In this talk, we present the PaStiX sparse supernodal solver, using hierarchical compression to reduce the burden on large blocks appearing during the nested dissection process. We compare the numerical stability, and the performance in terms of memory consumption and time to solution of different approaches by selecting when the compression of the factorized matrix occurs. In order to improve the efficiency of the sparse update kernel for both BLR (block low rank) and HODLR (hierarchically off-diagonal low-rank), we investigate the BDLR (boundary distance low-rank) method to preselect rows and columns in the low-rank approximation algorithm.