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An improved algorithm for the shallow water equations model reduction: Dynamic Mode Decomposition vs POD
Author(s) -
Bistrian D. A.,
Navon I. M.
Publication year - 2015
Publication title -
international journal for numerical methods in fluids
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.938
H-Index - 112
eISSN - 1097-0363
pISSN - 0271-2091
DOI - 10.1002/fld.4029
Subject(s) - dynamic mode decomposition , computation , proper orthogonal decomposition , algorithm , reduction (mathematics) , moore–penrose pseudoinverse , point of delivery , mode (computer interface) , model order reduction , decomposition , mathematics , shallow water equations , filter (signal processing) , computer science , mathematical analysis , inverse , projection (relational algebra) , geometry , ecology , machine learning , agronomy , computer vision , biology , operating system
Summary We propose an improved framework for dynamic mode decomposition (DMD) of 2‐D flows for problems originating from meteorology when a large time step acts like a filter in obtaining the significant Koopman modes, therefore, the classic DMD method is not effective. This study is motivated by the need to further clarify the connection between Koopman modes and proper orthogonal decomposition (POD) dynamic modes. We apply DMD and POD to derive reduced order models (ROM) of the shallow water equations. Key innovations for the DMD‐based ROM introduced in this paper are the use of the Moore–Penrose pseudoinverse in the DMD computation that produced an accurate result and a novel selection method for the DMD modes and associated amplitudes and Ritz values. A quantitative comparison of the spatial modes computed from the two decompositions is performed, and a rigorous error analysis for the ROM models obtained is presented. Copyright © 2015 John Wiley & Sons, Ltd.