I'm using the Pardiso solver in a research code (Fortran90). It has been working quite well, but since I stepped it up a notch recently it has been giving me a few failures of the type "Zero pivot, numerical factorization or iterative refinement problem", i.e. errmsg = -4.
The problem I wish to solve is a structurally symmetric (real)linear system with a single rhs. However, I use mtype = 11 due to recommendations from Konstantin Arturov in previous thread. I have Lagrange multipliers in my problem so there are a few zeros on the diagonal, whichI store explicitly. The problem size differs, but is on the order of 20k-100k number of equations, where about 0.25%-2.5% of these are Lagrange constraint(multiplier) equations. The resulting number of non-zerosis typically about 1-5 million, so it is not a crazy huge problem, but not in anyway tiny either.
I suspect that my system matrix may be quite ill-conditioned. (Is there any good way to determine that?) I have been using the solver defaults, i.e.iparm(1) = 0. Since my linear algebra skills are not as sharp as I would like, and my knowledge of sparse matrix methods areclose tonon-existant I was hoping to get some pointers as to what I may try to change in the settings to make this problem go away?