Structure-preserving reduced-order modeling of Korteweg-de Vries equation
Yazarlar (3)
Prof. Dr. Murat UZUNCA Sinop Üniversitesi, Türkiye
Bülent Karasözen
Middle East Technical University (Metu), Türkiye
Middle East Technical University (Metu), 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 | Mathematics and Computers in Simulation (Q1) | ||
| Dergi ISSN | 0378-4754 Dergi Bilgileri (2021) | ||
| Dergi Tarandığı Indeksler | SCI-Expanded | ||
| Makale Dili | İngilizce | Basım Tarihi | 10-2021 |
| Cilt / Sayı / Sayfa | 188 / 1 / 193–211 | DOI | 10.1016/j.matcom.2021.03.042 |
| Makale Linki | http://dx.doi.org/10.1016/j.matcom.2021.03.042 | ||
| UAK Araştırma Alanları |
Uygulamalı Matematik
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| Özet |
| Computationally efficient, structure-preserving reduced-order methods are developed for the Korteweg–de Vries (KdV) equations in Hamiltonian form. The semi-discretization in space by finite differences is based on the Hamiltonian structure. The resulting skew-gradient system of ordinary differential equations (ODEs) is integrated with the linearly implicit Kahan’s method, which preserves the Hamiltonian approximately. We have shown, using proper orthogonal decomposition (POD), the Hamiltonian structure of the full-order model (FOM) is preserved by the reduced-order model (ROM). The reduced model has the same linear–quadratic structure as the FOM. The quadratic nonlinear terms of the KdV equations are evaluated efficiently by the use of tensorial framework, clearly separating the offline–online cost of the FOMs and ROMs. The accuracy of the reduced solutions, preservation of the conserved quantities … |
| Anahtar Kelimeler |
| Energy preservation | Hamiltonian systems | Kahan's method | Model order reduction | Solitary waves | Tensor algebra |
Science Direct
Structure-preserving reduced-order modeling of Korteweg-de Vries equation
BM Sürdürülebilir Kalkınma Amaçları
| Atıf Sayıları | |
| Web of Science | 10 |
| Scopus | 10 |
| Google Scholar | 17 |