This section compares accurate with inaccurate solution of subdomain problems.
We consider both the cylinder problem from the previous section and
a Poisseuille flow in a rectangle 
.
The global grid for the cylinder problem consists of 12240 grid cells.
The single-block cylinder grid in Figure 5 consists of
10800 grid cells.
For the Poisseuille problem a Cartesian grid of 
cells
is used.
The subdomain problems are solved using GMRES with RILU(
)
preconditioning [50,48] and a relative
stopping criterion. For 
we get the standard ILU
preconditioner [36]
and for 
we get the Modified ILU preconditioner [27].
RILU(
) [1] lies in between these two.
With RILUD(
) we mean RILU(
) restricted to the diagonal.
The momentum equations are solved using
a RILUD(
preconditioner and the pressure equations using a
RILU(
). As a short-hand, we will use RILU(
) to mean
RILUD(
) whenever the momentum, and RILU(
) whenever the
pressure equations are involved.
The subdomain solution accuracy is varied. As a special
case the subdomain solution is approximated by means of the inverse of the
RILU(
) [20,50,48] preconditioner, thereby omitting
GMRES for subdomain solution.
The multi-block problem (the outer loop)
is solved up to a relative accuracy of 
.
In all experiments a Krylov space of dimension 20 is used for both
GMRES and GCR multi-block acceleration and for GMRES subdomain solution.
GMRES always uses a restart after 20 iterations. With GCR, we
investigate both optimized restart, denoted by GCR (restart), and truncation,
denoted by GCR (trunc).
Iteration counts and computing times are given in the tables in the
form time(iteration count). The iteration counts and times are summed over
all time steps taken (10 time steps are used in all examples).
The experiments are run on a HP9000/735 workstation.
In most of the experiments, the multiplicative algorithm is used.
Only section 6.4 examines the additive algorithm.
Section 6.1 examines the effect of lowering the accuracy of
the subdomain solution on the number of iterations and total computing time.
Section 6.2 compares single-block solution time with
multi-block solution time.
Section 6.3 examines the effect of the 
parameter
in the subdomain RILU(
) preconditioner on convergence using the
RIBLU(
) postconditioner.