报告题目：A Stabilized Semi-Implicit Euler Gauge-Invariant Method for the Time-Dependent Ginzburg–Landau Equations
报 告 人：高华东副教授、华中科技大学
时 间：2019年6月20日10:00地 点：数信学院3401
摘 要：
We propose and analyze a stabilized semi-implicit Euler gauge-invariant method for numerical solution of the time-dependent Ginzburg-Landau (TDGL) equations in the two-dimensional space. The proposed method uses the well-known gauge-invariant finite difference approximations with staggered variables in a rectangular mesh, and a stabilized semi-implicit Euler discretization for time integration. The resulted fully discrete system leads to two decoupled linear systems at each time step, thus can be efficiently solved. We prove that the proposed method unconditionally preserves the point-wise boundedness of the solution and is also energy-stable. Moreover, the proposed method under the zero-electric potential gauge is shown to be equivalent to a mass-lumped version of the lowest order rectangular Nédélec edge element approximation and the Lorentz gauge scheme to a mass-lumped mixed finite element method. These indicate the method is also effective in solving the TDGL problems in non-convex domains although the solutions are often of low-regularity in such situation. Various numerical experiments are also presented to demonstrate effectiveness and robustness of the proposed method.
报告人简介：
高华东博士，华中科技大学数学与统计学院副教授。分别在香港城市大学数学系(2014年)，南开大学数学科学学院(2011年)和大连理工大学应用数学系(2008年)获得博士，硕士，学士学位。研究方向包括数值分析: 微分方程数值解, 有限元方法与差分方法, 尤其是对非线性抛物问题的数值求解与分析; 数学建模与计算物理: 多孔介质中热和水汽的传导流动, 计算超导现象, 计算微磁学, 计算电热学。目前主持面上基金一项，已正式发表论文十余篇。
