If all processors execute their part of the preconditioner solve
without further communication, the overall method is technically a
block Jacobi preconditioner (see ยง
).
While their parallel execution is very efficient, they
may not be as effective as more complicated, less parallel
preconditioners, since improvement in the number of iterations
may be only modest.
To get a bigger improvement while retaining the efficient parallel
execution,
Radicati di Brozolo and Robert [178] suggest that one construct
incomplete decompositions on slightly overlapping domains. This requires
communication similar to that for matrix-vector products.