Parallel multilevel iterative methods Original Research Article

For large-scale system of linear equations with symmetric positive definite block coefficient matrix resulting from the discretization of a self-adjoint elliptic boundary-value problem, by making use of blocked multilevel iteration we construct preconditioning matrices for the coefficient matrix and set up a class of parallel multilevel iterative methods for solving such system. Theoretical analysis shows that besides lending themselves to strongly parallel computation these new methods have convergence rates independent of both the sizes and the level numbers of the grids, and their computational work loads are also bounded by linear functions about the step sizes of the finest grids.