Parallel cloud solution of large algebraic multivalued systems

IF 2.2 2区数学 Q1 MATHEMATICS, APPLIED

Applied Numerical Mathematics Pub Date : 2025-02-01 DOI:10.1016/j.apnum.2024.03.012

M.A. Rahhali , T. Garcia , P. Spiteri

引用次数: 0

Abstract

The present paper deals with the resolution on cloud architecture of synchronous and asynchronous iterative parallel algorithms of stationary or evolution variational inequations formulated by a multivalued model. The performances of synchronous and asynchronous iterative parallel methods are compared with previous ones obtained on cluster or when grid architecture is used. Thanks to the properties of the algebraic systems resulting from problem discretization we are able to analyze the behavior of the iterative algorithm in particular the convergence and the speed of convergence. The implementation of the studied methods on cloud architecture is described. Then we present various applications in particular the solidification of steel in continuous casting, the cavity pressure calculation described by a problem subject to unilateral constraints and finally a financial problem modeled by American option pricing.

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大型代数多值系统的并行云解法

本文论述了在云架构上解决由多值模型制定的静态或演化变分不等式的同步和异步迭代并行算法。同步和异步迭代并行方法的性能与之前在集群上或使用网格架构时获得的性能进行了比较。由于问题离散化产生的代数系统的特性，我们能够分析迭代算法的行为，特别是收敛性和收敛速度。我们介绍了所研究方法在云架构上的实现。然后，我们介绍了各种应用，特别是连铸钢的凝固、单边约束问题描述的空腔压力计算，以及最后以美式期权定价为模型的金融问题。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Applied Numerical Mathematics 数学-应用数学

CiteScore

5.60

自引率

7.10%

发文量

225

审稿时长

7.2 months

期刊介绍： The purpose of the journal is to provide a forum for the publication of high quality research and tutorial papers in computational mathematics. In addition to the traditional issues and problems in numerical analysis, the journal also publishes papers describing relevant applications in such fields as physics, fluid dynamics, engineering and other branches of applied science with a computational mathematics component. The journal strives to be flexible in the type of papers it publishes and their format. Equally desirable are: (i) Full papers, which should be complete and relatively self-contained original contributions with an introduction that can be understood by the broad computational mathematics community. Both rigorous and heuristic styles are acceptable. Of particular interest are papers about new areas of research, in which other than strictly mathematical arguments may be important in establishing a basis for further developments. (ii) Tutorial review papers, covering some of the important issues in Numerical Mathematics, Scientific Computing and their Applications. The journal will occasionally publish contributions which are larger than the usual format for regular papers. (iii) Short notes, which present specific new results and techniques in a brief communication.