Domain Decomposed Preconditioners with
          Krylov Subspace Methods as Subdomain Solves

                       Michael Pernice

                Utah Supercomputing Institute
                      University of Utah
                 Salt Lake City, Utah 84112
                usimap@sneffels.usi.utah.edu

Domain decomposed preconditioners for nonsymmetric partial
differential equations typically employ exact subdomain solves.
Iterative methods for subdomain problems require less storage and
allow flexibility in specifying accuracy on the subdomains.
Substantial savings in solution time is possible if the effectiveness
of the domain decomposed preconditioner is not reduced by lower
accuracy subdomain solutions.  Numerical experiments compare the
overall iteration count as the accuracy of the subdomain solutions is
varied.  The results demonstrate that the strategy is effective even
for low accuracy subdomain solutions.