Approximations of a Ginzburg-Landau model for superconducting hollow spheres based on spherical centroidal Voronoi tessellations |
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Authors: | Qiang Du Lili Ju |
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Institution: | Department of Mathematics, Pennsylvania State University, University Park, Pennsylvania 16802 ; Institute for Mathematics and its Applications, University of Minnesota, Minneapolis, Minnesota 55455 |
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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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Keywords: | Ginzburg-Landau model of superconductivity finite volume gauge invariance convergence spherical centroidal Voronoi tessellations |
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