The heterogeneous multiscale methods
type: Item
instance of: scholarly article
title: The heterogeneous multiscale methods
zbMATH Open document ID: 1093.35012
published in: Communications in Mathematical Sciences
publication date: 2006-02-08T00:00:00Z
full work available at URL: https://projecteuclid.org/euclid.cms/1118150402
review text: A general methodology is presented to discuss and develop the heterogeneous multiscale method for the numerical computation of problems on heterogeneous media. The traditional approach for such problems is to obtain either analytically or empirically explicit equations for the scale of interest, eliminating other scales in the problem. In this paper, the authors present a general framework for designing and analysing numerical methods that deal with variational and dynamic problems. An efficient usage is made of the macroscopic and microscopic formulations to cover many of the existing methods but also to derive new technique from the general formulation. Application to problems such as homogenization, molecular dynamics, kinetic models and interfacial dynamics are discussed.
Mathematics Subject Classification ID: 35B27
Mathematics Subject Classification ID: 35J20
Mathematics Subject Classification ID: 74Q05
Mathematics Subject Classification ID: 76N25
Mathematics Subject Classification ID: 35F20
Mathematics Subject Classification ID: 65J05
Mathematics Subject Classification ID: 76M25
Mathematics Subject Classification ID: 76M50
zbMATH DE Number: 5004827
zbMATH Keywords: heterogeneous media
zbMATH Keywords: homogenization
zbMATH Keywords: multiscale methods
zbMATH Keywords: molecular dynamics
zbMATH Keywords: kinetic models
zbMATH Keywords: interfacial dynamics
author: Weinan E
author: Björn Engquist
reviewed by: Marco Codegone
MaRDI profile type: Publication
OpenAlex ID: W1990157709
DOI: 10.4310/CMS.2003.V1.N1.A8
description: scientific article; zbMATH DE number 5004827