A major obstacle to achieving significant speed-up on parallel machines is the overhead associated with synchronizing the concurrent processes. Removing the synchronization constraint has the potential of speeding up the computation. Recently developed asynchronous finite-difference schemes for parabolic PDEs designed for parallel computation are surveyed. Specifically, we consider the asynchronous (AS), corrected asynchronous (CA), time stabilizing (TS), parametric (PAR), and hybrid (HYB) schemes. The AS scheme is applicable only to steady-state problems. AS, CA, and TS provide first-order spatial approximations. TS, however, minimizes the first-order errors by maintaining the time stabilizing property which also enables it to be implemented on parallel machines in which some processors have persistent speed differences. The PAR algorithm gives a second-order approximation that is inefficient. The HYB algorithms are high-order schemes which have the potential to be applicable also to nonlinear problems.
Bibliographical noteFunding Information:
Correspondence to: A. Averbuch, School of Mathematical Sciences, Tel Aviv University, Ramat Aviv, Tel Aviv 69978, Israel. * This research was partially supported by a grant from The Basic Research Foundation administrated by The Israel Academy of Sciences and Humanities. *This author was partially supported by the fund for the promotion of research at the Technion.