Parallel GMRES+LU-SGS method for mixed grids

A parallel matrix-free GMRES+LU-SGS implicit scheme is presented based on mixed grids. LU-SGS method is employed at the beginning process to obtain a better initial solution, and then switched to GMRES method with LU-SGS as preconditioner. To improve convergence efficiency, the CFL number is increased correspondingly to the reduction of the residual. A matrix-free approach is applied to reduce computational and memory cost. OpenMP method based on shared-memory system is used to achieve parallelization, and a special grids grouping method is applied to avoid memory contention. The numerical results demonstrated that the present methods can improve convergence efficiency greatly, produce exactly the same result as single processor case and show good agreement with experiments.