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

TL;DR

This paper presents a novel finite element method for simulating the time-dependent Ginzburg-Landau equations, especially effective in domains with reentrant corners, improving stability and accuracy over previous methods.

Contribution

The authors reformulate the TDGL equations by decomposing the magnetic potential, enabling more stable and accurate simulations in complex geometries.

Findings

Enhanced stability in reentrant corner domains

Comparable accuracy in convex domains

Improved numerical performance over traditional methods

Abstract

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 old 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 old approaches.