A new class of asynchronous iterative algorithms with order intervals

Abstract

Abstract. This paper deals with a new class of parallel asynchronous iterative algorithms for the solution of nonlinear systems of equations. The main feature of the new class of methods presented here is the possibility of flexible communication between processors. In particular partial updates can be exchanged. Approximation of the associated fixed point mapping is also considered. A detailed convergence study is presented. A connection with the Schwarz alternating method is made for the solution of nonlinear boundary value problems. Computational results on a shared memory multiprocessor IBM 3090 are briefly presented.

Asynchronous Power Flow on Graphic Processing Units

“…Accordingly, using shared memory in the proposed method increases the delay between threads, which affects convergence as discussed in Section III-C. The point where shared memory usage brings performance improvement is highly dependent of the problem parameters and setting this point could benefit from previous research conducted on flexible communication [20].…”

Parallel Scientific Computing on Loosely Coupled Networks of Computers

“…However, only the most recent information is included at the start of the next iteration step. Other kinds of asynchronous communication are possible [4,5,19,31,36]. For example, there exists asynchronous iterative methods that immediately incorporate newly received information.…”

Communication Study and Implementation Analysis of Parallel Asynchronous Iterative Algorithms on Message Passing Architectures

“…Classical asynchronous iterations (AI) (see [12], [1], [3] and [17]) are first considered, then, the section deals with a recent extension: flexible asynchronous iterations (FAI) (see [13] and [18] [3]) or chaotic iterations in the bounded delay context (see [4]) have been designed for a large number of applications including solution of discretized partial differential equations, optimization and optimal control, (see for example [8], [16] and [17]); their convergence has been studied in different contexts such as contraction and partial ordering (see [2], [7], [9], [14] and [17] The restrictions imposed to AI are very weak: no blockcomponent (or component) of the iterate vector is abandoned forever and more and more recent updates of the components have to be used as the computation progresses. The advantages of AI are computation flexibility, tolerance to problem data changes (the algorithm adapts itself to a modified environment) and fault tolerance (the algorithm can work well even if some data are lost or some processors fail).…”

“…flexible asynchronous iterations (FAI). For more details on FAI, the reader is referred to [11] to [13], see also [18].…”

“…In particular, parallel asynchronous iterative methods have been studied extensively (see for example [2], [3], [7], [9], [11], [13], [14], [18] and [20]). Asynchronous iterative algorithms were shown to be more efficient then their synchronous counterpart for many applications including optimization (see [9] and [13]) and numerical simulation (see for example: [18]). Today, the features of asynchronous algorithms such as: lack of synchronization, tolerance to problem data changes, fault tolerance, and flexibility make them very attractive for Grid computing, global computing and peer to peer computing.…”