Iterative linear solver for “ugly” saddle point systemvvpm9AMmWg HOo a7.Mmx30 w X Mmp QSs ygoaCc
I am a graduate student majoring scientific computing. The numeric model I made caused a very ugly-looking saddle-point linear system. It is not symmetric at all and I will attach the sparsity pattern below. So far, I've only dealt with matrices with non-zero diagonal entries, so incomplete LU-type preconditioner with GMRES worked fine. But GMRES tends to converge slowly on this one and even worse, I cannot use any LU type preconditioners.
Could you recommend an iterative linear solver for this problem?
1 Answer
You should stick with GMRES, it is the only method that is essentially guaranteed to get a solution here. The real problem appears to be you need a better preconditioner. You could try sticking with LU but adding a diagonal mass matrix to the system with a constant multiplier that decreases with the linear residual of the system. This would allow you to get closer to the actual system as you solve your modified system. This is essentially a CFL ramping strategy for the linear system and is often used in CFD as part of a dual CFL system, and has some good results for pretty difficult to solve systems.
