Journal
JOURNAL OF COMPUTATIONAL PHYSICS
Volume 295, Issue -, Pages 569-595Publisher
ACADEMIC PRESS INC ELSEVIER SCIENCE
DOI: 10.1016/j.jcp.2015.04.030
Keywords
Inverse problems; Proper orthogonal decomposition; Discrete empirical interpolation method (DEIM); Reduced-order models (ROMs); Shallow water equations; Finite difference methods
Funding
- NSF [CCF-1218454, ATM-0931198]
- AFOSR [FA9550-12-1-0293-DEF, 12-2640-06]
- Computational Science Laboratory at Virginia Tech
- Division of Computing and Communication Foundations
- Direct For Computer & Info Scie & Enginr [1218454] Funding Source: National Science Foundation
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This work studies reduced order modeling (ROM) approaches to speed up the solution of variational data assimilation problems with large scale nonlinear dynamical models. It is shown that a key requirement for a successful reduced order solution is that reduced order Karush-Kuhn-Tucker conditions accurately represent their full order counterparts. In particular, accurate reduced order approximations are needed for the forward and adjoint dynamical models, as well as for the reduced gradient. New strategies to construct reduced order based are developed for proper orthogonal decomposition (POD) ROM data assimilation using both Galerkin and Petrov-Galerkin projections. For the first time POD, tensorial POD, and discrete empirical interpolation method (DEIM) are employed to develop reduced data assimilation systems for a geophysical flow model, namely, the two dimensional shallow water equations. Numerical experiments confirm the theoretical framework for Galerkin projection. In the case of Petrov-Galerkin projection, stabilization strategies must be considered for the reduced order models. The new reduced order shallow water data assimilation system provides analyses similar to those produced by the full resolution data assimilation system in one tenth of the computational time. (C) 2015 Elsevier Inc. All rights reserved.
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