Energy preserving model order reduction of the nonlinear Schrodinger equation
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Tarih
2018
Yazarlar
Dergi Başlığı
Dergi ISSN
Cilt Başlığı
Yayıncı
Springer
Erişim Hakkı
info:eu-repo/semantics/openAccess
Özet
An energy preserving reduced order model is developed for two dimensional nonlinear Schrodinger 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 preservation of the energy and mass in the reduced order model for the two dimensional NLSE with and without the external potential. The POD-DMD makes a remarkable improvement in computational speed-up over the POD-DEIM. Both methods approximate accurately the FOM, whereas POD-DEIM is more accurate than the POD-DMD.
Açıklama
3rd Workshop on Model Reduction of Complex Dynamical Systems (MODRED) -- JAN 11-13, 2017 -- Univ Southern Denmark, Odense, DENMARK
Anahtar Kelimeler
Nonlinear Schrodinger equation, Discontinuous Galerkin method, Average vector field method, Proper orthogonal decomposition, Discrete empirical interpolation method, Dynamic mode decomposition
Kaynak
Advances in Computational Mathematics
WoS Q Değeri
Q1
Scopus Q Değeri
Q2
Cilt
44
Sayı
6
