论文标题
暂时仪表下动态的金茨堡 - 兰道方程的能量稳定和最大结合原理方案
An energy stable and maximum bound principle preserving scheme for the dynamic Ginzburg-Landau equations under the temporal gauge
论文作者
论文摘要
本文提出了时间量表下时间依赖的金兹堡 - landau方程的脱钩数值方案。对于磁电势和顺序参数，离散方案分别采用第二种类型的NED $ {\ rm \急性{e}} $ lec元素和线性元素分别用于空间离散化；以及一个线性的向后欧拉方法和时间离散化的一阶指数时间差异方法。在离散意义上，顺序参数的最大结合原理（MBP）已证明。离散的能量稳定性和MBP的保护可以保证数值模拟的稳定性和有效性，并进一步促进采用自适应时间稳定策略，该策略通常在涡旋动力学的长期模拟中起着重要作用，尤其是当应用磁场很强时。还给出了提出的方案的最佳误差估计。数值示例验证了所提出的方案的理论结果，并证明了外部磁场中超导体的涡旋运动。
This paper proposes a decoupled numerical scheme of the time-dependent Ginzburg--Landau equations under the temporal gauge. For the magnetic potential and the order parameter, the discrete scheme adopts the second type Ned${\rm \acute{e}}$lec element and the linear element for spatial discretization, respectively; and a linearized backward Euler method and the first order exponential time differencing method for time discretization, respectively. The maximum bound principle (MBP) of the order parameter and the energy dissipation law in the discrete sense are proved. The discrete energy stability and MBP-preservation can guarantee the stability and validity of the numerical simulations, and further facilitate the adoption of an adaptive time-stepping strategy, which often plays an important role in long-time simulations of vortex dynamics, especially when the applied magnetic field is strong. An optimal error estimate of the proposed scheme is also given. Numerical examples verify the theoretical results of the proposed scheme and demonstrate the vortex motions of superconductors in an external magnetic field.
