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A Multiscale Finite Element Method For Elliptic Problems In Composite Materials And Porous Media (1997)
| Venue: | JOURNAL OF COMPUTATIONAL PHYSICS |
| Citations: | 307 - 26 self |
BibTeX
@ARTICLE{Hou97amultiscale,
author = {Thomas Y. Hou and Xiao-hui Wu},
title = {A Multiscale Finite Element Method For Elliptic Problems In Composite Materials And Porous Media},
journal = {JOURNAL OF COMPUTATIONAL PHYSICS},
year = {1997},
volume = {134},
pages = {169--189}
}
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Abstract
In this paper, we study a multiscale finite element method for solving a class of elliptic problems arising from composite materials and flows in porous media, which contain many spatial scales. The method is designed to efficiently capture the large scale behavior of the solution without resolving all the small scale features. This is accomplished by constructing the multiscale finite element base functions that are adaptive to the local property of the differential operator. Our method is applicable to general multiple-scale problems without restrictive assumptions. The construction of the base functions is fully decoupled from element to element; thus, the method is perfectly parallel and is naturally adapted to massively parallel computers. For the same reason, the method has the ability to handle extremely large degrees of freedom due to highly heterogeneous media, which are intractable by conventional finite element (difference) methods. In contrast to some empirical numerical ...
Keyphrases
multiscale finite element method composite material porous medium elliptic problem base function conventional finite element many spatial scale multiscale finite element base function heterogeneous medium differential operator restrictive assumption large degree local property large scale behavior general multiple-scale problem parallel computer small scale feature
