1Parallel Multilevel Iterative Linear Solvers for Large-Scale Computation

Preconditioned iterative solver is one of the most powerful choice such as IC (Incomplete Cholesky) or ILU (Incomplete LU) factorization method for large-scale scientific computation. But in these methods, iteration number until con-vergence increases as the problem size becomes larger. In multigrid solvers, the rate of convergence is independent of problem size and the number of iterations remains fairly constant. Multigrid is also a good preconditioner for Krylov itera-tive solvers. In this study, multigrid preconditioned conjugate gradient iterative method (MGCG) on parallel computers has been developed and applied to the Poisson equation in the region between dual sphere surfaces on semi-unstructured prismatic grids generated adaptively. Moreover this procedure has been also applied to the grids with local refinement