Reduced order modelling of nonlinear cross-diffusion systems
Yazarlar (4)
Bülent Karasözen
Middle East Technical University (Metu), Türkiye
Middle East Technical University (Metu), Türkiye
Gülden Mülayim Middle East Technical University (Metu), Türkiye
Prof. Dr. Murat UZUNCA Sinop Üniversitesi, Türkiye
Doç. Dr. Süleyman Yıldız Middle East Technical University (Metu), Türkiye
| Makale Türü | Özgün Makale (SSCI, AHCI, SCI, SCI-Exp dergilerinde yayınlanan tam makale) | ||
| Dergi Adı | Applied Mathematics and Computation (Q1) | ||
| Dergi ISSN | 0096-3003 Dergi Bilgileri (2021) | ||
| Dergi Tarandığı Indeksler | SCI-Expanded | ||
| Makale Dili | Türkçe | Basım Tarihi | 07-2021 |
| Cilt / Sayı / Sayfa | 401 / 1 / 126058–0 | DOI | 10.1016/j.amc.2021.126058 |
| Makale Linki | http://dx.doi.org/10.1016/j.amc.2021.126058 | ||
| UAK Araştırma Alanları |
Uygulamalı Matematik
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| Özet |
| In this work, we present reduced-order models (ROMs) for a nonlinear cross-diffusion problem from population dynamics, the Shigesada-Kawasaki-Teramoto (SKT) equation with Lotka-Volterra kinetics. The formation of the patterns of the SKT equation consists of a fast transient phase and a long stationary phase. Reduced order solutions are computed by separating the time into two time-intervals. In numerical experiments, we show for one- and two-dimensional SKT equations with pattern formation, the reduced-order solutions obtained in the time-windowed form, i.e., principal decomposition framework, are more accurate than the global proper orthogonal decomposition solutions obtained in the whole time interval. The finite-difference discretization of the SKT equation in space results in a system of linear-quadratic ordinary differential equations. The ROMs have the same linear-quadratic structure as the full … |
| Anahtar Kelimeler |
| Entropy | Finite differences | Pattern formation | Principal interval decomposition | Proper orthogonal decomposition | Tensor algebra |
Science Direct
Reduced order modelling of nonlinear cross-diffusion systems
BM Sürdürülebilir Kalkınma Amaçları
| Atıf Sayıları | |
| Web of Science | 4 |
| Scopus | 4 |
| Google Scholar | 8 |