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Multiscale finite element for problems with highly oscillatory coefficients

Efendiev, Yalchin R. and Wu, Xiao-Hui (2002) Multiscale finite element for problems with highly oscillatory coefficients. Numerische Mathematik, 90 (3). pp. 459-486. ISSN 0029-599X. doi:10.1007/s002110100274. https://resolver.caltech.edu/CaltechAUTHORS:20200320-084023593

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Abstract

In this paper, we study a multiscale finite element method for solving a class of elliptic problems with finite number of well separated scales. The method is designed to efficiently capture the large scale behavior of the solution without resolving all 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. 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. We present the convergence analysis of the method along with the results of our numerical experiments. Some generalizations of the multiscale finite element method are also discussed.


Item Type:Article
Related URLs:
URLURL TypeDescription
https://doi.org/10.1007/s002110100274DOIArticle
https://rdcu.be/b288KPublisherFree ReadCube access
ORCID:
AuthorORCID
Efendiev, Yalchin R.0000-0001-9626-303X
Additional Information:© 2001 Springer-Verlag. Received April 17, 1998; Revised version received March 25, 2000; Published online June 7, 2001. We are grateful to Professor Thomas Y. Hou and Dr. Yu Zhang for reading the manuscript and for many interesting and helpful discussions. We also would like to thank Caltech HPCC for providing the parallel computing resource. This work is supported in part by ONR under the grant N00014-94-0310, by DOE under the grant DEFG03-89ER25073, and by NSF under the grant DMS-9704976.
Funders:
Funding AgencyGrant Number
Office of Naval Research (ONR)N00014-94-0310
Department of Energy (DOE)DE-FG03-89ER25073
NSFDMS-9704976
Issue or Number:3
Classification Code:Mathematics Subject Classification (1991): 65N30
DOI:10.1007/s002110100274
Record Number:CaltechAUTHORS:20200320-084023593
Persistent URL:https://resolver.caltech.edu/CaltechAUTHORS:20200320-084023593
Official Citation:Efendiev, Y., Wu, X. Multiscale finite element for problems with highly oscillatory coefficients. Numer. Math. 90, 459–486 (2002). https://doi.org/10.1007/s002110100274
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:102017
Collection:CaltechAUTHORS
Deposited By: Tony Diaz
Deposited On:20 Mar 2020 15:46
Last Modified:16 Nov 2021 18:08

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