α-GMRES: A New Parallelizable AIterative Solver for Large Sparse Nonsymmetric Linear Systems Arising from CFD. G.U. Aero Report 9110

Linearization of the non-linear systems arising from fully implicit schemes in computational fluid dynamics often result in a large sparse non-symmetric linear system. Practical experience shows that these linear systems are ill-conditioned if a higher than first order spatial discretization scheme is used. To solve these linear systems, an efficient multilevel iterative method, the a-GMRES method, is proposed which incorporates a diagonal preconditioning with a damping factor a so that a balanced fast convergence of the inner GMRES iteration and the outer damping loop can be achieved. With this simple and efficient preconditioning and damping of the matrix, the resulting method can be effectively parallelized. The parallelization maintains the effectiveness of the original scheme due to the algorithm equivalence of the sequential and the parallel versions