itk::fem::SolverCrankNicolson Class Reference

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

#include <itkFEMSolverCrankNicolson.h>

Inheritance diagram for itk::fem::SolverCrankNicolson:

[legend]Collaboration diagram for itk::fem::SolverCrankNicolson:

[legend]List of all members.

Public Methods
void	InitializeForSolution ()
void	AssembleKandM ()
void	AssembleFforTimeStep (int dim=0)
void	Solve ()
void	SetAlpha (Float a=0.5)
void	SetDeltatT (Float T)
void	SetRho (Float rho)
void	RecomputeForceVector (unsigned int index)
void	FindBracketingTriplet (Float *a, Float *b, Float *c)
void	SetEnergyToMin (Float xmin)
LinearSystemWrapper *	GetLS ()
void	PrintMinMaxOfSolution ()
	SolverCrankNicolson ()
	~SolverCrankNicolson ()
void	AddToDisplacements (Float optimum=1.0)
void	AverageLastTwoDisplacements (Float t=0.5)
void	ZeroVector (int which=0)
void	PrintDisplacements ()
void	PrintForce ()
Float	GoldenSection (Float tol=0.01, unsigned int MaxIters=25)
Float	BrentsMethod (Float tol=0.01, unsigned int MaxIters=25)
Float	EvaluateResidual (Float t=1.0)
Float	GetDeformationEnergy (Float t=1.0)
Float	GSSign (Float a, Float b)
Float	GSMax (Float a, Float b)
Public Attributes
Float	m_deltaT
Float	m_rho
Float	m_alpha
unsigned int	ForceTIndex
unsigned int	ForceTotalIndex
unsigned int	ForceTMinus1Index
unsigned int	SolutionTIndex
unsigned int	SolutionTMinus1Index
unsigned int	SolutionVectorTMinus1Index
unsigned int	TotalSolutionIndex
unsigned int	DifferenceMatrixIndex
unsigned int	SumMatrixIndex
unsigned int	DiffMatrixBySolutionTMinus1Index

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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 63 of file itkFEMSolverCrankNicolson.h.

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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 141 of file itkFEMSolverCrankNicolson.h. References DifferenceMatrixIndex, DiffMatrixBySolutionTMinus1Index, ForceTIndex, ForceTMinus1Index, ForceTotalIndex, m_alpha, SolutionTIndex, SolutionTMinus1Index, SolutionVectorTMinus1Index, SumMatrixIndex, and TotalSolutionIndex.

itk::fem::SolverCrankNicolson::~SolverCrankNicolson (    )  [inline]

Definition at line 160 of file itkFEMSolverCrankNicolson.h. References itk::fem::Solver::Float, and m_alpha.

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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

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.

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.

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

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

Float itk::fem::SolverCrankNicolson::BrentsMethod (  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;

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

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

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

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

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

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

Definition at line 132 of file itkFEMSolverCrankNicolson.h. References m_deltaT, and m_rho.

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;

Float itk::fem::SolverCrankNicolson::GSMax (  Float    a, Float    b )  [inline]

Finds the optimum value between the last two solutions and sets the current solution to that value. Uses Evaluate Residual; Definition at line 128 of file itkFEMSolverCrankNicolson.h. References itk::fem::Solver::Float, and itk::fem::Solver::m_ls.

Float itk::fem::SolverCrankNicolson::GSSign (  Float    a, Float    b )  [inline]

Finds the optimum value between the last two solutions and sets the current solution to that value. Uses Evaluate Residual; Definition at line 127 of file itkFEMSolverCrankNicolson.h.

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

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

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

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

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

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

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

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.

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

Set stability step for the solution. Definition at line 104 of file itkFEMSolverCrankNicolson.h.

void itk::fem::SolverCrankNicolson::SetDeltatT (  Float    T )  [inline]

Set time step for the solution. Should be 1/2. Definition at line 107 of file itkFEMSolverCrankNicolson.h.

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

void itk::fem::SolverCrankNicolson::SetRho (  Float    rho )  [inline]

Set density constant. Definition at line 110 of file itkFEMSolverCrankNicolson.h.

void itk::fem::SolverCrankNicolson::Solve (    )  [virtual]

Solve for the displacement vector u at a given time. Update the total solution as well. Reimplemented from itk::fem::Solver.

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

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

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Member Data Documentation

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

Definition at line 173 of file itkFEMSolverCrankNicolson.h. Referenced by SolverCrankNicolson().

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

Definition at line 175 of file itkFEMSolverCrankNicolson.h. Referenced by SolverCrankNicolson().

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

Definition at line 166 of file itkFEMSolverCrankNicolson.h. Referenced by SolverCrankNicolson().

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

Definition at line 168 of file itkFEMSolverCrankNicolson.h. Referenced by SolverCrankNicolson().

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

Definition at line 167 of file itkFEMSolverCrankNicolson.h. Referenced by SolverCrankNicolson().

Float itk::fem::SolverCrankNicolson::m_alpha

Definition at line 164 of file itkFEMSolverCrankNicolson.h. Referenced by SolverCrankNicolson(), and ~SolverCrankNicolson().

Float itk::fem::SolverCrankNicolson::m_deltaT

Definition at line 162 of file itkFEMSolverCrankNicolson.h. Referenced by GetLS().

Float itk::fem::SolverCrankNicolson::m_rho

Definition at line 163 of file itkFEMSolverCrankNicolson.h. Referenced by GetLS().

unsigned int itk::fem::SolverCrankNicolson::SolutionTIndex

Definition at line 169 of file itkFEMSolverCrankNicolson.h. Referenced by SolverCrankNicolson().

unsigned int itk::fem::SolverCrankNicolson::SolutionTMinus1Index

Definition at line 170 of file itkFEMSolverCrankNicolson.h. Referenced by SolverCrankNicolson().

unsigned int itk::fem::SolverCrankNicolson::SolutionVectorTMinus1Index

Definition at line 171 of file itkFEMSolverCrankNicolson.h. Referenced by SolverCrankNicolson().

unsigned int itk::fem::SolverCrankNicolson::SumMatrixIndex

Definition at line 174 of file itkFEMSolverCrankNicolson.h. Referenced by SolverCrankNicolson().

unsigned int itk::fem::SolverCrankNicolson::TotalSolutionIndex

Definition at line 172 of file itkFEMSolverCrankNicolson.h. Referenced by SolverCrankNicolson().

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

• itkFEMSolverCrankNicolson.h

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