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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
Published electronically: December 8, 2004
MathSciNet review: 2137002
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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

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

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