Preconditioning By Incomplete Block Cyclic Reduction

Iterative methods for solving linear systems arising from the discretization of elliptic/parabolic partial differential equations require the use of preconditioners to gain increased rates of convergence. Preconditioners arising from incomplete factorizations have been shown to be very effective. However, the recursiveness of these methods can offset these gains somewhat on a vector processor. In this paper, an incomplete factorization based on block cyclic reduction is developed. It is shown that under block diagonal dominance conditions the off-diagonal terms decay quadratically, yielding more effective algorithms. Introduction. Iterative methods are frequently used for solving the linear systems arising from the differencing of 2-dimensional elliptic or parabolic partial differential equations, [19]. These systems are often very large and take on the structure