An Incomplete Factorization Preconditioner
Based on a Non-Overlapping
Domain Decomposition Data Distribution

Gundolf Haase

Johannes Kepler University
Institut fur Mathematik 
A-4040 Linz, Altenbergerstrasse 69, Austria                     

INSTITUT FUR MATHEMATIK 
A-4040 LINZ, ALTENBERGERSTRASSE 69, AUSTRIA                  
Institutsbericht Nr. 510 Dezember 1996

December 10, 1996

Abstract

The paper analyzes various parallel matrix-vector multiplications with
different matrix and vector types resulting from a non-overlapping domain
decomposition.  Under certain requirements to the f.e. mesh all given matrix
and vector types can be used in the multiplication.  The general framework
is applied to the investigation of the preconditioning step in cg-like
methods.  Not only the well-known domain decomposition preconditioners fit
into the concept but also parallelized global incomplete factorizations
are feasible.  Additionally, those global incomplete factorizationscan can be
used as smoothers in global multilevel methods.  Numerical results on a SPMD
parallel machine are presented.

Keywords :  Parallel iterative solvers, Incomplete Factorization,
Preconditioning, Domain decomposition, Finite element method.