Summary: A Survey of Asynchronous Finite­Difference Methods
for Parabolic PDEs on Multiprocessors \Lambda
appeared in Applied Numerical Methods, Vol 12, pp. 27­45, May 1993
D. Amitai y , A. Averbuch y , M. Israeli z , S. Itzikowitz y
E. Turkel y
y School of Mathematical Sciences, Tel Aviv University, Tel Aviv 69978, Israel
z Faculty of Computer Science, Technion, Haifa 32000,Israel
Abstract
A major obstacle to achieving significant speed­up on parallel machines is the over­
head associated with synchronizing the concurrent processes. Removing the synchro­
nization constraint has the potential of speeding up the computation. Recently de­
veloped asynchronous finite­difference schemes for parabolic PDEs designed for par­
allel computation are surveyed. Specifically, we consider the asynchronous (AS),
corrected­asynchronous (CA), time­stabilizing (TS), parametric (PAR) and hybrid
(HYB) schemes. The AS scheme is applicable only to steady­state problems. AS,
CA and TS provide first­order spatial approximations. TS, however, minimizes the
first order errors by maintaining the time­stabilizing property which also enables it to
be implemented on parallel machines in which some processors have persistent speed
differences. The PAR algorithm gives a second­order approximation is inefficient. The
HYB algorithms are high­order schemes which have the potential to be applicable also

Source: Averbuch, Amir - School of Computer Science, Tel Aviv University

Collections: Computer Technologies and Information Sciences