Approximations of a Ginzburg-Landau model for superconducting hollow spheres based on spherical centroidal Voronoi tessellations

Authors:
Qiang Du and Lili Ju

Journal:
Math. Comp. **74** (2005), 1257-1280

MSC (2000):
Primary 65N15, 65N99; Secondary 82D55

DOI:
https://doi.org/10.1090/S0025-5718-04-01719-3

Published electronically:
December 8, 2004

MathSciNet review:
2137002

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Abstract | References | Similar Articles | Additional Information

Abstract: In this paper the numerical approximations of the Ginzburg- Landau model for a superconducting hollow spheres are constructed using a gauge invariant discretization on spherical centroidal Voronoi tessellations. A reduced model equation is used on the surface of the sphere which is valid in the thin spherical shell limit. We present the numerical algorithms and their theoretical convergence as well as interesting numerical results on the vortex configurations. Properties of the spherical centroidal Voronoi tessellations are also utilized to provide a high resolution scheme for computing the supercurrent and the induced magnetic field.

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Additional Information

**Qiang Du**

Affiliation:
Department of Mathematics, Pennsylvania State University, University Park, Pennsylvania 16802

Email:
qdu@math.psu.edu

**Lili Ju**

Affiliation:
Institute for Mathematics and its Applications, University of Minnesota, Minneapolis, Minnesota 55455

Email:
ju@ima.umn.edu

DOI:
https://doi.org/10.1090/S0025-5718-04-01719-3

Keywords:
Ginzburg-Landau model of superconductivity,
finite volume,
gauge invariance,
convergence,
spherical centroidal Voronoi tessellations

Received by editor(s):
July 13, 2003

Received by editor(s) in revised form:
January 5, 2004

Published electronically:
December 8, 2004

Additional Notes:
This work is supported in part by NSF-DMS 0196522 and NSF-ITR 0205232

Article copyright:
© Copyright 2004
American Mathematical Society