Block-ADI Preconditioners for Solving Sparse Nonsymmetric Linear Systems of Equations

There is currently a regain of interest in the Alternating Direction Implicit (ADI) algorithms as preconditioners for iterative methods for solving large sparse linear systems, because of their suitability for parallel computing. However, the classical ADI iteration is not directly applicable to Finite Element (FE) matrices, tends to converge too slowly for 3-D problems, and the selection of adequate acceleration parameters, remains a diicult task. In this paper we propose a Block-ADI approach, which overcomes some of these problems. In particular we derive a simple inexpensive heuristic for selecting the acceleration parameters. The new approach can be viewed as a combination of the classical ADI method and a domain decomposition approach.