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.
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| 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. | |||||||||
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| 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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