Summary: Implicit­Explicit Parallel Asynchronous Solver of Parabolic
PDEs
Dganit Amitai \Lambda Amir Averbuch y Moshe Israeli y Samuel Itzikowitz z
Abstract
This paper presents a method for the solution of parabolic PDEs on parallel com­
puters, which is a combination of implicit and explicit finite difference schemes based on
a domain decomposition (DD) strategy. Moreover, this method is asynchronous (i.e.,
no explicit synchronization is required among processors). We determine the values at
sub­domains' boundaries by our new high­order asynchronous explicit schemes. Then,
any known high­order implicit finite difference scheme can be applied within each sub­
domain. We present a technique for derivation of appropriate asynchronous­explicit
schemes based on Green's functions. Synchronous versions of these schemes are ob­
tained as special cases. The applicability of this method is also demonstrated for a
family of non­linear problems.
Our new explicit schemes are of high­order and yet stable for a large time step,
as established in our analysis of their numerical properties. Moreover, these schemes
provide attractive properties for parallel implementation. Being asynchronous, they
allow local time stepping, thus eliminating the need for a global synchronized time
step. Moreover, our asynchronous computation is time­stabilizing, in the sense that the
calculation implicitly prevents a growing time gap between neighboring sub­domains.

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

Collections: Computer Technologies and Information Sciences