Parallel multilevel iterative linear solvers with unstructured adaptive grids for simulations in earth science

摘要

A new multigrid-preconditioned conjugate gradient (MGCG) iterative method for parallel computers is presented. Iterative solvers with preconditioning, such as the incomplete Cholesky or incomplete LU factorization methods, represent some of the most powerful tools for large-scale scientific computation. However, the number of iterations required for convergence by these methods increases with the size of the problem. 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 preconditioning algorithm for Krylov iterative solvers. In this study, the MGCG method is applied to Poisson equations in the region between two spherical surfaces on semi-unstructured, adaptively generated prismatic grids, and to grids with local refinement. Computations using this method on a Hitachi SR2201 with up to 128 processors demonstrated good scalability.