Deciding Non-Compressible Blocks in Sparse Direct Solvers using Incomplete Factorization

Low-rank compression techniques are very promising for reducing memory footprint and execution time on a large spectrum of linear solvers. Sparse direct supernodal approaches are one of these techniques. However, despite providing a very good scalability and reducing the memory footprint, they suffer from an important flops overhead in their unstructured low-rank updates. As a consequence, the execution time is not improved as expected. In this paper, we study a solution to improve low-rank compression techniques in sparse supernodal solvers. The proposed method tackles the overprice of the low-rank updates by identifying the blocks that have poor compression rates. We show that the fill-in levels of the graph based block incomplete LU factorization can be used in a new context to identify most of these non-compressible blocks at low cost. This identification enables to postpone the low-rank compression step to trade small extra memory consumption for a better time to solution. The solution is validated within the PASTIX library with a large set of application matrices. It demonstrates sequential and multi-threaded speedup up to 8.5 ×, for small memory overhead of less than 1.49 × with respect to the original version.