Block Low-rank Algebraic Clustering for Sparse Direct Solvers

International audienceWe will discuss challenges in building clusters for the Block Low-Rank (BLR) approach, for nodes inside separators appearing during the factorization of sparse matrices. We will illustrate limitations for methods that consider only intra-separators connectivity (i.e., k-way and recursive bisection) as well as methods focusing only on reducing the number of updates between separators. The new strategy we propose considers interactions between a separator and its children in the nested dissection. It allows reducing the computational cost of BLR, and the number of off-diagonal blocks. We demonstrate that this method enhances the BLR strategies in the sparse direct supernodal solver PaStiX, and discuss how it can be extended to low-rank formats with more than one level of hierarchy