Solving a cardiac problem

This page gives a high-level overview of the code execution flow when solving a cardiac problem. To run simulations, see UserTutorials. For an overview of the PDE solver hierarchy, see FiniteElementAssemblersAndSolvers. The steps that occur are as follows

• The user calls AbstractCardiacProblem::Solve() on their monodomain or bidomain problem object (after calling Initialise)
• The AbstractCardiacProblem owns a particular mono/bidomain finite element solver (of base-class type AbstractDynamicLinearPdeSolver; the concrete class can be matrix-based or not; see FiniteElementAssemblersAndSolvers for more details); and for each printing timestep, does the following:
  • sets the current time and end time on the solver
  • sets the latest voltage solution on the solver as the initial condition
  • calls Solve on the solver.

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The Solve method on AbstractDynamicLinearPdeSolver does the following, for each PDE timestep

• calls PrepareForSetupLinearSystem -- solves cell models, see below
• calls SetupLinearSystem -- see below
• calls FinaliseLinearSystem -- relevant for bidomain solves, things like checking compatibility, setting up a null space
• solves the linear system to obtain the solution (voltage, and phi_e in bidomain setting) at the next timestep

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1. PrepareForLinearSystem is where the cell models are solved. It is implemented in AbstractMonodomainSolver/AbstractBidomainSolver, where it just calls SolveCellSystems on the MonodomainTissue/BidomainTissue. This is implemented in AbstractCardiacTissue::SolveCellSystems, which essentially does the following for each cell:

1. Set V from the current PDE solution
2. Call the cell's ComputeExceptVoltage to solve for all state variables except V until the next PDE time step
3. Call UpdateCaches. This calls the cell's GetIIonic to compute the I_ion term and stores it in mIionicCacheReplicated (replicated over each process so no parallel communication is required later). It similarly also calculates and caches the intracellular stimulus at each cell.

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2. SetupLinearSystem uses any assemblers it has to set up the linear system Ax=b that will be solved that timestep. A is just assembled once the first timestep. For b the solver (or its assemblers) will require the ionic current and stimulus at each cell; this is obtained by calling, for example, mpMonodomainTissue->rGetIionicCacheReplicated()[index]. For more details on setting up b and the method SetupLinearSystem see FiniteElementAssemblersAndSolvers.