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On the double critical-state model for type-II superconductivity in 3D
| Title: | On the double critical-state model for type-II superconductivity in 3D |
| Authors: | Kashima, Yohei Browse this author |
| Keywords: | The double critical-state model for superconductivity | | evolution variational inequality | | Maxwell's equations | | edge nite element | | convergence | | computational electromagnetism |
| Issue Date: | 2007 |
| Publisher: | Department of Mathematics, Hokkaido University |
| Journal Title: | Hokkaido University Preprint Series in Mathematics |
| Volume: | 881 |
| Start Page: | 1 |
| End Page: | 43 |
| Abstract: | In this paper we mathematically analyse an evolution variational inequality which formulates the double critical-state model for type-II superconductivity in 3D space and propose a finite element method to discretize the formulation. The double critical-state model originally proposed by Clem and Perez-Gonzalez is formulated as a model in 3D space which characterises the nonlinear relation between the electric field, the electric current, the perpendicular component of the electric current to the magnetic flux, and the parallel component of the current to the magnetic flux in bulk type-II superconductor. The existence of a solution to the variational inequality formulation is proved and the representation theorem of subdifferential for a class of energy functionals including our energy is established. The variational inequality formulation is discretized in time by a semi-implicit scheme and in space by the edge finite element of lowest order on a tetrahedral mesh. The fully discrete formulation is an unconstrained optimisation problem. The subsequence convergence property of the fully discrete solution is proved. Some numerical results computed under a rotating applied magnetic field are presented. |
| Type: | bulletin (article) |
| URI: | http://hdl.handle.net/2115/69690 |
| Appears in Collections: | 理学院・理学研究院 (Graduate School of Science / Faculty of Science) > Hokkaido University Preprint Series in Mathematics
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Submitter: 数学紀要登録作業用
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