OperatorSplittingMonodomainSolver< ELEMENT_DIM, SPACE_DIM > Class Template Reference

#include <OperatorSplittingMonodomainSolver.hpp>

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List of all members.

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
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)

Unlike the other two solvers this currently does not inherit from AbstractMonodomainSolver.

Definition at line 67 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 
) [inline]

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 173 of file OperatorSplittingMonodomainSolver.cpp.

References AbstractDynamicLinearPdeSolver< ELEMENT_DIM, SPACE_DIM, 1 >::mMatrixIsConstant, OperatorSplittingMonodomainSolver< ELEMENT_DIM, SPACE_DIM >::mpMonodomainAssembler, OperatorSplittingMonodomainSolver< ELEMENT_DIM, SPACE_DIM >::mVecForConstructingRhs, and AbstractCardiacTissue< ELEMENT_DIM, SPACE_DIM >::SetCacheReplication().

template<unsigned ELEMENT_DIM, unsigned SPACE_DIM>
OperatorSplittingMonodomainSolver< ELEMENT_DIM, SPACE_DIM >::~OperatorSplittingMonodomainSolver (  )  [inline]


Member Function Documentation

template<unsigned ELEMENT_DIM, unsigned SPACE_DIM>
void OperatorSplittingMonodomainSolver< ELEMENT_DIM, SPACE_DIM >::SetupLinearSystem ( Vec  currentSolution,
bool  computeMatrix 
) [inline, 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 33 of file OperatorSplittingMonodomainSolver.cpp.

References AbstractFeObjectAssembler< ELEMENT_DIM, SPACE_DIM, 1, false, true, NORMAL >::Assemble(), PetscMatTools::AssembleFinal(), LinearSystem::AssembleFinalLhsMatrix(), LinearSystem::AssembleRhsVector(), DistributedVector::Begin(), GenericEventHandler< 13, HeartEventHandler >::BeginEvent(), DistributedVectorFactory::CreateDistributedVector(), DistributedVector::End(), GenericEventHandler< 13, HeartEventHandler >::EndEvent(), HeartConfig::GetCapacitance(), PdeSimulationTime::GetPdeTimeStepInverse(), HeartConfig::GetSurfaceAreaToVolumeRatio(), HeartConfig::Instance(), OperatorSplittingMonodomainSolver< ELEMENT_DIM, SPACE_DIM >::mMassMatrix, OperatorSplittingMonodomainSolver< ELEMENT_DIM, SPACE_DIM >::mNumQuadPoints, OperatorSplittingMonodomainSolver< ELEMENT_DIM, SPACE_DIM >::mpBoundaryConditions, AbstractLinearPdeSolver< ELEMENT_DIM, SPACE_DIM, PROBLEM_DIM >::mpLinearSystem, 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 >::mVecForConstructingRhs, DistributedVector::Restore(), LinearSystem::rGetLhsMatrix(), LinearSystem::rGetRhsVector(), and AbstractFeObjectAssembler< ELEMENT_DIM, SPACE_DIM, 1, false, true, NORMAL >::SetMatrixToAssemble().

template<unsigned ELEMENT_DIM, unsigned SPACE_DIM>
void OperatorSplittingMonodomainSolver< ELEMENT_DIM, SPACE_DIM >::PrepareForSetupLinearSystem ( Vec  currentSolution  )  [inline, 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 111 of file OperatorSplittingMonodomainSolver.cpp.

References PdeSimulationTime::GetPdeTimeStep(), PdeSimulationTime::GetTime(), and OperatorSplittingMonodomainSolver< ELEMENT_DIM, SPACE_DIM >::mpMonodomainTissue.

template<unsigned ELEMENT_DIM, unsigned SPACE_DIM>
void OperatorSplittingMonodomainSolver< ELEMENT_DIM, SPACE_DIM >::FollowingSolveLinearSystem ( Vec  currentSolution  )  [inline, 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 120 of file OperatorSplittingMonodomainSolver.cpp.

References PdeSimulationTime::GetPdeTimeStep(), PdeSimulationTime::GetTime(), and OperatorSplittingMonodomainSolver< ELEMENT_DIM, SPACE_DIM >::mpMonodomainTissue.

template<unsigned ELEMENT_DIM, unsigned SPACE_DIM>
void OperatorSplittingMonodomainSolver< ELEMENT_DIM, SPACE_DIM >::InitialiseForSolve ( Vec  initialSolution  )  [inline, virtual]


Member Data Documentation

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

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

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

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 84 of file OperatorSplittingMonodomainSolver.hpp.

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

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

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 96 of file OperatorSplittingMonodomainSolver.hpp.

Referenced by OperatorSplittingMonodomainSolver< ELEMENT_DIM, SPACE_DIM >::InitialiseForSolve(), OperatorSplittingMonodomainSolver< ELEMENT_DIM, SPACE_DIM >::OperatorSplittingMonodomainSolver(), OperatorSplittingMonodomainSolver< ELEMENT_DIM, SPACE_DIM >::SetupLinearSystem(), and OperatorSplittingMonodomainSolver< ELEMENT_DIM, SPACE_DIM >::~OperatorSplittingMonodomainSolver().


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

Generated on Mon Apr 18 11:37:40 2011 for Chaste by  doxygen 1.5.5