TY - JOUR
T1 - Numerical Study of Quantized Vortex Interaction in the Ginzburg-Landau Equation on Bounded Domains
AU - Weizhu Bao & Qinglin Tang
JO - Communications in Computational Physics
VL - 3
SP - 819
EP - 850
PY - 2013
DA - 2013/09
SN - 14
DO - http://doi.org/10.4208/cicp.250112.061212a
UR - https://global-sci.org/intro/article_detail/cicp/7183.html
KW - 
AB - <p style="text-align: justify;">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&gt;0 on bounded domains under either Dirichlet or homogeneous
Neumann boundary condition. We begin with a review of 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.</p>