🚀 go-pugleaf

           Department of Computer Science, University of Toronto
            (LP = D. L. Pratt Building, 6 King's College Road)

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                            NUMERICAL ANALYSIS
               LP266, at 10:00 a.m., Friday 16 October 1992

                                Youcef Saad
           Computer Science Department, University of Minnesota

                        "ILUM: a massively parallel
              multi-elimination incomplete LU factorization"

Preconditioned  Krylov subspace  techniques are rapidly gaining ground
against  direct solvers in the solution of large sparse linear systems
arising from 3-dimensional models.  When implementing these methods on
parallel  machines   one  faces  the   difficulty  that  the  standard
preconditioners   are   often   sequential  and   can   cause  serious
bottlenecks. In this talk  we will consider several different  ways of
circumventiong  the  difficulty.  A  new  approach  called  ILUM which
allows  a  high  degree of  parallelism  is presented.  This  approach
consists of  using  an `independent set ordering' to determine all the
unknowns  that can be eliminated simultaeously. Then a reduced  system is
formed  and the process  is recursively repeated a  few  times.  In order
to avoid  a large  amount of  fill-in during  this  elimination process, a
dropping strategy is added  thus  providing  an  incomplete factorization
similar to ILUT and  other  strategies introduced in the literature. A few
preliminary numerical experiments will be presented.