A new approach for numerical simulation of the time-dependent Ginzburg-Landau equations

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• 作者：Buyang Li^a ; ^b ; ^{buyangli@nju.edu.cn" class="auth_mail" title="E-mail the corresponding author} ; Zhimin Zhang^c ; ^d ; ^{ag7761@wayne.edu" class="auth_mail" title="E-mail the corresponding author}
• 关键词：Superconductivity ; Reentrant corner ; Singularity ; Finite element method ; Hodge decomposition
• 刊名：Journal of Computational Physics
• 出版年：2015
• 出版时间：15 December 2015
• 年：2015
• 卷：303
• 期：Complete
• 页码：238-250
• 全文大小：15955 K

文摘

We introduce a new approach for finite element simulations of the time-dependent Ginzburg–Landau equations (TDGL) in a general curved polygon, possibly with reentrant corners. Specifically, we reformulate the TDGL into an equivalent system of equations by decomposing the magnetic potential to the sum of its divergence-free and curl-free parts, respectively. Numerical simulations of vortex dynamics show that, in a domain with reentrant corners, the new approach is much more stable and accurate than the traditional approaches of solving the TDGL directly (under either the temporal gauge or the Lorentz gauge); in a convex domain, the new approach gives comparably accurate solutions as the traditional approaches.