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A Fast Semi-Implicit Finite Difference Method for the TDGL Equations

T. Winiecki·C. S. Adams
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Abstract

We propose a finite-difference algorithm for solving the time-dependent Ginzburg-Landau (TDGL) equation coupled to the appropriate Maxwell equation. The time derivatives are discretized using a second order semi-implicit scheme which, for intermediate values of the Ginzburg-Landau parameter $κ$, allows time-steps two orders of magnitude larger than commonly used in explicit schemes. We demonstrate the use of the method by solving a fully three-dimensional problem of a current-carrying wire with longitudinal and transverse magnetic fields.

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T. Winiecki, C. S. Adams. 2001-06-22. A Fast Semi-Implicit Finite Difference Method for the TDGL Equations. https://doi.org/10.1006/jcph.2002.7047

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