Hypergraph-Based Unsymmetric Nested Dissection Ordering for Sparse LU Factorization

In this paper we present HUND, a hypergraph-based unsymmetric nested dissection ordering algorithm for reducing the fill-in incurred during Gaussian elimination. HUND has several important properties. It takes a global perspective of the entire matrix, as opposed to local heuristics. It takes into account the assymetry of the input matrix by using a hypergraph to represent its structure. It is suitable for performing Gaussian elimination in parallel, with partial pivoting. This is possible because the row permutations performed due to partial pivoting do not destroy the column separators identified by the nested dissection approach. The hypergraph nested dissection approach is essentially equivalent to graph nested dissection on the matrix AT A, but we only need the original matrix A and never form the usually denser matrix AT A. Our implementation also uses weighted matching (MC64) and local reordering (CCOLAMD) to further improve the ordering. Experimental results on 27 medium and la...

• Type: Journal
• Year: 2010
• Where: SIAMSC
• Authors: Laura Grigori, Erik G. Boman, Simplice Donfack, Timothy A. Davis
• Keywords: Dissection, Nested, Nested Dissection, SIAMSC 2010