Please use this identifier to cite or link to this item: https://doi.org/10.4208/cicp.250112.061212a
Title: Numerical study of quantized vortex interaction in the ginzburg-landau equation on bounded domains
Authors: Bao, W. 
Tang, Q.
Keywords: Compact finite differencemethod
Dirichlet boundary condition
Finite element method
Ginzburg-landau equation
Homogeneous neumann boundary condition
Quantized vortex
Reduced dynamical laws
Time splitting
Issue Date: Sep-2013
Citation: Bao, W., Tang, Q. (2013-09). Numerical study of quantized vortex interaction in the ginzburg-landau equation on bounded domains. Communications in Computational Physics 14 (3) : 819-850. ScholarBank@NUS Repository. https://doi.org/10.4208/cicp.250112.061212a
Abstract: In this paper,we study numerically quantized vortex dynamics and their interaction in the two-dimensional (2D) Ginzburg-Landau equation (GLE)with a dimensionless parameter ε>0 on bounded domains under either Dirichlet or homogeneous Neumann boundary condition. We begin with a reviewof the reduced dynamical laws for time evolution of quantized vortex centers in GLE and show how to solve these nonlinear ordinary differential equations numerically. Then we present efficient and accurate numerical methods for discretizing the GLE on either a rectangular or a disk domain under either Dirichlet or homogeneous Neumann boundary condition. Based on these efficient and accurate numerical methods for GLE and the reduced dynamical laws, we simulate quantized vortex interaction of GLE with different ε and under different initial setups including single vortex, vortex pair, vortex dipole and vortex lattice, compare them with those obtained from the corresponding reduced dynamical laws, and identify the cases where the reduced dynamical laws agree qualitatively and/or quantitatively as well as fail to agree with those from GLE on vortex interaction. Finally, we also obtain numerically different patterns of the steady states for quantized vortex lattices under the GLE dynamics on bounded domains. © 2013 Global-Science Press.
Source Title: Communications in Computational Physics
URI: http://scholarbank.nus.edu.sg/handle/10635/103657
ISSN: 18152406
DOI: 10.4208/cicp.250112.061212a
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