Multiscale asymptotic analysis and parallel algorithm of parabolic equation in composite materials
type: Item
instance of: scholarly article
title: Multiscale asymptotic analysis and parallel algorithm of parabolic equation in composite materials
zbMATH Open document ID: 1407.74093
DOI: 10.1155/2014/217869
author: Xin Wang
author: Xi-liang Duan
author: Yang Gao
published in: Mathematical Problems in Engineering
publication date: 2019-02-08T00:00:00Z
review text: Summary: An efficient parallel multiscale numerical algorithm is proposed for a parabolic equation with rapidly oscillating coefficients representing heat conduction in composite material with periodic configuration. Instead of following the classical multiscale asymptotic expansion method, the Fourier transform in time is first applied to obtain a set of complex-valued elliptic problems in frequency domain. The multiscale asymptotic analysis is presented and multiscale asymptotic solutions are obtained in frequency domain which can be solved in parallel essentially without data communications. The inverse Fourier transform will then recover the approximate solution in time domain. Convergence result is established. Finally, a novel parallel multiscale FEM algorithm is proposed and some numerical examples are reported.
Mathematics Subject Classification ID: 74S05
Mathematics Subject Classification ID: 65M80
Mathematics Subject Classification ID: 35Q74
Mathematics Subject Classification ID: 35B27
Mathematics Subject Classification ID: 35K20
zbMATH DE Number: 7015929
Wikidata QID: Q59063934
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1155/2014/217869
OpenAlex ID: W2006294612
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description: scientific article; zbMATH DE number 7015929