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Gamblets for opening the complexity-bottleneck of implicit schemes for hyperbolic and parabolic ODEs/PDEs with rough coefficients

Owhadi, Houman and Zhang, Lei (2017) Gamblets for opening the complexity-bottleneck of implicit schemes for hyperbolic and parabolic ODEs/PDEs with rough coefficients. Journal of Computational Physics, 347 . pp. 99-128. ISSN 0021-9991. http://resolver.caltech.edu/CaltechAUTHORS:20170707-092240450

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Abstract

Implicit schemes are popular methods for the integration of time dependent PDEs such as hyperbolic and parabolic PDEs. However the necessity to solve corresponding linear systems at each time step constitutes a complexity bottleneck in their application to PDEs with rough coefficients. We present a generalization of gamblets introduced in [62] enabling the resolution of these implicit systems in near-linear complexity and provide rigorous a-priori error bounds on the resulting numerical approximations of hyperbolic and parabolic PDEs. These generalized gamblets induce a multiresolution decomposition of the solution space that is adapted to both the underlying (hyperbolic and parabolic) PDE (and the system of ODEs resulting from space discretization) and to the time-steps of the numerical scheme.


Item Type:Article
Related URLs:
URLURL TypeDescription
https://doi.org/10.1016/j.jcp.2017.06.037DOIArticle
http://www.sciencedirect.com/science/article/pii/S0021999117304916PublisherArticle
https://arxiv.org/abs/1606.07686arXivDiscussion Paper
ORCID:
AuthorORCID
Owhadi, Houman0000-0002-5677-1600
Additional Information:© 2017 Elsevier Inc. Received 24 June 2016, Revised 16 June 2017, Accepted 24 June 2017, Available online 28 June 2017. H. Owhadi gratefully acknowledges the support of the Air Force Office of Scientific Research and the DARPA EQUiPS Program under award number FA9550-16-1-0054 (Computational Information Games). L. Zhang gratefully acknowledges the support of the National Natural Science Foundation of China grant 11471214 and the One Thousand Plan of China for young scientists. The authors also thank two anonymous referees for comments and suggestions.
Funders:
Funding AgencyGrant Number
Air Force Office of Scientific Research (AFOSR)FA9550-16-1-0054
National Natural Science Foundation of China11471214
One Thousand Plan of China for Young ScientistsUNSPECIFIED
Subject Keywords:Wavelets; Multigrid; Multi-resolution; Implicit schemes; Hyperbolic; Parabolic
Record Number:CaltechAUTHORS:20170707-092240450
Persistent URL:http://resolver.caltech.edu/CaltechAUTHORS:20170707-092240450
Official Citation:Houman Owhadi, Lei Zhang, Gamblets for opening the complexity-bottleneck of implicit schemes for hyperbolic and parabolic ODEs/PDEs with rough coefficients, Journal of Computational Physics, Volume 347, 2017, Pages 99-128, ISSN 0021-9991, http://dx.doi.org/10.1016/j.jcp.2017.06.037. (http://www.sciencedirect.com/science/article/pii/S0021999117304916)
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:78836
Collection:CaltechAUTHORS
Deposited By: Tony Diaz
Deposited On:07 Jul 2017 18:16
Last Modified:02 Aug 2017 23:33

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