The properties of the blocked RIBLU(
) preconditioner depend on the
parameter 
.
Figure 7 shows the effect of the 
parameter on
convergence of domain decomposition for the momentum and pressure equations
for the Poisseuille flow problem.
Figure 7: Effect of the 
parameter
using the RIBLU(
)
preconditioner on the reduction factor: (a) Momentum and (b) Pressure equations
Figure 7 confirms
the observation in [9] that
with standard ILU preconditioning (RILU(
)), the number of iterations
shows a relatively small increase when the number of subdomains is increased.
Larger values of 
can have a significant effect on
convergence, but this effect diminishes rapidly as more subdomains are used.
Clearly, varying the 
parameter for multi-domain problems has
a much lower influence on convergence than for single-domain problems.
Also, the optimal value of 
is lower for multi-domain problems.