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 the User Tutorials. For an overview of the PDE solver hierarchy, see Finite Element Assemblers and Solvers. 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 Finite Element Assemblers and Solvers 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.

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

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.

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 Finite Element Assemblers and Solvers.