Volume 2, Issue 4
Numerical Solutions to Bean's Critical-State Model for Type-II Superconductors

Int. J. Numer. Anal. Mod., 2 (2005), pp. 479-488.

Published online: 2005-02

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• Abstract

In this paper we study the numerical solution for an $p$-Laplacian type of evolution system $H_t + \nabla \times [|\nabla \times H|^{p-2} \nabla \times H] = F (x, t)$, $p > 2$ in two space dimensions. For large $p$ this system is an approximation of Bean's critical-state model for type-II superconductors. By introducing suitable transformation, the system is equivalent to a nonlinear parabolic equation. For the nonlinear parabolic problem we obtain the numerical solution by combining approximation schemes for the linear equation and the nonlinear semigroup. The convergence and stability of the scheme are proved. Finally, a numerical experiment is presented.

• Keywords

approximation of Bean's critical-state model, numerical solutions.

35Q60, 35K50, 65M60

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@Article{IJNAM-2-479, author = {}, title = {Numerical Solutions to Bean's Critical-State Model for Type-II Superconductors}, journal = {International Journal of Numerical Analysis and Modeling}, year = {2005}, volume = {2}, number = {4}, pages = {479--488}, abstract = {

In this paper we study the numerical solution for an $p$-Laplacian type of evolution system $H_t + \nabla \times [|\nabla \times H|^{p-2} \nabla \times H] = F (x, t)$, $p > 2$ in two space dimensions. For large $p$ this system is an approximation of Bean's critical-state model for type-II superconductors. By introducing suitable transformation, the system is equivalent to a nonlinear parabolic equation. For the nonlinear parabolic problem we obtain the numerical solution by combining approximation schemes for the linear equation and the nonlinear semigroup. The convergence and stability of the scheme are proved. Finally, a numerical experiment is presented.

}, issn = {2617-8710}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/ijnam/942.html} }
TY - JOUR T1 - Numerical Solutions to Bean's Critical-State Model for Type-II Superconductors JO - International Journal of Numerical Analysis and Modeling VL - 4 SP - 479 EP - 488 PY - 2005 DA - 2005/02 SN - 2 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/ijnam/942.html KW - approximation of Bean's critical-state model, numerical solutions. AB -

In this paper we study the numerical solution for an $p$-Laplacian type of evolution system $H_t + \nabla \times [|\nabla \times H|^{p-2} \nabla \times H] = F (x, t)$, $p > 2$ in two space dimensions. For large $p$ this system is an approximation of Bean's critical-state model for type-II superconductors. By introducing suitable transformation, the system is equivalent to a nonlinear parabolic equation. For the nonlinear parabolic problem we obtain the numerical solution by combining approximation schemes for the linear equation and the nonlinear semigroup. The convergence and stability of the scheme are proved. Finally, a numerical experiment is presented.

W. Wei & H.-M. Yin. (1970). Numerical Solutions to Bean's Critical-State Model for Type-II Superconductors. International Journal of Numerical Analysis and Modeling. 2 (4). 479-488. doi:
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