Domain oriented analysis of PDE splitting algorithms

Abstract

We consider the performance of Schwarz splitting algorithms for PDE problems on the hypothetical Multi- flex machine. The particular multi- flex considered consists of eight clusters of flex/32 multiprocessors. We introduce the concept of execution domains to model the three levels of memory on these machines: local, locally shared, and global. We apply the method of stochastic high level Petri nets (SHLPN) to model the performance of these PDE splitting algorithms on a Multi- flex machine. For very large, but realistic, applications we project potential speedup of 300 for 2D problems and more for 3D problems along with processor utilization of over 99 percent. Real computations on real machines can fall far short of this potential and still be very successful.