近期，李东方教授团队的文章《A second-order, linearly implicit and energy-stable scheme for the time-dependent Ginzburg-Landau equations》在国际期刊《Journal of Computational Physics》发表。

       摘要：The time-dependent Ginzburg-Landau (TDGL) equations are essential for investigating vortex dynamics and the transient behavior of superconductors under external magnetic fields. It is challenging to develop linear and structure-preserving numerical schemes for these equations due to the two coupled variables, the nonlinearity, and the complex characteristics of the discrete operator. To address these issues, we have modified the leap-frog time discretization method by carefully selecting intermediate approximations for the key variables, ψ and A, within the nonlinear terms. Our approach ensures that the decoupled scheme is linearly implicit and energy-stable. It is also proved that the scheme achieves second-order convergence in the temporal direction. Numerical experiments on both convex and non-convex domains are presented to confirm the effectiveness of our method.

       论文链接：https://www.sciencedirect.com/science/article/pii/S0021999126003207?pes=vor&utm_source=clarivate&getft_integrator=clarivate