>

Float itk::fem::SolverCrankNicolson< TDimension >::GoldenSection	(	Float	tol = `0.01`,
		unsigned int	MaxIters = `25`
	)

Finds the optimum value between the last two solutions and sets the current solution to that value. Uses Evaluate Residual;

template<unsigned int TDimension = 3>

Float itk::fem::SolverCrankNicolson< TDimension >::GSMax	(	Float	a,
		Float	b
	)		`[inline]`

Definition at line 183 of file itkFEMSolverCrankNicolson.h.

template<unsigned int TDimension = 3>

Float itk::fem::SolverCrankNicolson< TDimension >::GSSign	(	Float	a,
		Float	b
	)		`[inline]`

Definition at line 179 of file itkFEMSolverCrankNicolson.h.

template<unsigned int TDimension = 3>

void itk::fem::SolverCrankNicolson< TDimension >::InitializeForSolution ( ) [protected]

helper initialization function before assembly but after generate GFN.

template<unsigned int TDimension = 3>

itk::fem::SolverCrankNicolson< TDimension >::itkGetConstMacro	(	Iterations	,
		unsigned	int
	)

Get the number of iterations run for the solver

template<unsigned int TDimension = 3>

itk::fem::SolverCrankNicolson< TDimension >::itkGetMacro	(	UseMassMatrix	,
		bool
	)

Get/Set the use of the Mass Matrix for the solution

template<unsigned int TDimension = 3>

itk::fem::SolverCrankNicolson< TDimension >::itkGetMacro	(	TotalSolutionIndex	,
		unsigned	int
	)

Get the index for the current solution

template<unsigned int TDimension = 3>

itk::fem::SolverCrankNicolson< TDimension >::itkGetMacro	(	SolutionTMinus1Index	,
		unsigned	int
	)

Get the index for the previous solution

template<unsigned int TDimension = 3>

itk::fem::SolverCrankNicolson< TDimension >::itkGetMacro	(	Alpha	,
		Float
	)

Set stability step for the solution. Initialized to 0.5

template<unsigned int TDimension = 3>

itk::fem::SolverCrankNicolson< TDimension >::itkGetMacro	(	Rho	,
		Float
	)

Set density constant.

template<unsigned int TDimension = 3>

itk::fem::SolverCrankNicolson< TDimension >::itkNewMacro ( Self )

Method for creation through the object factory.

template<unsigned int TDimension = 3>

itk::fem::SolverCrankNicolson< TDimension >::itkSetMacro	(	UseMassMatrix	,
		bool
	)

Get/Set the use of the Mass Matrix for the solution

template<unsigned int TDimension = 3>

itk::fem::SolverCrankNicolson< TDimension >::itkSetMacro	(	Alpha	,
		Float
	)

Set stability step for the solution. Initialized to 0.5

template<unsigned int TDimension = 3>

itk::fem::SolverCrankNicolson< TDimension >::itkSetMacro	(	Rho	,
		Float
	)

Set density constant.

template<unsigned int TDimension = 3>

itk::fem::SolverCrankNicolson< TDimension >::itkTypeMacro	(	SolverCrankNicolson< TDimension >	,
		Solver< TDimension >
	)

Run-time type information (and related methods)

template<unsigned int TDimension = 3>

void itk::fem::SolverCrankNicolson< TDimension >::operator= ( const Self & ) [private]

Make a DataObject of the correct type to be used as the specified output.

Reimplemented from itk::fem::Solver< TDimension >.

template<unsigned int TDimension = 3>

void itk::fem::SolverCrankNicolson< TDimension >::PrintDisplacements ( )

template<unsigned int TDimension = 3>

void itk::fem::SolverCrankNicolson< TDimension >::PrintForce ( )

template<unsigned int TDimension = 3>

void itk::fem::SolverCrankNicolson< TDimension >::PrintMinMaxOfSolution ( )

Compute and print the minimum and maximum of the total solution and the last solution.

template<unsigned int TDimension = 3>

void itk::fem::SolverCrankNicolson< TDimension >::RecomputeForceVector ( unsigned int index )

compute the current state of the right hand side and store the current force for the next iteration.

template<unsigned int TDimension = 3>

void itk::fem::SolverCrankNicolson< TDimension >::ResetIterations ( void ) [inline]

Reset the number of iterations for the solver. This will prompt the Solver to Assemble the master stiffness and mass matrix again. This is only generated before the first iteration.

Definition at line 106 of file itkFEMSolverCrankNicolson.h.

References itk::fem::SolverCrankNicolson< TDimension >::m_Iterations.

template<unsigned int TDimension = 3>

virtual void itk::fem::SolverCrankNicolson< TDimension >::RunSolver ( void ) [protected, virtual]

Solve for the displacement vector u at a given time. Update the total solution as well.

Reimplemented from itk::fem::Solver< TDimension >.

template<unsigned int TDimension = 3>

void itk::fem::SolverCrankNicolson< TDimension >::SetEnergyToMin ( Float xmin )

template<unsigned int TDimension = 3>

virtual void itk::fem::SolverCrankNicolson< TDimension >::SetTimeStep ( Float dt ) [inline, virtual]

Sets the time step used for dynamic problems.

Parameters:

dt	New time step.

Reimplemented from itk::fem::Solver< TDimension >.

Definition at line 152 of file itkFEMSolverCrankNicolson.h.

References itk::fem::SolverCrankNicolson< TDimension >::m_TimeStep.

template<unsigned int TDimension = 3>

void itk::fem::SolverCrankNicolson< TDimension >::ZeroVector ( int which = 0 )

Member Data Documentation

template<unsigned int TDimension = 3>

Float itk::fem::SolverCrankNicolson< TDimension >::m_Alpha [protected]

Definition at line 240 of file itkFEMSolverCrankNicolson.h.

template<unsigned int TDimension = 3>

Float itk::fem::SolverCrankNicolson< TDimension >::m_CurrentMaxSolution [protected]

Definition at line 241 of file itkFEMSolverCrankNicolson.h.

Referenced by itk::fem::SolverCrankNicolson< TDimension >::GetCurrentMaxSolution().

template<unsigned int TDimension = 3>

unsigned int itk::fem::SolverCrankNicolson< TDimension >::m_DifferenceMatrixIndex [protected]

Definition at line 253 of file itkFEMSolverCrankNicolson.h.

template<unsigned int TDimension = 3>

unsigned int itk::fem::SolverCrankNicolson< TDimension >::m_DiffMatrixBySolutionTMinus1Index [protected]

Definition at line 255 of file itkFEMSolverCrankNicolson.h.

template<unsigned int TDimension = 3>

unsigned int itk::fem::SolverCrankNicolson< TDimension >::m_ForceTIndex [protected]

Definition at line 246 of file itkFEMSolverCrankNicolson.h.

template<unsigned int TDimension = 3>

unsigned int itk::fem::SolverCrankNicolson< TDimension >::m_ForceTMinus1Index [protected]

Definition at line 248 of file itkFEMSolverCrankNicolson.h.

template<unsigned int TDimension = 3>

unsigned int itk::fem::SolverCrankNicolson< TDimension >::m_ForceTotalIndex [protected]

Definition at line 247 of file itkFEMSolverCrankNicolson.h.

template<unsigned int TDimension = 3>

unsigned int itk::fem::SolverCrankNicolson< TDimension >::m_Iterations [protected]

Definition at line 244 of file itkFEMSolverCrankNicolson.h.

Referenced by itk::fem::SolverCrankNicolson< TDimension >::ResetIterations().

template<unsigned int TDimension = 3>

Float itk::fem::SolverCrankNicolson< TDimension >::m_Rho [protected]

Definition at line 239 of file itkFEMSolverCrankNicolson.h.

template<unsigned int TDimension = 3>

unsigned int itk::fem::SolverCrankNicolson< TDimension >::m_SolutionTIndex [protected]

Definition at line 249 of file itkFEMSolverCrankNicolson.h.

template<unsigned int TDimension = 3>

unsigned int itk::fem::SolverCrankNicolson< TDimension >::m_SolutionTMinus1Index [protected]

Definition at line 250 of file itkFEMSolverCrankNicolson.h.

template<unsigned int TDimension = 3>

unsigned int itk::fem::SolverCrankNicolson< TDimension >::m_SolutionVectorTMinus1Index [protected]

Definition at line 251 of file itkFEMSolverCrankNicolson.h.

template<unsigned int TDimension = 3>

unsigned int itk::fem::SolverCrankNicolson< TDimension >::m_SumMatrixIndex [protected]

Definition at line 254 of file itkFEMSolverCrankNicolson.h.

template<unsigned int TDimension = 3>

Float itk::fem::SolverCrankNicolson< TDimension >::m_TimeStep [protected]

Definition at line 238 of file itkFEMSolverCrankNicolson.h.

Referenced by itk::fem::SolverCrankNicolson< TDimension >::GetTimeStep(), and itk::fem::SolverCrankNicolson< TDimension >::SetTimeStep().

template<unsigned int TDimension = 3>

unsigned int itk::fem::SolverCrankNicolson< TDimension >::m_TotalSolutionIndex [protected]

Definition at line 252 of file itkFEMSolverCrankNicolson.h.

template<unsigned int TDimension = 3>

bool itk::fem::SolverCrankNicolson< TDimension >::m_UseMassMatrix [protected]

Definition at line 243 of file itkFEMSolverCrankNicolson.h.

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

itkFEMSolverCrankNicolson.h

Public Types

Public Member Functions

Protected Member Functions

Protected Attributes

Private Member Functions

Detailed Description

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

Member Typedef Documentation

Constructor & Destructor Documentation

Member Function Documentation

Member Data Documentation

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