ABCD-Solver: A hybrid method for solving large sparse linear systems
Résumé
Although current work on direct methods has enabled the solution of very large systems efficiently, there are still applications that can cause problems particularly because of memory requirements. On the other hand, iterative methods can often be very slow to converge even with a good preconditioner. We are thus drawn to examine techniques that combine the best features of both approaches, and we term these hybrid methods. We look in particular at the Block Cimmino method which is a rather elementary iterativetechnique but can be accelerated in a number of ways. We examine a derivative of thismethod which is effectively a direct method and compare the performance of this against the MUMPS multifrontal solver and Block Cimmino accelerated by block conjugate gra-dients. A major strength of the block Cimmino method is that it is easily parallelizable. We also comment on this aspect of the approach.