Hi Ankit,

I have contacted a friend who suggested some algorithms to try out for solving the linear system:

1. algebraic brute force (does not address the nonlinearity, reported to work on moderately sized problems): gmres with ILU(0) preconditioning.

2. If ILU(0) does not work:

We are solving K*x = b where K has a block structure: K = | A B | | B^T -C | (C can be positive semi-definite or zero - our case)

Instead, an "augmented Lagrangian" technique would lead to Q*x = b with Q = | A + alpha*B*B^t B | | B^T -C | alpha>=0, small

Either the augmented system can be solved, or Q could be used in ILU(0) preconditioner.

3. Ultimately you want to solve a time-dependent problem, so try also the Chorin-Temam projection method [1]. This could be used even for the stationary case by solving in time until a steady state is (hopefully) obtained.

r.

[1] http://en.wikipedia.org/wiki/Projection_method_%28fluid_dynamics%29