Model order reduction for nonlinear Schrodinger equation

Download

index.pdf

Date

2015-05-01

Author

Karasözen, Bülent
Uzunca, Murat

Metadata

Show full item record

This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

Item Usage Stats

257
views

98
downloads

We apply the proper orthogonal decomposition (POD) to the nonlinear Schrodinger (NLS) equation to derive a reduced order model. The NLS equation is discretized in space by finite differences and is solved in time by structure preserving symplectic mid-point rule. A priori error estimates are derived for the POD reduced dynamical system. Numerical results for one and two dimensional NLS equations, coupled NLS equation with soliton solutions show that the low-dimensional approximations obtained by POD reproduce very well the characteristic dynamics of the system, such as preservation of energy and the solutions.

Subject Keywords

Nonlinear Schr¨odinger equation, Proper orthogonal decomposition, Model order reduction, Error analysis

URI

https://hdl.handle.net/11511/30498

Journal

APPLIED MATHEMATICS AND COMPUTATION

DOI

https://doi.org/10.1016/j.amc.2015.02.001

Collections

Graduate School of Applied Mathematics, Article

Suggestions

OpenMETU
Core

Reduced Order Optimal Control Using Proper Orthogonal Decomposition Sensitivities Karasözen, Bülent (2015-06-02) In general, reduced-order model (ROM) solutions obtained using proper orthogonal decomposition (POD) at a single parameter cannot approximate the solutions at other parameter values accurately. In this paper, parameter sensitivity analysis is performed for POD reduced order optimal control problems (OCPs) governed by linear diffusion-convection-reaction equations. The OCP is discretized in space and time by discontinuous Galerkin (dG) finite elements. We apply two techniques, extrapolating and expanding the...
Energy preserving model order reduction of the nonlinear Schrodinger equation Karasözen, Bülent (2018-12-01) 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 orth...
Exact Pseudospin Symmetric Solution of the Dirac Equation for Pseudoharmonic Potential in the Presence of Tensor Potential AYDOĞDU, OKTAY; Sever, Ramazan (Springer Science and Business Media LLC, 2010-04-01) Under the pseudospin symmetry, we obtain exact solution of the Dirac equation for the pseudoharmonic potential in the presence of the tensor potential with arbitrary spin-orbit coupling quantum number kappa. The energy eigenvalue equation of the Dirac particles is found and the corresponding radial wave functions are presented in terms of confluent hypergeometric functions. We investigate the tensor potential dependence of the energy of the each state in the pseudospin doublet. It is shown that degeneracy b...
EXACT BOUND STATES OF THE D-DIMENSIONAL KLEIN-GORDON EQUATION WITH EQUAL SCALAR AND VECTOR RING-SHAPED PSEUDOHARMONIC POTENTIAL IKHDAİR, SAMEER; Sever, Ramazan (World Scientific Pub Co Pte Lt, 2008-09-01) We present the exact solution of the Klein Gordon equation in D-dimensions in the presence of the equal scalar and vector pseudoharmonic potential plus the ring-shaped potential using the Nikiforov-Uvarov method. We obtain the exact bound state energy levels and the corresponding eigen functions for a spin-zero particles. We also find that the solution for this ring-shaped pseudoharmonic potential can be reduced to the three-dimensional (3D) pseudoharmonic solution once the coupling constant of the angular ...
Model order reduction for pattern formation in reaction-diffusion systems Karasözen, Bülent; Küçükseyhan, Tuğba; Mülayim, Gülden (null; 2017-09-22) We compare three reduced order modelling (ROM) techniques: the proper orthogonal decomposition (POD), discrete empirical interpolation (DEIM) [2], and dynamical mode decomposition (DMD) [1] to reaction diusion equations in biology. The formation of patterns in reaction-diusion equations require highly accurate solutions in space and time and therefore require large computational time to reach the steady states. The three reduced order methods are applied to the diusive FitzHugh-Nagumo equation [3] and th...

Citation Formats

B. Karasözen and M. Uzunca, “Model order reduction for nonlinear Schrodinger equation,” APPLIED MATHEMATICS AND COMPUTATION, pp. 509–519, 2015, Accessed: 00, 2020. [Online]. Available: https://hdl.handle.net/11511/30498.