Abstract

This paper is concerned with the distri uted parallel computation of an ordering for a symmetric positive de nite sparse matrix. The purpose of the ordering is to limit ll and enhance concurrency in the su se uent computation of the Cholesky factori ation of the matrix. We use a geometric approach to nested dissection ased on a given Cartesian em edding of the graph of the matrix in Euclidean space. The resulting algorithm can e implemented e ciently on massively parallel, distri uted memory computers. ne unusual feature of the distri uted algorithm is that its effectiveness does not depend strongly on data locality, which is critical in this context, since an appropriate partitioning of the pro lem is not known until after the ordering has een determined. The ordering algorithm is the rst component in a suite of scala le parallel algorithms currently under development for solving large sparse linear systems on massively parallel computers.

Citations