HYPERGRAPH-BASED UNSYMMETRIC NESTED DISSECTION ORDERING FOR SPARSE LU FACTORIZATION Academic Article uri icon

abstract

  • In this paper we discuss a hypergraph-based unsymmetric nested dissection (HUND) ordering for reducing the fill-in incurred during Gaussian elimination. It has several important properties. It takes a global perspective of the entire matrix, as opposed to local heuristics. It takes into account the asymmetry 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 ATA, but we need only the original matrix A and never form the usually denser matrix ATA. The usage of hypergraphs in our approach is fairly standard, and HUND can be implemented by calling an existing hypergraph partitioner that uses recursive bisection. Our implementation uses local reordering constrained column approximate minimum degree (CCOLAMD) to further improve the ordering. We also explain how weighted matching (HSL routine MC64) can be used in this context. Experimental results on 27 medium and large size matrices with highly unsymmetric structures compare our approach to four other wellknown reordering algorithms. The results show that it provides a robust reordering algorithm, in the sense that it is the best or close to the best (often within 10%) of all the other methods, in particular on matrices with highly unsymmetric structures. 2010 Society for Industrial and Applied Mathematics.

published proceedings

  • SIAM JOURNAL ON SCIENTIFIC COMPUTING

author list (cited authors)

  • Grigori, L., Boman, E. G., Donfack, S., & Davis, T. A.

complete list of authors

  • Grigori, Laura||Boman, Erik G||Donfack, Simplice||Davis, Timothy A

publication date

  • January 1, 2010 11:11 AM