Domain oriented analysis of PDE (partial differential equations) splitting algorithms

The authors consider the performance of Schwarz splitting algorithms for partial differential equation problems on the hypothetical Multi-FLEX machine. The particular multi-FLEX considered consists of eight clusters of FLEX-32 multiprocessors. The concept of execution domains is introduced to model the three levels of memory on these machines: local, locally shared, and global. The method of stochastic high-level Petri nets (SHLPN) is appliedto model the performance of these PDE splitting algorithms on a Multi-FLEX machine. For very large, but realistic, applications potential speedup to 300 for 2D problems and more for 3D problems is projected, along with processor utilization of over 90%. Real computations on real machines can fall far short of this potential and still be very successful.