  We introduce a preconditioner based on a hierarchical low-rank compression
scheme of Schur complements. The construction is inspired by standard nested
dissection, and relies on the assumption that the Schur complements can be
approximated, to high precision, by Hierarchically-Semi-Separable matrices. We
build the preconditioner as an approximate $LDM^t$ factorization of a given
matrix $A$, and no knowledge of $A$ in assembled form is required by the
construction. The $LDM^t$ factorization is amenable to fast inversion, and the
action of the inverse can be determined fast as well. We investigate the
behavior of the preconditioner in the context of DG finite element
approximations of elliptic and hyperbolic problems.
