On linear and nonlinear aspects of dynamic mode decomposition |
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| Authors: | A. K. Alekseev D. A. Bistrian A. E. Bondarev I. M. Navon |
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| Affiliation: | 1. Moscow Institute of Physics and Technology, Moscow, Russia;2. Department of Electrical Engineering and Industrial Informatics, Politehnica University of Timi?oara, Hunedoara, Romania;3. Keldysh Institute of Applied Mathematics RAS, Moscow, Russia;4. Department of Scientific Computing, Florida State University, Tallahassee, FL, USA |
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| Abstract: | The approximation of reduced linear evolution operator (propagator) via dynamic mode decomposition (DMD) is addressed for both linear and nonlinear events. The 2D unsteady supersonic underexpanded jet, impinging the flat plate in nonlinear oscillating mode, is used as the first test problem for both modes. Large memory savings for the propagator approximation are demonstrated. Corresponding prospects for the estimation of receptivity and singular vectors are discussed. The shallow water equations are used as the second large‐scale test problem. Excellent results are obtained for the proposed optimized DMD method of the shallow water equations when compared with recent POD‐based/discrete empirical interpolation‐based model reduction results in the literature. Copyright © 2016 John Wiley & Sons, Ltd. |
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| Keywords: | dynamic mode decomposition propagator unsteady Euler equations shallow water equations |
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