#include <OperatorSplittingMonodomainSolver.hpp>

Inheritance diagram for OperatorSplittingMonodomainSolver< ELEMENT_DIM, SPACE_DIM >:

Collaboration diagram for OperatorSplittingMonodomainSolver< ELEMENT_DIM, SPACE_DIM >:

Public Member Functions
void	InitialiseForSolve (Vec initialSolution)

	OperatorSplittingMonodomainSolver (AbstractTetrahedralMesh< ELEMENT_DIM, SPACE_DIM > pMesh, MonodomainTissue< ELEMENT_DIM, SPACE_DIM > pTissue, BoundaryConditionsContainer< ELEMENT_DIM, SPACE_DIM, 1 > *pBoundaryConditions)

	~OperatorSplittingMonodomainSolver ()

Public Member Functions inherited from AbstractDynamicLinearPdeSolver< ELEMENT_DIM, SPACE_DIM, 1 >
	AbstractDynamicLinearPdeSolver (AbstractTetrahedralMesh< ELEMENT_DIM, SPACE_DIM > *pMesh)

void	SetTimes (double tStart, double tEnd)

void	SetTimeStep (double dt)

void	SetInitialCondition (Vec initialCondition)

virtual Vec	Solve ()

void	SetMatrixIsNotAssembled ()

void	SetTimeAdaptivityController (AbstractTimeAdaptivityController *pTimeAdaptivityController)

void	SetOutputToVtk (bool output)

void	SetOutputToParallelVtk (bool output)

void	SetOutputToTxt (bool output)

void	SetOutputDirectoryAndPrefix (std::string outputDirectory, std::string prefix)

void	SetPrintingTimestepMultiple (unsigned multiple)

Public Member Functions inherited from AbstractLinearPdeSolver< ELEMENT_DIM, SPACE_DIM, PROBLEM_DIM >
	AbstractLinearPdeSolver (AbstractTetrahedralMesh< ELEMENT_DIM, SPACE_DIM > *pMesh)

virtual	~AbstractLinearPdeSolver ()

virtual void	FinaliseLinearSystem (Vec currentSolution)

LinearSystem *	GetLinearSystem ()

Private Member Functions
void	SetupLinearSystem (Vec currentSolution, bool computeMatrix)

void	PrepareForSetupLinearSystem (Vec currentSolution)

void	FollowingSolveLinearSystem (Vec currentSolution)

Private Attributes
BoundaryConditionsContainer< ELEMENT_DIM, SPACE_DIM, 1 > *	mpBoundaryConditions

MonodomainTissue< ELEMENT_DIM, SPACE_DIM > *	mpMonodomainTissue

MonodomainAssembler< ELEMENT_DIM, SPACE_DIM > *	mpMonodomainAssembler

NaturalNeumannSurfaceTermAssembler< ELEMENT_DIM, SPACE_DIM, 1 > *	mpNeumannSurfaceTermsAssembler

Mat	mMassMatrix

Vec	mVecForConstructingRhs

Additional Inherited Members
Protected Member Functions inherited from AbstractDynamicLinearPdeSolver< ELEMENT_DIM, SPACE_DIM, 1 >
void	InitialiseHdf5Writer ()

void	WriteOneStep (double time, Vec solution)

Protected Attributes inherited from AbstractDynamicLinearPdeSolver< ELEMENT_DIM, SPACE_DIM, 1 >
double	mTstart

double	mTend

bool	mTimesSet

Vec	mInitialCondition

bool	mMatrixIsAssembled

bool	mMatrixIsConstant

double	mIdealTimeStep

double	mLastWorkingTimeStep

AbstractTimeAdaptivityController *	mpTimeAdaptivityController

bool	mOutputToVtk

bool	mOutputToParallelVtk

bool	mOutputToTxt

std::string	mOutputDirectory

std::string	mFilenamePrefix

unsigned	mPrintingTimestepMultiple

Hdf5DataWriter *	mpHdf5Writer

std::vector< int >	mVariableColumnIds

Protected Attributes inherited from AbstractLinearPdeSolver< ELEMENT_DIM, SPACE_DIM, PROBLEM_DIM >
LinearSystem *	mpLinearSystem

AbstractTetrahedralMesh< ELEMENT_DIM, SPACE_DIM > *	mpMesh

Detailed Description

template<unsigned ELEMENT_DIM, unsigned SPACE_DIM>
class OperatorSplittingMonodomainSolver< ELEMENT_DIM, SPACE_DIM >

A monodomain solver that uses Strang operator splitting of the diffusion (conductivity) term and the reaction (ionic current) term, instead of solving the full reaction-diffusion PDE. This does NOT refer to operator splitting of the two PDEs in the bidomain equations. For details see for example Sundnes et al "Computing the Electrical Activity of the Heart".

The algorithm is, for solving from t=T to T+dt.

(i) Solve ODEs dV/dt = Iionic for t=T to T+dt/2 [giving updated V (internally, and in solution vector) and updated state variables] (ii) Solve PDE dV/dt = div sigma grad V for t=T to dt [using V from step i, –> updated V] (iii) Solve ODEs dV/dt = Iionic for t=T+dt/2 to T+dt [using V from step ii, –> final V]

Notes (a) Stages (iii) and (i) can normally be solved together in one go, except just before/after printing the voltage to file. However for simplicity of code this has not been implemented (b) Therefore, the effective ODE timestep will be: min(ode_dt, pde_dt/2), where ode_dt and pde_dt are those given via HeartConfig. (c) This solver is FOR COMPARING ACCURACY, NOT PERFORMANCE. It has not been optimised and may or may not perform well in parallel. (d) We don't implement the simpler form of operator splitting, Godunov splitting, where the ODEs are solved for one timestep and the PDEs are solved for one timestep, since this is formally equivalent to the default implementation where the ionic current is interpolated from the nodal values (ie ICI - see ICI/SVI discussion in documentation)

Definition at line 72 of file OperatorSplittingMonodomainSolver.hpp.

Constructor & Destructor Documentation

◆ OperatorSplittingMonodomainSolver()

template<unsigned ELEMENT_DIM, unsigned SPACE_DIM>

OperatorSplittingMonodomainSolver< ELEMENT_DIM, SPACE_DIM >::OperatorSplittingMonodomainSolver	(	AbstractTetrahedralMesh< ELEMENT_DIM, SPACE_DIM > *	pMesh,
		MonodomainTissue< ELEMENT_DIM, SPACE_DIM > *	pTissue,
		BoundaryConditionsContainer< ELEMENT_DIM, SPACE_DIM, 1 > *	pBoundaryConditions
	)

Constructor

Parameters

pMesh	pointer to the mesh
pTissue	pointer to the tissue
pBoundaryConditions	pointer to the boundary conditions

Definition at line 167 of file OperatorSplittingMonodomainSolver.cpp.

References AbstractDynamicLinearPdeSolver< ELEMENT_DIM, SPACE_DIM, 1 >::mMatrixIsConstant, AbstractLinearPdeSolver< ELEMENT_DIM, SPACE_DIM, PROBLEM_DIM >::mpMesh, OperatorSplittingMonodomainSolver< ELEMENT_DIM, SPACE_DIM >::mpMonodomainAssembler, OperatorSplittingMonodomainSolver< ELEMENT_DIM, SPACE_DIM >::mpMonodomainTissue, OperatorSplittingMonodomainSolver< ELEMENT_DIM, SPACE_DIM >::mpNeumannSurfaceTermsAssembler, OperatorSplittingMonodomainSolver< ELEMENT_DIM, SPACE_DIM >::mVecForConstructingRhs, and AbstractCardiacTissue< ELEMENT_DIM, SPACE_DIM >::SetCacheReplication().

◆ ~OperatorSplittingMonodomainSolver()

template<unsigned ELEMENT_DIM, unsigned SPACE_DIM>

OperatorSplittingMonodomainSolver< ELEMENT_DIM, SPACE_DIM >::~OperatorSplittingMonodomainSolver ( )

Destructor

Definition at line 188 of file OperatorSplittingMonodomainSolver.cpp.

References PetscTools::Destroy().

Member Function Documentation

◆ FollowingSolveLinearSystem()

template<unsigned ELEMENT_DIM, unsigned SPACE_DIM>

void OperatorSplittingMonodomainSolver< ELEMENT_DIM, SPACE_DIM >::FollowingSolveLinearSystem ( Vec currentSolution )

privatevirtual

Called after solving the linear system, used to solve the cell models for second half timestep (step (iii) above)

Parameters

currentSolution the latest solution vector (ie the solution of the linear system).

Reimplemented from AbstractLinearPdeSolver< ELEMENT_DIM, SPACE_DIM, PROBLEM_DIM >.

Definition at line 117 of file OperatorSplittingMonodomainSolver.cpp.

References PdeSimulationTime::GetNextTime(), PdeSimulationTime::GetPdeTimeStep(), and PdeSimulationTime::GetTime().

◆ InitialiseForSolve()

template<unsigned ELEMENT_DIM, unsigned SPACE_DIM>

void OperatorSplittingMonodomainSolver< ELEMENT_DIM, SPACE_DIM >::InitialiseForSolve ( Vec initialSolution )

virtual

Overloaded InitialiseForSolve() which calls base version but also initialises mMassMatrix and mVecForConstructingRhs.

Parameters

initialSolution initial solution

Reimplemented from AbstractLinearPdeSolver< ELEMENT_DIM, SPACE_DIM, PROBLEM_DIM >.

Definition at line 126 of file OperatorSplittingMonodomainSolver.cpp.

References AbstractLinearPdeSolver< ELEMENT_DIM, SPACE_DIM, PROBLEM_DIM >::InitialiseForSolve(), HeartConfig::Instance(), NEVER_REACHED, and PetscTools::SetupMat().

◆ PrepareForSetupLinearSystem()

template<unsigned ELEMENT_DIM, unsigned SPACE_DIM>

void OperatorSplittingMonodomainSolver< ELEMENT_DIM, SPACE_DIM >::PrepareForSetupLinearSystem ( Vec currentSolution )

privatevirtual

Called before setting up the linear system, used to solve the cell models for first half timestep (step (i) above)

Parameters

currentSolution the latest solution vector

Reimplemented from AbstractLinearPdeSolver< ELEMENT_DIM, SPACE_DIM, PROBLEM_DIM >.

Definition at line 109 of file OperatorSplittingMonodomainSolver.cpp.

References PdeSimulationTime::GetPdeTimeStep(), and PdeSimulationTime::GetTime().

◆ SetupLinearSystem()

template<unsigned ELEMENT_DIM, unsigned SPACE_DIM>

void OperatorSplittingMonodomainSolver< ELEMENT_DIM, SPACE_DIM >::SetupLinearSystem	(	Vec	currentSolution,
		bool	computeMatrix
	)

privatevirtual

Implementation of SetupLinearSystem() which uses the assembler to compute the LHS matrix, but sets up the RHS vector using the mass-matrix (constructed using a separate assembler) multiplied by a vector

Parameters