On the Uniqueness of Stationary Solutions of an Asynchronous Parallel and Distributed Algorithm for Diffusion Equations

In this paper, we study the uniqueness of stationary solutions of an asynchronous parallel and distributed algorithm for diffusion equations. In the literature, it has been reported that asynchronous stationary solutions can be affected by randomness of asynchrony, leading to variations in solutions...

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Bibliographic Details
Published in:2019 IEEE 9th Annual Computing and Communication Workshop and Conference (CCWC) pp. 0062 - 0068
Main Authors: Lee, Kooktae, Bhattacharya, Raktim
Format: Conference Proceeding
Language:English
Published: IEEE 01.01.2019
Subjects:
Asynchronous Parallel and Distributed Algorithm
Boundary conditions
Diffusion Equations
Distributed computing
Mathematical model
Stochastic processes
Switched systems
Switches
Synchronization
Unique Stationary Solution
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Summary:In this paper, we study the uniqueness of stationary solutions of an asynchronous parallel and distributed algorithm for diffusion equations. In the literature, it has been reported that asynchronous stationary solutions can be affected by randomness of asynchrony, leading to variations in solutions. The uniqueness in this context implies that the stationary solutions obtained by asynchronous communications between parallel and distributed computing devices are the same as the synchronous one, regardless of asynchrony. In some applications, inexact stationary solutions as an outcome of asynchrony may result in serious consequences. Therefore, it is critical to guarantee the existence of the unique stationary solution for a given problem. As a case study, we analyze the uniqueness of stationary solutions for diffusion equations with a fixed boundary condition, by employing the dynamical system framework and nonnegative matrix theory. The numerical results are presented to validate the proposed method with performance analysis of the asynchronous parallel and distributed algorithm.
DOI:10.1109/CCWC.2019.8666522