Cleanup of linear solver logic needed

[Anders Logg (Chalmers)]

AL: The naming of linear solvers (direct, iterative, krylov, lu, gmres etc) is somewhat of a jungle and the parameter sets (krylov_solver, lu_solver) must match and do not really correspond to the solvers. This should be discussed on the mailing list and cleaned up (after the release of 1.3).

JB: Yes, there are plenty of defficienscis, for example: When DOLFIN is not compiled with CHOLMOD, then LinearSolver('cholesky') redirects to CholmodCholeskySolver which implements a fallback to UmfpackLUSolver. It should be discussed if LinearSolver('cholesky') should call rather LUSolver with symmetric=True option.

In PETScLUSolver::select_solver there is missing a logic for picking Cholesky-capable (as indicated by PETScLUSolver::_methods_cholesky) solver when symmetric=True.

[Jan Blechta]

I wouldn't hurry with picking Cholesky whenever it could seem favourable. There is a bug in PETSc which affects default Cholesky-capable PETScLUSolver MUMPS. It's fixed but not yet released.

[Prof Garth Wells]

This is a symptom of the GenericFoo interface not being a good design for linear solvers. Solvers are too specialised for a viable and extensive GenericFoo interface.

[Anders Logg (Chalmers)]

I agree that the GenericFoointerface requires quite a bit of stretch to work for solvers.

One option could be to remove all those interfaces to solvers and replace them with PETScLinearSolver etc in combination with the following two important points:

1. Keep the very high level solve()interface to enable solve(A, x, b, "gmres", "ilu")without needing to care about la backend.

2. Allow sending in a Matrix to the specialized solvers which could start by making a dynamic_castto check whether solve is possible and otherwise issue an informative error message.

[Prof Garth Wells]

We could allow the PDE solve function solve(a==L) to optionally take a (non)linear solver. Linear solvers should be able to return a suitable matrix that is assembled into. A user can than set more advanced options on the solver object. This reduces the need for a collection of linear solvers to have an extensive common interface.

[Anders Logg (Chalmers)]

Yes, sounds like a good idea.

[Anders Logg (Chalmers)]

Removing milestone: 1.7 (automated comment)

[Prof Garth Wells]

This is largely complete on the backend side. Needs some polishing.