Asymptotic expansions for high-contrast elliptic equations
In this paper, we present a high-order expansion for elliptic equations in high-contrast media. The background conductivity is taken to be one and we assume the medium contains high (or low) conductivity inclusions. We derive an asymptotic expansion with respect to the contrast and provide a procedu...
| Main Authors: | , , |
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| Format: | Journal Article |
| Published: |
2014
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| Online Access: | http://hdl.handle.net/20.500.11937/51549 |
| _version_ | 1848758725466128384 |
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| author | Calo, Victor Efendiev, Y. Galvis, J. |
| author_facet | Calo, Victor Efendiev, Y. Galvis, J. |
| author_sort | Calo, Victor |
| building | Curtin Institutional Repository |
| collection | Online Access |
| description | In this paper, we present a high-order expansion for elliptic equations in high-contrast media. The background conductivity is taken to be one and we assume the medium contains high (or low) conductivity inclusions. We derive an asymptotic expansion with respect to the contrast and provide a procedure to compute the terms in the expansion. The computation of the expansion does not depend on the contrast which is important for simulations. The latter allows avoiding increased mesh resolution around high conductivity features. This work is partly motivated by our earlier work in [Domain decomposition preconditioners for multiscale flows in high-contrast media, Multiscale Model Simul. 8 (2010) 1461-1483] where we design efficient numerical procedures for solving high-contrast problems. These multiscale approaches require local solutions and our proposed high-order expansion can be used to approximate these local solutions inexpensively. In the case of a large-number of inclusions, the proposed analysis can help to design localization techniques for computing the terms in the expansion. In the paper, we present a rigorous analysis of the proposed high-order expansion and estimate the remainder of it. We consider both high-and low-conductivity inclusions. © 2014 World Scientific Publishing Company. |
| first_indexed | 2025-11-14T09:48:33Z |
| format | Journal Article |
| id | curtin-20.500.11937-51549 |
| institution | Curtin University Malaysia |
| institution_category | Local University |
| last_indexed | 2025-11-14T09:48:33Z |
| publishDate | 2014 |
| recordtype | eprints |
| repository_type | Digital Repository |
| spelling | curtin-20.500.11937-515492017-09-13T15:35:58Z Asymptotic expansions for high-contrast elliptic equations Calo, Victor Efendiev, Y. Galvis, J. In this paper, we present a high-order expansion for elliptic equations in high-contrast media. The background conductivity is taken to be one and we assume the medium contains high (or low) conductivity inclusions. We derive an asymptotic expansion with respect to the contrast and provide a procedure to compute the terms in the expansion. The computation of the expansion does not depend on the contrast which is important for simulations. The latter allows avoiding increased mesh resolution around high conductivity features. This work is partly motivated by our earlier work in [Domain decomposition preconditioners for multiscale flows in high-contrast media, Multiscale Model Simul. 8 (2010) 1461-1483] where we design efficient numerical procedures for solving high-contrast problems. These multiscale approaches require local solutions and our proposed high-order expansion can be used to approximate these local solutions inexpensively. In the case of a large-number of inclusions, the proposed analysis can help to design localization techniques for computing the terms in the expansion. In the paper, we present a rigorous analysis of the proposed high-order expansion and estimate the remainder of it. We consider both high-and low-conductivity inclusions. © 2014 World Scientific Publishing Company. 2014 Journal Article http://hdl.handle.net/20.500.11937/51549 10.1142/S0218202513500565 restricted |
| spellingShingle | Calo, Victor Efendiev, Y. Galvis, J. Asymptotic expansions for high-contrast elliptic equations |
| title | Asymptotic expansions for high-contrast elliptic equations |
| title_full | Asymptotic expansions for high-contrast elliptic equations |
| title_fullStr | Asymptotic expansions for high-contrast elliptic equations |
| title_full_unstemmed | Asymptotic expansions for high-contrast elliptic equations |
| title_short | Asymptotic expansions for high-contrast elliptic equations |
| title_sort | asymptotic expansions for high-contrast elliptic equations |
| url | http://hdl.handle.net/20.500.11937/51549 |