PARALLEL HYBRID ALGEBRAIC MULTILEVEL ITERATIVE METHODS

For the large-scale system of linear equations with symmetric positive definite block coefficient matrix resulting from the discretization o f a self-adjoint elliptic boundary-value problem, by making use of the blocked multilevel iteration idea, we construct preconditioning matri ces for the coefficient matrix and set up a class of parallel hybrid a lgebraic multilevel iterative methods for solving this kind of system of linear equations. Theoretical analysis shows that not only do these new methods lend themselves to parallel computation, but also their c onvergence rates are independent of both the sizes and the level numbe rs of the grids, and their computational work loads are also hounded b y linear functions of the step sizes of the finest grids. (C) 1997 Els evier Science Inc.