#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, unsigned numQuadPoints=2)
	~OperatorSplittingMonodomainSolver ()
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
unsigned	mNumQuadPoints
Mat	mMassMatrix
Vec	mVecForConstructingRhs

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

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,
		unsigned	numQuadPoints = `2`
	)

Constructor

Parameters:

pMesh	pointer to the mesh
pTissue	pointer to the tissue
pBoundaryConditions	pointer to the boundary conditions
numQuadPoints	number of quadrature points (defaults to 2)

Definition at line 171 of file OperatorSplittingMonodomainSolver.cpp.

template<unsigned ELEMENT_DIM, unsigned SPACE_DIM>

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

Destructor

Definition at line 194 of file OperatorSplittingMonodomainSolver.cpp.

References PetscTools::Destroy().

Member Function Documentation

template<unsigned ELEMENT_DIM, unsigned SPACE_DIM>

void OperatorSplittingMonodomainSolver< ELEMENT_DIM, SPACE_DIM >::FollowingSolveLinearSystem ( Vec currentSolution ) [private, virtual]

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 118 of file OperatorSplittingMonodomainSolver.cpp.

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

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 128 of file OperatorSplittingMonodomainSolver.cpp.

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

template<unsigned ELEMENT_DIM, unsigned SPACE_DIM>

void OperatorSplittingMonodomainSolver< ELEMENT_DIM, SPACE_DIM >::PrepareForSetupLinearSystem ( Vec currentSolution ) [private, virtual]

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().

template<unsigned ELEMENT_DIM, unsigned SPACE_DIM>

void OperatorSplittingMonodomainSolver< ELEMENT_DIM, SPACE_DIM >::SetupLinearSystem	(	Vec	currentSolution,
		bool	computeMatrix
	)		`[private, virtual]`

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:

currentSolution	Solution at current time
computeMatrix	Whether to compute the matrix of the linear system

Implements AbstractLinearPdeSolver< ELEMENT_DIM, SPACE_DIM, PROBLEM_DIM >.

Definition at line 40 of file OperatorSplittingMonodomainSolver.cpp.

References AbstractFeAssemblerInterface< CAN_ASSEMBLE_VECTOR, CAN_ASSEMBLE_MATRIX >::Assemble(), DistributedVector::Begin(), GenericEventHandler< 16, HeartEventHandler >::BeginEvent(), DistributedVectorFactory::CreateDistributedVector(), DistributedVector::End(), GenericEventHandler< 16, HeartEventHandler >::EndEvent(), PetscMatTools::Finalise(), HeartConfig::GetCapacitance(), PdeSimulationTime::GetPdeTimeStepInverse(), HeartConfig::GetSurfaceAreaToVolumeRatio(), HeartConfig::Instance(), DistributedVector::Restore(), and AbstractFeAssemblerInterface< CAN_ASSEMBLE_VECTOR, CAN_ASSEMBLE_MATRIX >::SetMatrixToAssemble().

Member Data Documentation

template<unsigned ELEMENT_DIM, unsigned SPACE_DIM>

Mat OperatorSplittingMonodomainSolver< ELEMENT_DIM, SPACE_DIM >::mMassMatrix [private]

The mass matrix, used to computing the RHS vector

Definition at line 95 of file OperatorSplittingMonodomainSolver.hpp.

template<unsigned ELEMENT_DIM, unsigned SPACE_DIM>

unsigned OperatorSplittingMonodomainSolver< ELEMENT_DIM, SPACE_DIM >::mNumQuadPoints [private]

Number of quadrature points per dimension (only saved so it can be passed to the assembler

Definition at line 92 of file OperatorSplittingMonodomainSolver.hpp.

Referenced by OperatorSplittingMonodomainSolver< ELEMENT_DIM, SPACE_DIM >::OperatorSplittingMonodomainSolver().

template<unsigned ELEMENT_DIM, unsigned SPACE_DIM>

BoundaryConditionsContainer<ELEMENT_DIM,SPACE_DIM,1>* OperatorSplittingMonodomainSolver< ELEMENT_DIM, SPACE_DIM >::mpBoundaryConditions [private]

Boundary conditions

Definition at line 77 of file OperatorSplittingMonodomainSolver.hpp.

template<unsigned ELEMENT_DIM, unsigned SPACE_DIM>

MonodomainAssembler<ELEMENT_DIM,SPACE_DIM>* OperatorSplittingMonodomainSolver< ELEMENT_DIM, SPACE_DIM >::mpMonodomainAssembler [private]

The monodomain assembler, used to set up the LHS matrix

Definition at line 83 of file OperatorSplittingMonodomainSolver.hpp.

Referenced by OperatorSplittingMonodomainSolver< ELEMENT_DIM, SPACE_DIM >::OperatorSplittingMonodomainSolver().

template<unsigned ELEMENT_DIM, unsigned SPACE_DIM>

MonodomainTissue<ELEMENT_DIM,SPACE_DIM>* OperatorSplittingMonodomainSolver< ELEMENT_DIM, SPACE_DIM >::mpMonodomainTissue [private]

Monodomain tissue class (collection of cells, and conductivities)

Definition at line 80 of file OperatorSplittingMonodomainSolver.hpp.

Referenced by OperatorSplittingMonodomainSolver< ELEMENT_DIM, SPACE_DIM >::OperatorSplittingMonodomainSolver().

template<unsigned ELEMENT_DIM, unsigned SPACE_DIM>

NaturalNeumannSurfaceTermAssembler<ELEMENT_DIM,SPACE_DIM,1>* OperatorSplittingMonodomainSolver< ELEMENT_DIM, SPACE_DIM >::mpNeumannSurfaceTermsAssembler [private]

Assembler for surface integrals coming from any non-zero Neumann boundary conditions

Definition at line 86 of file OperatorSplittingMonodomainSolver.hpp.

Referenced by OperatorSplittingMonodomainSolver< ELEMENT_DIM, SPACE_DIM >::OperatorSplittingMonodomainSolver().

template<unsigned ELEMENT_DIM, unsigned SPACE_DIM>

Vec OperatorSplittingMonodomainSolver< ELEMENT_DIM, SPACE_DIM >::mVecForConstructingRhs [private]

The vector multiplied by the mass matrix. Ie, if the linear system to be solved is Ax=b, this vector is z where b=Mz.

In the normal solver this is equal to alpha*V + beta*Iionic + gamma*Istim, here there is no Iionic term.

Definition at line 104 of file OperatorSplittingMonodomainSolver.hpp.

Referenced by OperatorSplittingMonodomainSolver< ELEMENT_DIM, SPACE_DIM >::OperatorSplittingMonodomainSolver().

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

heart/src/solver/electrics/monodomain/OperatorSplittingMonodomainSolver.hpp
heart/src/solver/electrics/monodomain/OperatorSplittingMonodomainSolver.cpp

Public Member Functions

Private Member Functions

Private Attributes

Detailed Description

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

Constructor & Destructor Documentation

Member Function Documentation

Member Data Documentation

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