Ginzburg-Landau（GL）模型广泛用于描述低温和高温下的超导现象，由于方程的高度非线性本质、复杂的能源景观、及其解对外部条件的奇异动态响应，数值模拟已经成为更好地理解GL模型、模拟超导体的物理性质并为有趣的超导现象提供进一步的理论见解的有价值工具。本项目拟从GL自由能出发，利用能量泛函分裂技术分别给出求解零电势规范和Lorentz规范下的非定常GL方程的无条件稳定且保结构（散度自由、离散极值原理、规范不变性）的高效数值格式及其数值分析，也将探讨人工边界条件和隐式方程的快速计算（预处理）。本项目的研究结果将为超导材料的研究提供服务和理论支撑。

Ginzburg-Landau (GL) model is widely used to describe superconductivity at low temperature and high temperature. Because of the high nonlinear nature of the GL equation, complex energy landscape and the singular dynamic response of its solution to external conditions, numerical simulation has become a valuable tool for better understanding GL model, simulating physical properties of superconductors and providing further theoretical insights for interesting superconductor phenomena. .In this project, we use the energy splitting technology to give the efficient numerical schemes for the unsteady GL equation under the zero potential gauge and Lorentz gauge respectively. We also study their unconditional stability and physical properties (e.g. divergence freedom, discrete extreme value principle and gauge invariance etc.), and discuss artificial boundary conditions and the fast calculation (preconditioning) of implicit equations. The results of this project will provide service and theoretical support for the research of superconductor.