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.