Comparison of Iterative Solvers for Non-Symmetric Linear Systems in Porous Media Problems

Abstract

We investigate the performance of the IDR(s)-algorithms when solving nonsymmetric systems in porous media problems. We derive a mathematical model for the flow in porous media, and discretized this with the method known as Two-Point Flux-Approximation. By altering the permeability distribution and the grid size we design a series of systems with different sizes and properties. These systems have then been solved with IDR(s), using two different preconditioners, and the results have been compared against the popular GMRES. We shall see that the short recurrence algorithm of IDR(s) appears in our cases to be an attractive alternative, compared to GMRES. Especially in the cases where both methods require a large number of iterations to solve the system shall we see the IDR(s) algorithm excel. However, we also encounter badly conditioned systems where the stability of the IDR(s) is not as good as GMRES. This study is however not exhaustive, and more studies are need to identify under which conditions IDR(s) loses its stability. When this is identified, IDR(s) should after my consideration be considered as an attractive method for solving non-symmetric systems of linear equations in porous media problems.