Proof-of-Principle Calculation for the FANM Method

[sslattery]

A preliminary FANM calculation with the Navier-Stokes equations needs to be completed to ensure that is actually possible. Any problem will do and I will likely choose the therm convection cavity problem already available.

This task is done when a calculation has been completed with a nonlinear Navier-Stokes solve using a Newton method with automated Jacobian generation and MCSA as the linear solver.

[sslattery]

I have Drekar building against MCLS and have run a few natural convection problems with the Richardson solver. Surprisingly, it is actually converging but the iterative performance is poor. Preconditioning this one is tougher, but I've got matlab Jacobians to do some analysis with. For reference, here's the sparsity pattern for a 10x10x10 natural convection cavity:

[sslattery]

ParaSails and ILUT have been working nicely for this problem with respect to the Richardson iteration but MCSA is having issues. I think this is related to how I'm updating the Monte Carlo domain after getting a new Jacobian. If Richardson is converging in about as many iterations per nonlinear iteration as Problem 3 was, then MCSA should be working fine.