Solving Irregular Sparse Linear Systems On A Multicomputer Using The CGNR Method

. The efficient solution of irregular sparse linear systems on a distributed memory parallel computer is still a major challenge. Direct methods are concerned with unbalanced load processing or data distribution as well as difficulties pertaining to reuse efficient sequential codes. Iterative methods of the Krylov family are well suited for parallel computing but can provide disappointing convergence for general sparse problems. Therefore finding efficient parallel preconditioners is often required to obtain acceptable convergence rates. In this paper we explore the use of a preconditioned Conjugate Gradient algorithm for the parallel solution of irregular sparse nonsymmetric systems. A first step is the choice of a high quality algorithm for matrix partitioning. For this purpose we have selected the Metis package, developed by Karypis and Kumar of the University of Minnesota. A second step is the choice of the preconditioner. We have selected the Block Jacobi preconditioner for its in..