Certain preconditioners were not developed with parallelism in mind,
but they can be executed in parallel. Some examples are domain
decomposition methods (see §
), which
provide a high degree of coarse grained parallelism,
and polynomial preconditioners
(see §), which have the same parallelism as
the matrix-vector product.
Incomplete factorization preconditioners are usually much harder to parallelize: using wavefronts of independent computations (see for instance Paolini and Radicati di Brozolo [170]) a modest amount of parallelism can be attained, but the implementation is complicated. For instance, a central difference discretization on regular grids gives wavefronts that are hyperplanes (see Van der Vorst [205][203]).