Article

# A 2-D Robust FE-FV Mixed Method to Handle Strong Nonlinearities in Superconductors

Fac. des Sci., GREEN-INPL, Univ. Henri Poincare, Vandoeuvre-lès-Nancy, France

IEEE Transactions on Magnetics (Impact Factor: 1.42). 09/2010; DOI: 10.1109/TMAG.2010.2044025 Source: IEEE Xplore

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**ABSTRACT:**A numerical method is developed for analyzing the shielding current density in a high-temperature superconducting (HTS) film. When an HTS film contains a crack, an additional boundary condition is imposed on the crack surface and it can be incorporated into the weak form. Although the weak form can be numerically solved with the essential boundary conditions, the resulting solution does not exactly satisfy Faraday's law on the crack surface. In order to resolve this problem, the following method is proposed: a virtual voltage is applied around the crack so as to make Faraday's law satisfied numerically. A numerical code for analyzing the shielding current density is developed on the basis of the proposed method and, by means of the code, the permanent magnet method is investigated numerically. Especially, the influence of a film edge or a crack on accuracy is assessed.IEEE Transactions on Magnetics 01/2012; 48(2):727-730. · 1.42 Impact Factor - [Show abstract] [Hide abstract]

**ABSTRACT:**A discontinuous Galerkin method is proposed for computing the current density in superconductors characterized by a constitutive power law between the current density and the electric field. The method is formulated to solve the nonlinear diffusion problem satisfied by the electric field, both in the scalar and 2-D vectorial case. Application examples are given for a superconducting cylinder subjected to an external magnetic field. Results are compared to those given by the mixed finite-element/finite-volume method and those obtained using a standard finite-element software. Efficiency and robustness of the approach are illustrated on an example where the exponent in the power law is spatially dependent.IEEE Transactions on Magnetics 01/2012; 48(2):591-594. · 1.42 Impact Factor

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