Structure-preserving reduced-order modeling of Korteweg-de Vries equation
[ X ]
Tarih
2021
Dergi Başlığı
Dergi ISSN
Cilt Başlığı
Yayıncı
Elsevier
Erişim Hakkı
info:eu-repo/semantics/openAccess
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 (EOM) 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, and computational speed-up gained by ROMs are demonstrated for the one-dimensional single and coupled KdV equations, and two-dimensional Zakharov-Kuznetsov equation with soliton solutions. (C) 2021 International Association for Mathematics and Computers in Simulation (IMACS). Published by Elsevier B.V. All rights reserved.
Açıklama
Anahtar Kelimeler
Hamiltonian systems, Solitary waves, Kahan's method, Energy preservation, Model order reduction, Tensor algebra
Kaynak
Mathematics and Computers in Simulation
WoS Q Değeri
Q1
Scopus Q Değeri
Q1
Cilt
188
