A Posteriori Error Estimation for DEIM Reduced Nonlinear Dynamical Systems
| dc.citation.firstpage | A311 | en_US |
| dc.citation.issueNumber | 2 | en_US |
| dc.citation.journalTitle | SIAM Journal on Scientific Computing | en_US |
| dc.citation.lastpage | A338 | en_US |
| dc.citation.volumeNumber | 36 | en_US |
| dc.contributor.author | Wirtz, D. | en_US |
| dc.contributor.author | Sorensen, D.C. | en_US |
| dc.contributor.author | Haasdonk, B. | en_US |
| dc.date.accessioned | 2016-02-02T19:17:44Z | en_US |
| dc.date.available | 2016-02-02T19:17:44Z | en_US |
| dc.date.issued | 2014 | en_US |
| dc.description.abstract | In this work an efficient approach for a posteriori error estimation for POD-DEIM reduced nonlinear dynamical systems is introduced. The considered nonlinear systems may also include time- and parameter-affine linear terms as well as parametrically dependent inputs and outputs. The reduction process involves a Galerkin projection of the full system and approximation of the system's nonlinearity by the DEIM method [S. Chaturantabut and D. C. Sorensen,ļ¾ SIAM J. Sci. Comput., 32 (2010), pp. 2737--2764]. The proposed a posteriori error estimator can be efficiently decomposed in an offline/online fashion and is obtained by a one-dimensional auxiliary ODE during reduced simulations. Key elements for efficient online computation are partial similarity transformations and matrix-DEIM approximations of the nonlinearity Jacobians. The theoretical results are illustrated by application to an unsteady Burgers equation and a cell apoptosis model. | en_US |
| dc.identifier.citation | Wirtz, D., Sorensen, D.C. and Haasdonk, B.. "A Posteriori Error Estimation for DEIM Reduced Nonlinear Dynamical Systems." <i>SIAM Journal on Scientific Computing,</i> 36, no. 2 (2014) SIAM: A311-A338. http://dx.doi.org/10.1137/120899042. | en_US |
| dc.identifier.doi | http://dx.doi.org/10.1137/120899042 | en_US |
| dc.identifier.uri | https://hdl.handle.net/1911/88305 | en_US |
| dc.language.iso | eng | en_US |
| dc.publisher | SIAM | en_US |
| dc.rights | Article is made available in accordance with the publisher's policy and may be subject to US copyright law. Please refer to the publisher's site for terms of use. | en_US |
| dc.title | A Posteriori Error Estimation for DEIM Reduced Nonlinear Dynamical Systems | en_US |
| dc.type | Journal article | en_US |
| dc.type.dcmi | Text | en_US |
| dc.type.publication | publisher version | en_US |
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