Continuity 6 Solvers

Where are the important files?

• Electrophysiology
  • pcty/server/problem/Electrophysiology/Electrophysiology.py
  • pcty/server/problem/Electrophysiology/ContODESolver.py
  • src/ep/? (f2py wrappers)
  • src/ep/electrophys/? (actual fortran source)
• Biomechanics
  • pcty/server/problem/Biomechanics/SolversBM.py
  • pcty/server/problem/Biomechanics/SolversBMParallel.py
  • src/bm/? (f2py wrappers)
  • src/biomechanics/? (actual fortran source)

PDEs Solvers

How does it work?

• Iterations or time sequences of linear solves

Where are they found?

• Biomechanics (SolversBM*.py)
• Electrophysiology

  • Electrophysiology.py, Cont2Axb(), calls p_cont2axb()

Linear Solvers

Where are they found?

• Used within the time iterations or time sequences for both Biomechanics and Electrophysiology
  • For Biomechanics uses nonlinear Newton iterations within timestep loop
  • For Electrophysiology uses time steps
• Used for consistent stress and consistent strains
• Also maybe used by fitting (at least it could be used)

What do we use?

• A direct linear solver
  • SuperLU
    • Uses a sparse matrix representation
    • Sparse global matrix is assembled by summing element matrices

  • Previously we have used LaPack and NAG although they are MUCH slower

• Solves an [A][x] = [b] problem, by reducing it to [L][U][x] = [b]
• Requires 2 steps
  • Factorize
  • Back subsitution

What could we use?

• Distributed SuperLU
  • Solves the linear problem in parallel
  • A lot of communications overhead–need fast interconnect between nodes
• An “indirect” or “iterative” solver
  • How does it work?
    • [A][X*] – [b] until = 0
  • Advantages?
    • matrix-vector-product can be done matrix free (much less memory required, less communication overhead)
  • Disadvantages?

    • Requires a preconditioner

    • Not currently implemented in Continuity 6, although it was implemented in Continuity 5

      • See page 783 and references 8,18,21,28 of Vetter et al 2000

  • PETSc

    • http://acts.nersc.gov/petsc/

    • http://www-unix.mcs.anl.gov/petsc/petsc-as/ (has python bindings; looks very promising)

ODE Solvers

Where are they found?

• Biomechanics: circulatory model
• Electrophysiology
  • pcty/server/problem/Electrophysiology.py calls cont2ODESolver() (line 1026)
    • cont2ODESolver.py alls p_odesolver() (line 86)

What do we use?

• Radau
• Could be another implicit ODE solver e.g. Runge-Kutta