Energy preserving model order reduction of the nonlinear Schrödinger equation
Yazarlar (2)
Bülent Karasözen
Middle East Technical University (Metu), Türkiye
Middle East Technical University (Metu), Türkiye
Prof. Dr. Murat UZUNCA Sinop Üniversitesi, Türkiye
| Makale Türü |
Özgün Makale
(SSCI, AHCI, SCI, SCI-Exp dergilerinde yayınlanan tam makale)
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| Dergi Adı | Advances in Computational Mathematics (Q1) | ||
| Dergi ISSN | 1019-7168 Dergi Bilgileri (2018) | ||
| Dergi Tarandığı Indeksler | SCI-Expanded | ||
| Makale Dili | İngilizce | Basım Tarihi | 02-2018 |
| Cilt / Sayı / Sayfa | 44 / 6 / 1769–1796 | DOI | 10.1007/s10444-018-9593-9 |
| Makale Linki | http://link.springer.com/10.1007/s10444-018-9593-9 | ||
| UAK Araştırma Alanları |
Uygulamalı Matematik
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| Özet |
| An energy preserving reduced order model is developed for two dimensional nonlinear Schrödinger equation (NLSE) with plane wave solutions and with an external potential. The NLSE is discretized in space by the symmetric interior penalty discontinuous Galerkin (SIPG) method. The resulting system of Hamiltonian ordinary differential equations are integrated in time by the energy preserving average vector field (AVF) method. The mass and energy preserving reduced order model (ROM) is constructed by proper orthogonal decomposition (POD) Galerkin projection. The nonlinearities are computed for the ROM efficiently by discrete empirical interpolation method (DEIM) and dynamic mode decomposition (DMD). Preservation of the semi-discrete energy and mass are shown for the full order model (FOM) and for the ROM which ensures the long term stability of the solutions. Numerical simulations illustrate the … |
| Anahtar Kelimeler |
| Average vector field method | Discontinuous Galerkin method | Discrete empirical interpolation method | Dynamic mode decomposition | Nonlinear Schrödinger equation | Proper orthogonal decomposition |
