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Numerical Analysis and Simulation for a Generalized Planar Ginzburg-Landau Equation in a Circular Geometry

Published

Author(s)

Sean A. Colbert-Kelly, Geoffrey B. McFadden, Daniel Phillips, Jie Shen

Abstract

In this paper, a numerical scheme for a generalized planar Ginzburg-Landau energy in a circular geometry is studied. A spectral-Galerkin method is utilized, and a stability analysis and an error estimate for the scheme are presented. It is shown that the scheme is unconditionally stable. We present numerical simulation results that have been obtained by using the scheme with various sets of boundary data, including those the form u(θ ) = exp(idθ), where the integer d denotes the topological degree of the solution. These numerical results are in good agreement with the experimental and analytical results. Results include the computation of bifurcations from pure bend or splay patterns to spiral patterns for d = 1, and computations of metastable or unstable higher-energy solutions as well as the lowest energy ground state solutions for values of d ranging from two to five.
Citation
Communications in Mathematical Sciences
Volume
15
Issue
2

Keywords

Ginzburg-Landau Equation, Spectral-Galerkin Method, Stability Analysis, Error Estimate, Bend and Splay Patterns, Bifurcations

Citation

Colbert-Kelly, S. , McFadden, G. , Phillips, D. and Shen, J. (2017), Numerical Analysis and Simulation for a Generalized Planar Ginzburg-Landau Equation in a Circular Geometry, Communications in Mathematical Sciences, [online], https://doi.org/10.4310/CMS.2017.v15.n2.a3, https://tsapps.nist.gov/publication/get_pdf.cfm?pub_id=916315 (Accessed February 29, 2024)
Created February 20, 2017, Updated October 12, 2021