Supernodes ordering to enhance Block Low-Rank compression in sparse direct solvers

In this talk, we present new ordering heuristics to perform block low-rank clustering in supernodes issued from the nested dissection. As kway partitioning within supernodes does not take into account interactions between supernodes, there is room to improve compression rates. We combine kway partitioning with a reordering strategy that aims at minimizing the number of off-diagonal blocks in the symbolic structure and show that both methods are limited. In addition, we propose a selection of some non-compressible vertices to handle the corresponding blocks in full-rank and reduce the burden on managing low-rank blocks with high ranks.

Conference paper