Structure-preserving model reduction of multi-symplectic PDEs
Yazarlar (3)
Prof. Dr. Murat UZUNCA Sinop Üniversitesi, Türkiye
Bülent Karasözen
Dr. Öğr. Üyesi Ayhan Aydin Sinop Üniversitesi
| Makale Türü | Özgün Makale (Uluslararası alan indekslerindeki dergilerde yayınlanan tam makale) | ||
| Dergi Adı | Appl. Math. Comput. | ||
| Makale Dili | – | Basım Tarihi | 01-2023 |
| Cilt / Sayı / Sayfa | 436 / 0 / 21–0 | DOI | – |
| Makale Linki | https://www.researchgate.net/profile/Bulent-Karasozen/publication/358571890_STRUCTURE-PRESERVING_MODEL_REDUCTION_OF_MULTI-SYMPLECTIC_PDES_A_PREPRINT/links/6208effc634ff774f4c8caf0/STRUCTURE-PRESERVING-MODEL-REDUCTION-OF-MULTI-SYMPLECTIC-PDES-A-PREPRI | ||
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| Özet |
| Many Hamiltonian systems can be recast in multi-symplectic form. We develop a structurepreserving reduced-order model (ROM) for multi-symplectic Hamiltonian PDEs under periodic boundary conditions. The full-order solutions are obtained by finite difference discretization in space and the energy preserving average vector field (AVF) method. The ROM is constructed in the same way as the full-order model (FOM) applying proper orthogonal decomposition (POD) with the Galerkin projection. The reduced-order system has the same multi-symplectic structure as the FOM, and preserves the discrete reduced global energy. Applying the discrete empirical interpolation method (DEIM), the reduced-order solutions are computed efficiently in the online stage. An a priori error bound is derived for the DEIM approximation to the nonlinear Hamiltonian. The accuracy and computational efficiency of the ROMs are demonstrated for one-and two-dimensional multisymplectic Hamiltonian partial differential equations such as KdV equation, Zakharov-Kuznetzov equation, and NLS equation. Preservation of the reduced energies shows that the reduced-order solutions ensure the long-term stability of the solutions. |
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