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Mathematics of Computation

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ISSN 1088-6842 (online) ISSN 0025-5718 (print)

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Approximations of a Ginzburg-Landau model for superconducting hollow spheres based on spherical centroidal Voronoi tessellations
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by Qiang Du and Lili Ju PDF
Math. Comp. 74 (2005), 1257-1280 Request permission

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
  • MR Author ID: 191080
  • Email: qdu@math.psu.edu
  • Lili Ju
  • Affiliation: Institute for Mathematics and its Applications, University of Minnesota, Minneapolis, Minnesota 55455
  • MR Author ID: 645968
  • Email: ju@ima.umn.edu
  • 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
  • © Copyright 2004 American Mathematical Society
  • 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
  • MathSciNet review: 2137002