Comparative numerical analysis using reduced-order modeling strategies for nonlinear large-scale systems

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• 作者：Gabriel Dimitriu^a ; ^{dimitriu.gabriel@gmail.com" class="auth_mail" title="E-mail the corresponding author} ; Răzvan Ştefănescu^b ; ^{rstefan@ncsu.edu" class="auth_mail" title="E-mail the corresponding author} ; Ionel M. Navon^c ; ^{inavon@fsu.edu" class="auth_mail" title="E-mail the corresponding author}
• 关键词：Reduced-order modeling ; Proper Orthogonal Decomposition (POD) ; Gappy POD ; Discrete Empirical Interpolation ; Missing Point Estimation ; Predator-prey model
• 刊名：Journal of Computational and Applied Mathematics
• 出版年：2017
• 出版时间：15 January 2017
• 年：2017
• 卷：310
• 期：Complete
• 页码：32-43
• 全文大小：1104 K

文摘

We perform a comparative analysis using three reduced-order strategies–Missing Point Estimation (MPE) method, Gappy POD method, and Discrete Empirical Interpolation Method (DEIM)–applied to a biological model describing the spatio-temporal dynamics of a predator–prey community. The comparative study is focused on the efficiency of the reduced-order approximations and the complexity reduction of the nonlinear terms. Different variants are discussed related to the projection-based model reduction framework combined with selective spatial sampling to efficiently perform the online computations. Numerical results are presented.