A preconditioner based on low-rank approximation of Schur complements
We introduce a preconditioner based on low-rank compression of Schur complements. The construction is inspired by standard nested-dissection and relies on the as- sumption that the Schur complements can be approximated to high precision by Hierarchical-Block-Separable matrices. We build the preconditioner as an approxi- mate LDMt factorization of a given matrix A, and no knowledge of A in assembled form is required by the construction. The LDMt is amenable to fast inversion and the inverse can be applied fast as well. We investigate the behavior of the precondi- tioner in the context of DG finite element approximations of elliptic and hyperbolic problems.