Hierarchical solvers is an approximate sparse direct solver, entirely written in Julia. It can run in superlinear complexity as approximate solver employing lowrank and hierarchically structured low-rank (HSS) matrices to compress Gauss transforms and Schur complements.
Bonev, Boris; Hesthaven, Jan S. "A hierarchical preconditioner for wave problems in quasilinear complexity." Under Review. https://infoscience.epfl.ch/record/279971/files/article.pdf