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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 ) 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 ).