University of California, Los Angeles Progress Report 95/96


A number of parallel preconditioners have been and are being implemented, for the black box solution of large sparse linear systems, in particular arising from unstructured PDE problems. These can be easily used in standard Krylov subspace methods, such as the method of conjugate gradients, or GMRES.


A first release of ParPre, a package of parallel preconditioners, has been placed in the public domain. Currently released preconditioners are the additive and multiplicative Schwarz methods, with various exact and inexact subdomain solvers, and the Generalised Block SSOR class of preconditioners, which includes classical, sequential, methods such as point SSOR and point ILU, and parallel block generalisations of them involving subdomains.


More parallel preconditioners will be implemented and released, such as Schur complement methods, multi-colour methods, and especially the focus will be on black-box generation of a coarse grid operator. This is generally considered to be the key to (almost) optimal preconditioners.