Published November 20, 2014
| Published
Journal Article
Open
On the Compressive Spectral Method
- Creators
- Mackey, Alan
- Schaeffer, Hayden
- Osher, Stanley
Chicago
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Abstract
The authors of [Proc. Natl. Acad. Sci. USA, 110 (2013), pp. 6634--6639] proposed sparse Fourier domain approximation of solutions to multiscale PDE problems by soft thresholding. We show here that the method enjoys a number of desirable numerical and analytic properties, including convergence for linear PDEs and a modified equation resulting from the sparse approximation. We also extend the method to solve elliptic equations and introduce sparse approximation of differential operators in the Fourier domain. The effectiveness of the method is demonstrated on homogenization examples, where its complexity is dependent only on the sparsity of the problem and constant in many cases.
Additional Information
© 2014 Society for Industrial and Applied Mathematics. Received by the editors April 23, 2014; accepted for publication (in revised form) September 29, 2014; published electronically November 20, 2014. The first author's research was funded by UC Lab grant 12-LR-236660 and in part by NSF DMS 0907931. The third author's research was supported by ONR grant N00014-11-1-719. This author's research was supported by NSF DMS 1303892 and the University of California President's Postdoctoral Fellowship Program. The authors would like to thank Will Feldman, Inwon Kim, Chris Anderson, and Russel Caflisch for insightful discussions regarding the above.Attached Files
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Additional details
- Eprint ID
- 54288
- Resolver ID
- CaltechAUTHORS:20150202-095600251
- University of California
- 12-LR-236660
- NSF
- DMS-0907931
- Office of Naval Research (ONR)
- N00014-11-1-719
- NSF
- DMS-1303892
- Created
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2015-02-02Created from EPrint's datestamp field
- Updated
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2023-03-02Created from EPrint's last_modified field