Generic elliptic solver

Notes

Requirements:

• Steve: FunWave, need parallelism and mesh refinement;
• Ian: 6-variable, linear elliptic equation, need mesh refinement and perhaps parallelism;
• Eloisa: generic solver, easy to use and to experiment with more important than efficiency, no restriction on topology, mesh refinement would be good but doesn't need it for everything;

Existing tools:

• Scott's elliptic solver, second order with extension to fourth order coming soon; integrate with Cactus via own data conversions, but currently making it talk to Carpet. Available immediately via SVN;
• Eloisa has experimented with OpenFOAM: nice and flexible, not great for accuracy, need to import data to Cactus afterwards (not complicated, but unfeasible to do at each timestep).
• Current CactusElliptic: EllBase gives interface to register elliptic solvers, currently not much implemented (SOR), equation type is a little restrictive (linear), compatibility with AMR unknown;
• CarpetPETSc?
• Existing implementations:
  • TwoPunctures;
  • NoExcision;
  • Kranc-generated Laplace solver via relaxation;
  • BAM_Elliptic;

Possible directions: