The heterogeneous multiscale method*

IF 16.3 1区数学 Q1 MATHEMATICS

Acta Numerica Pub Date : 2012-04-19 DOI:10.1017/S0962492912000025

A. Abdulle, E. Weinan, B. Engquist, E. Vanden-Eijnden

引用次数: 562

Abstract

The heterogeneous multiscale method (HMM), a general framework for designing multiscale algorithms, is reviewed. Emphasis is given to the error analysis that comes naturally with the framework. Examples of finite element and finite difference HMM are presented. Applications to dynamical systems and stochastic simulation algorithms with multiple time scales, spall fracture and heat conduction in microprocessors are discussed.

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非均质多尺度方法*

本文综述了异构多尺度方法(HMM)这一设计多尺度算法的通用框架。重点放在框架自然产生的错误分析上。给出了有限元和有限差分HMM的实例。讨论了微处理器在动态系统、多时间尺度随机模拟算法、小碎裂和热传导等方面的应用。

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

Acta Numerica MATHEMATICS-

CiteScore

26.00

自引率

0.70%

发文量

期刊介绍： Acta Numerica stands as the preeminent mathematics journal, ranking highest in both Impact Factor and MCQ metrics. This annual journal features a collection of review articles that showcase survey papers authored by prominent researchers in numerical analysis, scientific computing, and computational mathematics. These papers deliver comprehensive overviews of recent advances, offering state-of-the-art techniques and analyses. Encompassing the entirety of numerical analysis, the articles are crafted in an accessible style, catering to researchers at all levels and serving as valuable teaching aids for advanced instruction. The broad subject areas covered include computational methods in linear algebra, optimization, ordinary and partial differential equations, approximation theory, stochastic analysis, nonlinear dynamical systems, as well as the application of computational techniques in science and engineering. Acta Numerica also delves into the mathematical theory underpinning numerical methods, making it a versatile and authoritative resource in the field of mathematics.