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

#include <itkFEMSolverCrankNicolson.h>

Inheritance diagram for itk::fem::SolverCrankNicolson:

Collaboration diagram for itk::fem::SolverCrankNicolson:

Public Types
typedef Element::ArrayType	ElementArray
typedef Element::Float	Float
typedef itk::Image < Element::ConstPointer, MaxGridDimensions >	InterpolationGridType
typedef Load::ArrayType	LoadArray
typedef Material::ArrayType	MaterialArray
typedef Node::ArrayType	NodeArray
typedef Element::VectorType	VectorType

Public Member Functions
	SolverCrankNicolson ()
	~SolverCrankNicolson ()
void	AddToDisplacements (Float optimum=1.0)
void	ApplyBC (int dim=0, unsigned int matrix=0)
virtual void	AssembleElementMatrix (Element::Pointer e)
void	AssembleF (int dim=0)
void	AssembleFforTimeStep (int dim=0)
void	AssembleK (void)
void	AssembleKandM ()
virtual void	AssembleLandmarkContribution (Element::Pointer e, float)
void	AverageLastTwoDisplacements (Float t=0.5)
Float	BrentsMethod (Float tol=0.01, unsigned int MaxIters=25)
virtual void	Clear (void)
void	DecomposeK (void)
Float	EvaluateResidual (Float t=1.0)
virtual void	FinalizeMatrixAfterAssembly (void)
void	FindBracketingTriplet (Float a, Float b, Float *c)
void	GenerateGFN (void)
Float	GetCurrentMaxSolution ()
Float	GetDeformationEnergy (Float t=1.0)
Float	GetDeformationEnergy (unsigned int SolutionIndex=0)
const Element *	GetElementAtPoint (const VectorType &pt) const
const InterpolationGridType *	GetInterpolationGrid (void) const
LinearSystemWrapper::Pointer	GetLinearSystemWrapper ()
LinearSystemWrapper *	GetLS ()
unsigned int	GetNumberOfDegreesOfFreedom (void)
Float	GetSolution (unsigned int i, unsigned int which=0)
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)
void	InitializeForSolution ()
void	InitializeInterpolationGrid (const VectorType &size, const VectorType &bb1, const VectorType &bb2)
void	InitializeInterpolationGrid (const VectorType &size)
virtual void	InitializeLinearSystemWrapper (void)
virtual void	InitializeMatrixForAssembly (unsigned int N)
void	PrintDisplacements ()
void	PrintForce ()
void	PrintMinMaxOfSolution ()
void	Read (std::istream &f)
void	RecomputeForceVector (unsigned int index)
void	SetAlpha (Float a=0.5)
void	SetDeltatT (Float T)
void	SetEnergyToMin (Float xmin)
void	SetLinearSystemWrapper (LinearSystemWrapper::Pointer ls)
void	SetRho (Float rho)
virtual void	SetTimeStep (Float)
void	Solve ()
void	UpdateDisplacements (void)
void	Write (std::ostream &f)
void	ZeroVector (int which=0)

Public Attributes
unsigned int	DifferenceMatrixIndex
unsigned int	DiffMatrixBySolutionTMinus1Index
ElementArray	el
unsigned int	ForceTIndex
unsigned int	ForceTMinus1Index
unsigned int	ForceTotalIndex
LoadArray	load
Float	m_alpha
Float	m_CurrentMaxSolution
Float	m_deltaT
Float	m_rho
MaterialArray	mat
NodeArray	node
unsigned int	SolutionTIndex
unsigned int	SolutionTMinus1Index
unsigned int	SolutionVectorTMinus1Index
unsigned int	SumMatrixIndex
unsigned int	TotalSolutionIndex

Static Public Attributes
static const unsigned int	MaxGridDimensions = 3

Protected Attributes
LinearSystemWrapper::Pointer	m_ls
unsigned int	NGFN
unsigned int	NMFC

Detailed Description

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. One must call AssembleKandM instead of AssembleK and AssembleFforTimeStep instead of AssembleF. FIXMEs: 1) Members should be privatized, etc. 2) 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 64 of file itkFEMSolverCrankNicolson.h.

Member Typedef Documentation

typedef Element::ArrayType itk::fem::Solver::ElementArray

inherited

Array that holds pointers to all elements. since we want to be able to manipulate the array we have to use special pointers

Definition at line 54 of file itkFEMSolver.h.

typedef Element::Float itk::fem::Solver::Float

inherited

Local float type

Definition at line 48 of file itkFEMSolver.h.

typedef itk::Image<Element::ConstPointer,MaxGridDimensions> itk::fem::Solver::InterpolationGridType

inherited

Type used to store interpolation grid

Definition at line 95 of file itkFEMSolver.h.

typedef Load::ArrayType itk::fem::Solver::LoadArray

inherited

Array that holds special pointers to all external loads

Definition at line 66 of file itkFEMSolver.h.

typedef Material::ArrayType itk::fem::Solver::MaterialArray

inherited

Array that holds pointers to the materials

Definition at line 72 of file itkFEMSolver.h.

typedef Node::ArrayType itk::fem::Solver::NodeArray

inherited

Array that holds special pointers to the nodes

Definition at line 60 of file itkFEMSolver.h.

typedef Element::VectorType itk::fem::Solver::VectorType

inherited

VectorType from the Element base class

Definition at line 78 of file itkFEMSolver.h.

Constructor & Destructor Documentation

itk::fem::SolverCrankNicolson::SolverCrankNicolson ( )

inline

Default constructor which sets the indices for the matrix and vector storage. Time step and other parameters are also initialized.

Definition at line 142 of file itkFEMSolverCrankNicolson.h.

References DifferenceMatrixIndex, DiffMatrixBySolutionTMinus1Index, ForceTIndex, ForceTMinus1Index, ForceTotalIndex, m_alpha, m_CurrentMaxSolution, m_deltaT, m_rho, SolutionTIndex, SolutionTMinus1Index, SolutionVectorTMinus1Index, SumMatrixIndex, and TotalSolutionIndex.

itk::fem::SolverCrankNicolson::~SolverCrankNicolson ( )

inline

Definition at line 162 of file itkFEMSolverCrankNicolson.h.

Member Function Documentation

void itk::fem::SolverCrankNicolson::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

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

Copy the resulting displacements from solution vector back to node objects.

Definition at line 613 of file itkFEMSolverCrankNicolson.cxx.

References itk::fem::LinearSystemWrapper::AddSolutionValue(), itk::fem::LinearSystemWrapper::AddVectorValue(), ForceTIndex, ForceTMinus1Index, ForceTotalIndex, itk::fem::Solution::GetSolutionValue(), itk::fem::LinearSystemWrapper::GetVectorValue(), m_CurrentMaxSolution, itk::fem::Solver::m_ls, itk::fem::Solver::NGFN, itk::fem::LinearSystemWrapper::SetSolutionValue(), itk::fem::LinearSystemWrapper::SetVectorValue(), SolutionTIndex, SolutionTMinus1Index, SolutionVectorTMinus1Index, and TotalSolutionIndex.

Referenced by itk::fem::FEMRegistrationFilter< TMovingImage, TFixedImage >::IterativeSolve().

void itk::fem::Solver::ApplyBC	(	int	dim = `0`,
		unsigned int	matrix = `0`
	)

inherited

Apply the boundary conditions to the system.

Note:: This function must be called after AssembleK().

Parameters:

matrix	Index of a matrix, to which the BCs should be applied (master stiffness matrix). Normally this is zero, but in derived classes many matrices may be used and this index must be specified.
dim	This is a parameter that can be passed to the function and is normally used with isotropic elements to specify the dimension in which the DOF is fixed.

Apply the boundary conditions to the system.

   Store a temporary pointer to load object for later,
   so that we don't have to access it via the iterator

   Apply boundary conditions in form of MFC loads.

   We add the multi freedom constraints contribution to the master
   stiffness matrix using the lagrange multipliers. Basically we only
   change the last couple of rows and columns in K.

   Apply essential boundary conditions

Definition at line 643 of file itkFEMSolver.cxx.

References itk::fem::LinearSystemWrapper::AddVectorValue(), itk::fem::LinearSystemWrapper::DestroyVector(), itk::fem::LinearSystemWrapper::GetColumnsOfNonZeroMatrixElementsInRow(), itk::fem::LinearSystemWrapper::GetMatrixValue(), itk::fem::LinearSystemWrapper::InitializeVector(), itk::fem::LinearSystemWrapper::IsVectorInitialized(), itk::fem::Solver::load, itk::fem::Solver::m_ls, itk::fem::Solver::NGFN, and itk::fem::LinearSystemWrapper::SetMatrixValue().

Referenced by AssembleKandM(), and itk::fem::Solver::FinalizeMatrixAfterAssembly().

void itk::fem::Solver::AssembleElementMatrix ( Element::Pointer e )

virtualinherited

Copy the element stiffness matrix into the correct position in the master stiffess matrix. Since more complex Solver classes may need to assemble many matrices and may also do some funky stuff to them, this function is virtual and can be overriden in a derived solver class.

Here we finaly update the corresponding element in the master stiffness matrix. We first check if element in Ke is zero, to prevent zeros from being allocated in sparse matrix.

Reimplemented in itk::fem::SolverHyperbolic.

Definition at line 347 of file itkFEMSolver.cxx.

References itk::fem::LinearSystemWrapper::AddMatrixValue(), itk::fem::Element::GetDegreeOfFreedom(), itk::fem::Element::GetNumberOfDegreesOfFreedom(), itk::fem::Element::GetStiffnessMatrix(), itk::fem::Solver::m_ls, and itk::fem::Solver::NGFN.

Referenced by itk::fem::Solver::AssembleK().

void itk::fem::Solver::AssembleF ( int dim = 0 )

inherited

Assemble the master force vector.

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.

Assemble the master force vector

 Convert the external loads to the nodal loads and
 add them to the master force vector F.

   Store a temporary pointer to load object for later,
   so that we don't have to access it via the iterator

   Pass the vector to the solution to the Load object.

   Here we only handle Nodal loads

       If using the extra dim parameter, we can apply the force to
       different isotropic dimension.

       FIXME: We assume that the implementation of force vector
       inside the LoadNode class is correct for given number of
       dimensions

   Element loads...

       If array of element pointers is not empty,
       we apply the load to all elements in that array

       If the list of element pointers in load object is empty,
       we apply the load to all elements in a system.

   Handle boundary conditions in form of MFC loads are handled next.

   Handle essential boundary conditions.

   If we got here, we were unable to handle that class of Load object.
   We do nothing...

 Adjust the master force vector for essential boundary
 conditions as required.

Definition at line 389 of file itkFEMSolver.cxx.

References itk::fem::LinearSystemWrapper::AddVectorValue(), itk::fem::Solver::el, itk::fem::Element::GetDegreeOfFreedom(), itk::fem::Element::GetLoadVector(), itk::fem::Element::GetNumberOfDegreesOfFreedom(), itk::fem::LinearSystemWrapper::GetVectorValue(), itk::fem::LinearSystemWrapper::InitializeVector(), itk::fem::LinearSystemWrapper::IsVectorInitialized(), itk::fem::Solver::load, itk::fem::Solver::m_ls, itk::fem::Solver::NGFN, itk::fem::Solver::NMFC, and itk::fem::LinearSystemWrapper::SetVectorValue().

Referenced by AssembleFforTimeStep(), and itk::fem::FEMRegistrationFilter< TMovingImage, TFixedImage >::IterativeSolve().

void itk::fem::SolverCrankNicolson::AssembleFforTimeStep ( int dim = 0 )

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.

Assemble the master force vector

Definition at line 203 of file itkFEMSolverCrankNicolson.cxx.

References itk::fem::Solver::AssembleF(), DifferenceMatrixIndex, DiffMatrixBySolutionTMinus1Index, ForceTIndex, itk::fem::Solver::load, itk::fem::Solver::m_ls, itk::fem::LinearSystemWrapper::MultiplyMatrixVector(), itk::fem::Solver::NGFN, RecomputeForceVector(), itk::fem::LinearSystemWrapper::SetSolutionValue(), itk::fem::LinearSystemWrapper::SetVectorValue(), SolutionTMinus1Index, SolutionVectorTMinus1Index, and TotalSolutionIndex.

Referenced by itk::fem::FEMRegistrationFilter< TMovingImage, TFixedImage >::IterativeSolve().

void itk::fem::Solver::AssembleK ( void )

inherited

Assemble the master stiffness matrix (also apply the MFCs to K)

 Before we can start the assembly procedure, we need to know,
 how many boundary conditions if form of MFCs are there in a system.

 Now we can assemble the master stiffness matrix from
 element stiffness matrices.

 Since we're using the Lagrange multiplier method to apply the MFC,
 each constraint adds a new global DOF.

 Step over all elements

 Step over all the loads again to add the landmark contributions
 to the appropriate place in the stiffness matrix

Definition at line 241 of file itkFEMSolver.cxx.

References itk::fem::Solver::AssembleElementMatrix(), itk::fem::Solver::AssembleLandmarkContribution(), itk::fem::Solver::el, itk::fem::Solver::FinalizeMatrixAfterAssembly(), itk::fem::Solver::InitializeMatrixForAssembly(), itk::fem::Solver::load, itk::fem::Solver::NGFN, and itk::fem::Solver::NMFC.

Referenced by itk::fem::FEMRegistrationFilter< TMovingImage, TFixedImage >::MultiResSolve(), and itk::fem::FEMRegistrationFilter< TMovingImage, TFixedImage >::RunRegistration().

void itk::fem::SolverCrankNicolson::AssembleKandM ( )

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

Assemble the master stiffness matrix (also apply the MFCs to K)

 Now we can assemble the master stiffness matrix
 from element stiffness matrices

 Step over all elements

 Step over all the loads to add the landmark contributions to the
 appropriate place in the stiffness matrix

Definition at line 57 of file itkFEMSolverCrankNicolson.cxx.

References itk::fem::LinearSystemWrapper::AddMatrixValue(), itk::fem::Solver::ApplyBC(), DifferenceMatrixIndex, itk::fem::Solver::el, itk::fem::Element::GetDegreeOfFreedom(), itk::fem::Element::GetLandmarkContributionMatrix(), itk::fem::Element::GetNumberOfDegreesOfFreedom(), InitializeForSolution(), itk::fem::Solver::load, m_alpha, m_deltaT, itk::fem::Solver::m_ls, m_rho, itk::fem::Solver::NGFN, itk::fem::Solver::NMFC, and SumMatrixIndex.

Referenced by itk::fem::FEMRegistrationFilter< TMovingImage, TFixedImage >::MultiResSolve(), and itk::fem::FEMRegistrationFilter< TMovingImage, TFixedImage >::RunRegistration().

void itk::fem::Solver::AssembleLandmarkContribution	(	Element::Pointer	e,
		float	eta
	)

virtualinherited

Add the contribution of the landmark-containing elements to the correct position in the master stiffess matrix. Since more complex Solver classes may need to assemble many matrices and may also do some funky stuff to them, this function is virtual and can be overriden in a derived solver class.

Here we finaly update the corresponding element in the master stiffness matrix. We first check if element in Le is zero, to prevent zeros from being allocated in sparse matrix.

Definition at line 311 of file itkFEMSolver.cxx.

References itk::fem::LinearSystemWrapper::AddMatrixValue(), itk::fem::Element::GetDegreeOfFreedom(), itk::fem::Element::GetLandmarkContributionMatrix(), itk::fem::Element::GetNumberOfDegreesOfFreedom(), itk::fem::Solver::m_ls, and itk::fem::Solver::NGFN.

Referenced by itk::fem::Solver::AssembleK().

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

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

Definition at line 697 of file itkFEMSolverCrankNicolson.cxx.

References itk::fem::Solution::GetSolutionValue(), itk::fem::Solver::m_ls, itk::fem::Solver::NGFN, itk::fem::LinearSystemWrapper::SetSolutionValue(), itk::fem::LinearSystemWrapper::SetVectorValue(), SolutionTIndex, SolutionTMinus1Index, and SolutionVectorTMinus1Index.

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

Definition at line 353 of file itkFEMSolverCrankNicolson.cxx.

References EvaluateResidual(), FindBracketingTriplet(), GSSign(), and SetEnergyToMin().

void itk::fem::Solver::Clear ( void )

virtualinherited

Cleans all data members, and initializes the solver to initial state.

Definition at line 47 of file itkFEMSolver.cxx.

References itk::fem::Solver::el, itk::fem::Solver::load, itk::fem::Solver::m_lsVNL, itk::fem::Solver::mat, itk::fem::Solver::NGFN, itk::fem::Solver::NMFC, itk::fem::Solver::node, and itk::fem::Solver::SetLinearSystemWrapper().

void itk::fem::Solver::DecomposeK ( void )

inherited

Decompose matrix using svd, qr, whatever ...

Decompose matrix using svd, qr, whatever ... if needed

Definition at line 586 of file itkFEMSolver.cxx.

Element::Float itk::fem::SolverCrankNicolson::EvaluateResidual ( Float t = 1.0 )

Definition at line 564 of file itkFEMSolverCrankNicolson.cxx.

References itk::Statistics::Energy, ForceTIndex, ForceTMinus1Index, ForceTotalIndex, itk::fem::LinearSystemWrapper::GetMatrixValue(), itk::fem::Solution::GetSolutionValue(), itk::fem::LinearSystemWrapper::GetVectorValue(), itk::fem::Solver::m_ls, itk::fem::Solver::NGFN, SolutionTIndex, SolutionTMinus1Index, SumMatrixIndex, and TotalSolutionIndex.

Referenced by BrentsMethod(), FindBracketingTriplet(), and GoldenSection().

virtual void itk::fem::Solver::FinalizeMatrixAfterAssembly ( void )

inlinevirtualinherited

This function is called after the assebly has been completed. In this class it is only used to apply the BCs. You may however use it to perform other stuff in derived solver classes.

Reimplemented in itk::fem::SolverHyperbolic.

Definition at line 188 of file itkFEMSolver.h.

References itk::fem::Solver::ApplyBC().

Referenced by itk::fem::Solver::AssembleK().

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

Definition at line 264 of file itkFEMSolverCrankNicolson.cxx.

References EvaluateResidual(), GSMax(), and GSSign().

Referenced by BrentsMethod(), and GoldenSection().

void itk::fem::Solver::GenerateGFN ( void )

inherited

System solver functions. Call all six functions below (in listed order) to solve system. Assign a global freedom numbers to each DOF in a system. This must be done before any other solve function can be called.

Assign a global freedom number to each DOF in a system.

Assign new ID to every DOF in a system

Definition at line 186 of file itkFEMSolver.cxx.

References itk::fem::Solver::el, itk::fem::Element::InvalidDegreeOfFreedomID, itk::fem::Solver::NGFN, and itk::fem::Solver::node.

Referenced by itk::fem::FEMRegistrationFilter< TMovingImage, TFixedImage >::CreateMesh().

Float itk::fem::SolverCrankNicolson::GetCurrentMaxSolution ( )

inline

Definition at line 133 of file itkFEMSolverCrankNicolson.h.

References m_CurrentMaxSolution.

Referenced by itk::fem::FEMRegistrationFilter< TMovingImage, TFixedImage >::IterativeSolve().

Element::Float itk::fem::SolverCrankNicolson::GetDeformationEnergy ( Float t = 1.0 )

Definition at line 528 of file itkFEMSolverCrankNicolson.cxx.

References itk::fem::LinearSystemWrapper::GetMatrixValue(), itk::fem::Solution::GetSolutionValue(), itk::fem::Solver::m_ls, itk::fem::Solver::NGFN, SolutionTIndex, SolutionTMinus1Index, SumMatrixIndex, and TotalSolutionIndex.

Solver::Float itk::fem::Solver::GetDeformationEnergy ( unsigned int SolutionIndex = 0 )

inherited

Get the total deformation energy using the chosen solution

Definition at line 620 of file itkFEMSolver.cxx.

References itk::fem::Solver::el, itk::fem::Solution::GetSolutionValue(), and itk::fem::Solver::m_ls.

const Element * itk::fem::Solver::GetElementAtPoint ( const VectorType & pt ) const

inherited

Returns the pointer to the element which contains global point pt.

Parameters:

pt	Point in global coordinate system.

Note:: Interpolation grid must be initializes before you can call this function.

Definition at line 883 of file itkFEMSolver.cxx.

References itk::fem::Solver::m_InterpolationGrid, and itk::fem::Solver::MaxGridDimensions.

Referenced by itk::fem::FEMRegistrationFilter< TMovingImage, TFixedImage >::InterpolateVectorField().

const InterpolationGridType* itk::fem::Solver::GetInterpolationGrid ( void ) const

inlineinherited

Returns pointer to interpolation grid, which is an itk::Image of pointers to Element objects. Normally you would use physical coordinates to get specific points (pointers to elements) from the image. You can then use the Elemenet::InterpolateSolution member function on the returned element to obtain the solution at this point.

Note:: Physical coordinates in an image correspond to the global coordinate system in which the mesh (nodes) are.

Definition at line 131 of file itkFEMSolver.h.

References itk::SmartPointer< TObjectType >::GetPointer(), and itk::fem::Solver::m_InterpolationGrid.

LinearSystemWrapper::Pointer itk::fem::Solver::GetLinearSystemWrapper ( )

inlineinherited

Gets the LinearSystemWrapper object.

See also:: SetLinearSystemWrapper

Definition at line 297 of file itkFEMSolver.h.

References itk::fem::Solver::m_ls.

Referenced by itk::fem::FEMRegistrationFilter< TMovingImage, TFixedImage >::EnforceDiffeomorphism(), and itk::fem::FEMRegistrationFilter< TMovingImage, TFixedImage >::SampleVectorFieldAtNodes().

LinearSystemWrapper* itk::fem::SolverCrankNicolson::GetLS ( )

inline

Definition at line 131 of file itkFEMSolverCrankNicolson.h.

References itk::fem::Solver::m_ls.

Referenced by itk::fem::FEMRegistrationFilter< TMovingImage, TFixedImage >::InterpolateVectorField().

unsigned int itk::fem::Solver::GetNumberOfDegreesOfFreedom ( void )

inlineinherited

Definition at line 256 of file itkFEMSolver.h.

References itk::fem::Solver::NGFN.

Referenced by itk::fem::FEMRegistrationFilter< TMovingImage, TFixedImage >::MultiResSolve(), and itk::fem::FEMRegistrationFilter< TMovingImage, TFixedImage >::RunRegistration().

Float itk::fem::Solver::GetSolution	(	unsigned int	i,
		unsigned int	which = `0`
	)

inlineinherited

Definition at line 251 of file itkFEMSolver.h.

References itk::fem::Solution::GetSolutionValue(), and itk::fem::Solver::m_ls.

virtual Float itk::fem::Solver::GetTimeStep ( void ) const

inlinevirtualinherited

Returns the time step used for dynamic problems.

Reimplemented in itk::fem::SolverHyperbolic.

Definition at line 308 of file itkFEMSolver.h.

Element::Float itk::fem::SolverCrankNicolson::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;

Definition at line 445 of file itkFEMSolverCrankNicolson.cxx.

References EvaluateResidual(), FindBracketingTriplet(), and SetEnergyToMin().

Float itk::fem::SolverCrankNicolson::GSMax	(	Float	a,
		Float	b
	)

inline

Definition at line 128 of file itkFEMSolverCrankNicolson.h.

Referenced by FindBracketingTriplet(), and itk::fem::FEMRegistrationFilter< TMovingImage, TFixedImage >::FindBracketingTriplet().

Float itk::fem::SolverCrankNicolson::GSSign	(	Float	a,
		Float	b
	)

inline

Definition at line 127 of file itkFEMSolverCrankNicolson.h.

Referenced by BrentsMethod(), FindBracketingTriplet(), and itk::fem::FEMRegistrationFilter< TMovingImage, TFixedImage >::FindBracketingTriplet().

void itk::fem::SolverCrankNicolson::InitializeForSolution ( )

helper initialization function before assembly but after generate GFN.

Definition at line 36 of file itkFEMSolverCrankNicolson.cxx.

References DifferenceMatrixIndex, DiffMatrixBySolutionTMinus1Index, ForceTIndex, ForceTMinus1Index, ForceTotalIndex, itk::fem::LinearSystemWrapper::InitializeMatrix(), itk::fem::LinearSystemWrapper::InitializeSolution(), itk::fem::LinearSystemWrapper::InitializeVector(), itk::fem::Solver::m_ls, itk::fem::Solver::NGFN, itk::fem::Solver::NMFC, itk::fem::LinearSystemWrapper::SetNumberOfMatrices(), itk::fem::LinearSystemWrapper::SetNumberOfSolutions(), itk::fem::LinearSystemWrapper::SetNumberOfVectors(), itk::fem::LinearSystemWrapper::SetSystemOrder(), SolutionTIndex, SolutionTMinus1Index, SolutionVectorTMinus1Index, SumMatrixIndex, and TotalSolutionIndex.

Referenced by AssembleKandM(), itk::fem::FEMRegistrationFilter< TMovingImage, TFixedImage >::MultiResSolve(), and itk::fem::FEMRegistrationFilter< TMovingImage, TFixedImage >::RunRegistration().

void itk::fem::Solver::InitializeInterpolationGrid	(	const VectorType &	size,
		const VectorType &	bb1,
		const VectorType &	bb2
	)

inherited

Initialize the interpolation grid. The interpolation grid is used to find elements that containg specific points in a mesh. The interpolation grid stores pointers to elements for each point on a grid thereby providing a fast way (lookup table) to perform interpolation of results.

Note:: Interpolation grid must be reinitialized each time a mesh changes.

Parameters:

size	Vector that represents number of points on a grid in each dimension.
bb1	Lower limit of a bounding box of a grid.
bb2	Upper limit of a bounding box of a grid.

See also:: GetInterpolationGrid

Initialize the interpolation grid

Definition at line 758 of file itkFEMSolver.cxx.

References itk::fem::Solver::el, itk::ImageConstIterator< TImage >::GetIndex(), itk::ImageRegionConstIterator< TImage >::GoToBegin(), itk::ImageConstIterator< TImage >::IsAtEnd(), itk::fem::Solver::m_InterpolationGrid, itk::fem::Solver::MaxGridDimensions, itk::Image< TPixel, VImageDimension >::New(), and itk::ImageRegionIterator< TImage >::Set().

Referenced by itk::fem::FEMRegistrationFilter< TMovingImage, TFixedImage >::CreateMesh(), and itk::fem::Solver::InitializeInterpolationGrid().

void itk::fem::Solver::InitializeInterpolationGrid ( const VectorType & size )

inlineinherited

Same as InitializeInterpolationGrid(size, {0,0...}, size);

Definition at line 116 of file itkFEMSolver.h.

References itk::fem::Solver::InitializeInterpolationGrid().

void itk::fem::Solver::InitializeLinearSystemWrapper ( void )

virtualinherited

Performs any initialization needed for LinearSystemWrapper object i.e. sets the maximum number of matrices and vectors.

Reimplemented in itk::fem::SolverHyperbolic.

Definition at line 72 of file itkFEMSolver.cxx.

References itk::fem::Solver::m_ls, itk::fem::LinearSystemWrapper::SetNumberOfMatrices(), itk::fem::LinearSystemWrapper::SetNumberOfSolutions(), and itk::fem::LinearSystemWrapper::SetNumberOfVectors().

Referenced by itk::fem::Solver::SetLinearSystemWrapper().

void itk::fem::Solver::InitializeMatrixForAssembly ( unsigned int N )

virtualinherited

This function is called before assembling the matrices. You can override it in a derived class to account for special needs.

Parameters:

N	Size of the matrix.

Reimplemented in itk::fem::SolverHyperbolic.

Definition at line 303 of file itkFEMSolver.cxx.

References itk::fem::LinearSystemWrapper::InitializeMatrix(), itk::fem::Solver::m_ls, and itk::fem::LinearSystemWrapper::SetSystemOrder().

Referenced by itk::fem::Solver::AssembleK().

void itk::fem::SolverCrankNicolson::PrintDisplacements ( )

Definition at line 721 of file itkFEMSolverCrankNicolson.cxx.

References itk::fem::Solution::GetSolutionValue(), itk::fem::Solver::m_ls, itk::fem::Solver::NGFN, and TotalSolutionIndex.

void itk::fem::SolverCrankNicolson::PrintForce ( )

Definition at line 730 of file itkFEMSolverCrankNicolson.cxx.

References ForceTIndex, itk::fem::LinearSystemWrapper::GetVectorValue(), itk::fem::Solver::m_ls, and itk::fem::Solver::NGFN.

void itk::fem::SolverCrankNicolson::PrintMinMaxOfSolution ( )

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

Compute maximum and minimum solution values.

Copy the resulting displacements from solution vector back to node objects.

Definition at line 674 of file itkFEMSolverCrankNicolson.cxx.

References itk::fem::Solution::GetSolutionValue(), itk::fem::Solver::m_ls, itk::fem::Solver::NGFN, SolutionTIndex, and TotalSolutionIndex.

void itk::fem::Solver::Read ( std::istream & f )

inherited

Reads the whole system (nodes, materials and elements) from input stream

   If CreateFromStream returned 0, we're ok. That was the signal
   for the end of stream. Just continue reading... and consequently
   exit the do loop.

   Find out what kind of object did we read from stream
   and store it in the appropriate array

   If we got here, something strange was in the file...

Definition at line 84 of file itkFEMSolver.cxx.

References itk::fem::FEMLightObject::CreateFromStream(), itk::fem::Solver::el, itk::fem::Solver::load, itk::fem::Solver::mat, and itk::fem::Solver::node.

Referenced by itk::fem::FEMRegistrationFilter< TMovingImage, TFixedImage >::ApplyLoads(), and itk::fem::FEMRegistrationFilter< TMovingImage, TFixedImage >::CreateMesh().

void itk::fem::SolverCrankNicolson::RecomputeForceVector ( unsigned int index )

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

Definition at line 242 of file itkFEMSolverCrankNicolson.cxx.

References DiffMatrixBySolutionTMinus1Index, ForceTIndex, ForceTMinus1Index, itk::fem::LinearSystemWrapper::GetVectorValue(), m_alpha, m_deltaT, itk::fem::Solver::m_ls, and itk::fem::LinearSystemWrapper::SetVectorValue().

Referenced by AssembleFforTimeStep().

void itk::fem::SolverCrankNicolson::SetAlpha ( Float a = 0.5 )

inline

Set stability step for the solution.

Definition at line 103 of file itkFEMSolverCrankNicolson.h.

References m_alpha.

Referenced by itk::fem::FEMRegistrationFilter< TMovingImage, TFixedImage >::MultiResSolve(), and itk::fem::FEMRegistrationFilter< TMovingImage, TFixedImage >::RunRegistration().

void itk::fem::SolverCrankNicolson::SetDeltatT ( Float T )

inline

Set time step for the solution. Should be 1/2.

Definition at line 106 of file itkFEMSolverCrankNicolson.h.

References m_deltaT.

Referenced by itk::fem::FEMRegistrationFilter< TMovingImage, TFixedImage >::MultiResSolve(), and itk::fem::FEMRegistrationFilter< TMovingImage, TFixedImage >::RunRegistration().

void itk::fem::SolverCrankNicolson::SetEnergyToMin ( Float xmin )

Definition at line 505 of file itkFEMSolverCrankNicolson.cxx.

References ForceTIndex, ForceTMinus1Index, itk::fem::Solution::GetSolutionValue(), itk::fem::LinearSystemWrapper::GetVectorValue(), itk::fem::Solver::m_ls, itk::fem::Solver::NGFN, itk::fem::LinearSystemWrapper::SetSolutionValue(), itk::fem::LinearSystemWrapper::SetVectorValue(), SolutionTIndex, and SolutionTMinus1Index.

Referenced by BrentsMethod(), GoldenSection(), and itk::fem::FEMRegistrationFilter< TMovingImage, TFixedImage >::GoldenSection().

void itk::fem::Solver::SetLinearSystemWrapper ( LinearSystemWrapper::Pointer ls )

inherited

Sets the LinearSystemWrapper object that will be used when solving the master equation. If this function is not called, a default VNL linear system representation will be used (class LinearSystemWrapperVNL).

Parameters:

ls	Pointer to an object of class which is derived from LinearSystemWrapper.

Note:: Once the LinearSystemWrapper object is changed, it is used until the member function SetLinearSystemWrapper is called again. Since LinearSystemWrapper object was created outside the Solver class, it should also be destroyed outside. Solver class will not destroy it when the Solver object is destroyed.

Change the LinearSystemWrapper object used to solve system of equations.

Definition at line 64 of file itkFEMSolver.cxx.

References itk::fem::Solver::InitializeLinearSystemWrapper(), and itk::fem::Solver::m_ls.

Referenced by itk::fem::Solver::Clear(), itk::fem::FEMRegistrationFilter< TMovingImage, TFixedImage >::MultiResSolve(), itk::fem::FEMRegistrationFilter< TMovingImage, TFixedImage >::RunRegistration(), and itk::fem::Solver::Solver().

void itk::fem::SolverCrankNicolson::SetRho ( Float rho )

inline

Set density constant.

Definition at line 109 of file itkFEMSolverCrankNicolson.h.

References m_rho.

Referenced by itk::fem::FEMRegistrationFilter< TMovingImage, TFixedImage >::MultiResSolve(), and itk::fem::FEMRegistrationFilter< TMovingImage, TFixedImage >::RunRegistration().

virtual void itk::fem::Solver::SetTimeStep ( Float )

inlinevirtualinherited

Sets the time step used for dynamic problems.

Parameters:

dt	New time step.

Reimplemented in itk::fem::SolverHyperbolic.

Definition at line 315 of file itkFEMSolver.h.

void itk::fem::SolverCrankNicolson::Solve ( void )

virtual

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

Solve for the displacement vector u

Reimplemented from itk::fem::Solver.

Definition at line 254 of file itkFEMSolverCrankNicolson.cxx.

References itk::fem::LinearSystemWrapper::InitializeSolution(), itk::fem::Solver::m_ls, SolutionTIndex, and itk::fem::LinearSystemWrapper::Solve().

Referenced by itk::fem::FEMRegistrationFilter< TMovingImage, TFixedImage >::IterativeSolve().

void itk::fem::Solver::UpdateDisplacements ( void )

inherited

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

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

Definition at line 616 of file itkFEMSolver.cxx.

void itk::fem::Solver::Write ( std::ostream & f )

inherited

Writes everything (nodes, materials and elements) to output stream

Definition at line 155 of file itkFEMSolver.cxx.

References itk::fem::Solver::el, itk::fem::Solver::load, itk::fem::Solver::mat, and itk::fem::Solver::node.

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

Definition at line 713 of file itkFEMSolverCrankNicolson.cxx.

References itk::fem::Solver::m_ls, itk::fem::Solver::NGFN, and itk::fem::LinearSystemWrapper::SetVectorValue().

Member Data Documentation

unsigned int itk::fem::SolverCrankNicolson::DifferenceMatrixIndex

Definition at line 176 of file itkFEMSolverCrankNicolson.h.

Referenced by AssembleFforTimeStep(), AssembleKandM(), InitializeForSolution(), and SolverCrankNicolson().

unsigned int itk::fem::SolverCrankNicolson::DiffMatrixBySolutionTMinus1Index

Definition at line 178 of file itkFEMSolverCrankNicolson.h.

Referenced by AssembleFforTimeStep(), InitializeForSolution(), RecomputeForceVector(), and SolverCrankNicolson().

ElementArray itk::fem::Solver::el

inherited

Definition at line 55 of file itkFEMSolver.h.

Referenced by itk::fem::FEMRegistrationFilter< TMovingImage, TFixedImage >::ApplyLoads(), itk::fem::Solver::AssembleF(), itk::fem::Solver::AssembleK(), AssembleKandM(), itk::fem::Solver::Clear(), itk::fem::FEMRegistrationFilter< TMovingImage, TFixedImage >::EvaluateResidual(), itk::fem::Generate2DRectilinearMesh(), itk::fem::Generate3DRectilinearMesh(), itk::fem::Solver::GenerateGFN(), itk::fem::Solver::GetDeformationEnergy(), itk::fem::Solver::InitializeInterpolationGrid(), itk::fem::FEMRegistrationFilter< TMovingImage, TFixedImage >::InterpolateVectorField(), itk::fem::Solver::Read(), and itk::fem::Solver::Write().

unsigned int itk::fem::SolverCrankNicolson::ForceTIndex

Definition at line 169 of file itkFEMSolverCrankNicolson.h.

Referenced by AddToDisplacements(), AssembleFforTimeStep(), EvaluateResidual(), InitializeForSolution(), PrintForce(), RecomputeForceVector(), SetEnergyToMin(), and SolverCrankNicolson().

unsigned int itk::fem::SolverCrankNicolson::ForceTMinus1Index

Definition at line 171 of file itkFEMSolverCrankNicolson.h.

Referenced by AddToDisplacements(), EvaluateResidual(), InitializeForSolution(), RecomputeForceVector(), SetEnergyToMin(), and SolverCrankNicolson().

unsigned int itk::fem::SolverCrankNicolson::ForceTotalIndex

Definition at line 170 of file itkFEMSolverCrankNicolson.h.

Referenced by AddToDisplacements(), EvaluateResidual(), InitializeForSolution(), and SolverCrankNicolson().

LoadArray itk::fem::Solver::load

inherited

Definition at line 67 of file itkFEMSolver.h.

Referenced by itk::fem::Solver::ApplyBC(), itk::fem::FEMRegistrationFilter< TMovingImage, TFixedImage >::ApplyImageLoads(), itk::fem::FEMRegistrationFilter< TMovingImage, TFixedImage >::ApplyLoads(), itk::fem::Solver::AssembleF(), AssembleFforTimeStep(), itk::fem::Solver::AssembleK(), AssembleKandM(), itk::fem::Solver::Clear(), itk::fem::FEMRegistrationFilter< TMovingImage, TFixedImage >::EnforceDiffeomorphism(), itk::fem::Generate2DRectilinearMesh(), itk::fem::Solver::Read(), and itk::fem::Solver::Write().

Float itk::fem::SolverCrankNicolson::m_alpha

Definition at line 166 of file itkFEMSolverCrankNicolson.h.

Referenced by AssembleKandM(), RecomputeForceVector(), SetAlpha(), and SolverCrankNicolson().

Float itk::fem::SolverCrankNicolson::m_CurrentMaxSolution

Definition at line 167 of file itkFEMSolverCrankNicolson.h.

Referenced by AddToDisplacements(), GetCurrentMaxSolution(), and SolverCrankNicolson().

Float itk::fem::SolverCrankNicolson::m_deltaT

Definition at line 164 of file itkFEMSolverCrankNicolson.h.

Referenced by AssembleKandM(), RecomputeForceVector(), SetDeltatT(), and SolverCrankNicolson().

LinearSystemWrapper::Pointer itk::fem::Solver::m_ls

protectedinherited

Pointer to LinearSystemWrapper object.

Definition at line 331 of file itkFEMSolver.h.

Float itk::fem::SolverCrankNicolson::m_rho

Definition at line 165 of file itkFEMSolverCrankNicolson.h.

Referenced by AssembleKandM(), SetRho(), and SolverCrankNicolson().

MaterialArray itk::fem::Solver::mat

inherited

Definition at line 73 of file itkFEMSolver.h.

Referenced by itk::fem::Solver::Clear(), itk::fem::FEMRegistrationFilter< TMovingImage, TFixedImage >::CreateMesh(), itk::fem::Solver::Read(), and itk::fem::Solver::Write().

const unsigned int itk::fem::Solver::MaxGridDimensions = 3

staticinherited

Since the itk::Image is templated over the number of dimensions, we have to know this at compile time. Solver class, however, can handle elements in any number of dimensions. In order to be able to use the Image, we choose the maximum number of space dimension that this function will be able to handle. Any unused dimensions are filled with zero.

For example: If a 2D node coordinates are {1.0,3.0} then the corresponding phisycal point in an image is {1.0,3.0,0.0};

Definition at line 90 of file itkFEMSolver.h.

Referenced by itk::fem::Solver::GetElementAtPoint(), and itk::fem::Solver::InitializeInterpolationGrid().

unsigned int itk::fem::Solver::NGFN

protectedinherited

Number of global degrees of freedom in a system

Definition at line 322 of file itkFEMSolver.h.

Referenced by AddToDisplacements(), itk::fem::Solver::ApplyBC(), itk::fem::Solver::AssembleElementMatrix(), itk::fem::Solver::AssembleF(), AssembleFforTimeStep(), itk::fem::Solver::AssembleK(), AssembleKandM(), itk::fem::Solver::AssembleLandmarkContribution(), AverageLastTwoDisplacements(), itk::fem::Solver::Clear(), EvaluateResidual(), itk::fem::Solver::GenerateGFN(), GetDeformationEnergy(), itk::fem::Solver::GetNumberOfDegreesOfFreedom(), InitializeForSolution(), PrintDisplacements(), PrintForce(), PrintMinMaxOfSolution(), SetEnergyToMin(), and ZeroVector().