A Fast Semi-Implicit Finite Difference Method for the TDGL Equations
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 , 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.
Turn this paper into a full lesson
ArcXiv compiles a staged curriculum from this paper: 8-12 lessons across beginner → advanced, synthesised section guides, visuals, flashcards, a quiz, exercises, and on-demand deep dives per section. Grounded in the abstract, never invented.