arXiv subjects

Muhammad Hassan

Publications and source records attributed to Muhammad Hassan.

39 records · Page 3Linked to original sources

arXiv2019

On the Scalability of the Parallel Schwarz Method in One-Dimension

In contrast with classical Schwarz theory, recent results in computational chemistry have shown that for special domain geometries, the one-level parallel Schwarz method can be scalable. This property is not true in general, and the issue of quantifying the lack of scalability remains an open problem. Even though heuristic explanations are given in the literature, a rigorous and systematic analysis is still missing. In this short manuscript, we provide a first rigorous result that precisely quantifies the lack of scalability of the classical one-level parallel Schwarz method for the solution to the one-dimensional Laplace equation. Our analysis technique provides a possible roadmap for a systematic extension to more realistic problems in higher dimensions.

math.NA↗

arXiv2019

On the Scalability of the Schwarz Method

In this article, we analyse the convergence behaviour and scalability properties of the one-level Parallel Schwarz method (PSM) for domain decomposition problems in which the boundaries of many subdomains lie in the interior of the global domain. Such problems arise, for instance, in solvation models in computational chemistry. Existing results on the scalability of the one-level PSM are limited to situations where each subdomain has access to the external boundary, and at most only two subdomains have a common overlap. We develop a systematic framework that allows us to bound the norm of the Schwarz iteration operator for domain decomposition problems in which subdomains may be completely embedded in the interior of the global domain and an arbitrary number of subdomains may have a common overlap.

math.NA↗

arXiv2019

The Road Ahead for Networking: A Survey on ICN-IP Coexistence Solutions

In recent years, the current Internet has experienced an unexpected paradigm shift in the usage model, which has pushed researchers towards the design of the Information-Centric Networking (ICN) paradigm as a possible replacement of the existing architecture. Even though both Academia and Industry have investigated the feasibility and effectiveness of ICN, achieving the complete replacement of the Internet Protocol (IP) is a challenging task. Some research groups have already addressed the coexistence by designing their own architectures, but none of those is the final solution to move towards the future Internet considering the unaltered state of the networking. To design such architecture, the research community needs now a comprehensive overview of the existing solutions that have so far addressed the coexistence. The purpose of this paper is to reach this goal by providing the first comprehensive survey and classification of the coexistence architectures according to their features (i.e., deployment approach, deployment scenarios, addressed coexistence requirements and architecture or technology used) and evaluation parameters (i.e., challenges emerging during the deployment and the runtime behaviour of an architecture). We believe that this paper will finally fill the gap required for moving towards the design of the final coexistence architecture.

cs.NI↗