Parallel IQMR method for unsymmetric large and sparse linear systems in computational fluid dynamics

We mainly examine the application of the improved version of the quasi-minimal residual (IQMR) method [20, 21] for the solutions of linear systems of equations with unsymmetric coefficient matrices arising from the discretization of fluid dynamic problems on massively parallel distributed memory computers. We will deal with implicit finite difference schemes for solving the Euler equations. These schemes may arise from the implicit treatment of the time dependent equations or from the use of Newton's method for the solution of the steady state equations. In both situations it is very necessary to solve a large and sparse unsymmetric linear systems at each iteration. We will examine the effectiveness of IQMR in the solution of these systems. We compared the resulting method to some existed approaches by numerical experimental results carried out on massively parallel distributed memory computer Parsytec GC/PowerPlus. Our goal is to shout that the IQMR method is a more efficient alternative for solving implicit computational fluid dynamics problems.