Aydın, Ayhan

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https://hdl.handle.net/20.500.14411/6774
Name Variants
Aydın,A.
Aydin, Ayhan
A.,Aydın
A., Ayhan
Aydın, Ayhan
Aydin,Ayhan
Ayhan Aydın
A., Aydın
Aydin A.
A.,Aydin
Ayhan, Aydin
Aydın A.
AYDIN A.
A.,Ayhan
A., Aydin
Aydin,A.
Ayhan, Aydın
Job Title
Profesör Doktor
Email Address
ayhan.aydin@atilim.edu.tr
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Mathematics
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Website
ORCID ID
0000-0002-0837-9364
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Turkish CoHE Profile ID
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WoS Researcher ID
AAL-5690-2020

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Applied Mathematics and Computation1
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    Article
    Citation - WoS: 3
    Citation - Scopus: 5
    Global Energy Preserving Model Reduction for Multi-Symplectic Pdes
    (Elsevier Science inc, 2023) Uzunca, Murat; Karasozen, Bulent; Aydin, Ayhan
    Many Hamiltonian systems can be recast in multi-symplectic form. We develop a reduced -order model (ROM) for multi-symplectic Hamiltonian partial differential equations (PDEs) that preserves the global energy. The full-order solutions are obtained by finite difference discretization in space and the global 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 structure as the FOM, and preserves the discrete reduced global energy. Ap-plying the discrete empirical interpolation method (DEIM), the reduced-order solutions are computed efficiently in the online stage. A priori error bound is derived for the DEIM ap-proximation to the nonlinear Hamiltonian. The accuracy and computational efficiency of the ROMs are demonstrated for the Korteweg de Vries (KdV) equation, Zakharov-Kuznetzov (ZK) equation, and nonlinear Schrodinger (NLS) equation in multi-symplectic form. Preser-vation of the reduced energies shows that the reduced-order solutions ensure the long-term stability of the solutions.(c) 2022 Elsevier Inc. All rights reserved.