we are using a first order implicit finite volume code for simulation of incompressible flows. At its core, the code utilizes a (non-preconditioned) GMRES method for solving linear systems given in webpage
In general, it is quite difficult to find an "ideal" setup of the GMRES algorithm for a given problem, i.e. especially to find a suitable size of the maximum Krylov space dimension (inner iterations). I wonder if there are any estimates for determining such parameters beforehand, in order to circumvent some of the trial and error procedure (which is really cumbersome and painful for large problems). Maybe someone can point me to literature where such an issue might be discussed....?
Is there any sparse matrix solver better or other than GMRES?