线性非局部Drude模型的一种解耦格式的稳定性和收敛性分析

Stability and Convergence Analysis for a Decoupled Scheme on the Linear Nonlocal Drude Model

本文针对线性非局部Drude模型,基于二阶向后差分(BDF)和间断伽辽金(DG)方法提出了一种能量稳定的解耦格式,证明了半离散格式和全离散格式的能量稳定性,以及全离散格式的最优收敛速率。为了有效求解全离散系统,采用“解耦”技术将整个系统分解为2个更小的系统,即电流密度函数在电场方程中是显式的,且电场函数在电流密度方程中是显式的。这种“解耦”技术在系统较大的时候可以提高计算效率。最后,通过数值实验对理论结果进行了验证,结果表明所提格式具有二阶时间和空间精度且能量函数递减,与理论分析吻合。

This paper proposes a decoupled energy-stable scheme for the linear nonlocal Drude model based on the second-order backward differentiation formula(BDF) and discontinuous Galerkin(DG) method.The energy stability of both semi-discrete and fully discrete schemes,and the optimal convergence rate of the fully discrete scheme are proved.The "decoupled" technique is adopted to divide the whole system into two smaller sub-systems so as to efficiently solve the fully discrete system.Namely,the current density function is explicit in the electric field equation and the electric field function is explicit in the current density equation.This “decoupled” technique is capable of increasing the computational efficiency when the system is large.In the end,the theoretical results are verified by numerical experiments.It shows that the proposed scheme is characterized by second-order temporal and spetial accuracy and decaying energy function,which is in agreement with the theoretical analysis.