  This paper introduces a new preconditioning technique that is suitable for
matrices arising from the discretization of a system of PDEs on unstructured
grids. The preconditioner satisfies a so-called filtering property, which
ensures that the input matrix is identical with the preconditioner on a given
filtering vector. This vector is chosen to alleviate the effect of low
frequency modes on convergence and so decrease or eliminate the plateau which
is often observed in the convergence of iterative methods. In particular, the
paper presents a general approach that allows to ensure that the filtering
condition is satisfied in a matrix decomposition. The input matrix can have an
arbitrary sparse structure. Hence, it can be reordered using nested dissection,
to allow a parallel computation of the preconditioner and of the iterative
process.
