Splitting multisymplectic integrators for Maxwell's equations
Splitting multisymplectic integrators for Maxwell's equations
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DOI：
10.1016/j.jcp.2010.02.010
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发表时间：
2010-06-01
影响因子：
4.1
通讯作者：
Zhang, Jingjing
中科院分区：
文献类型：
--
作者：
Kong, Linghua;Hong, Jialin;Zhang, Jingjing
本文提出了一种新的求解三维麦克斯韦方程组的多辛方法。将三维麦克斯韦方程组分解为三个局部一维（LOD）方程组，然后用一对辛龙格库塔方法对每个LOD方程组进行离散，得到分裂多辛积分器。我们称这类格式为LOD多辛格式（LOD-MS）。研究了离散格式的守恒律、收敛性、色散关系、耗散性和稳定性。理论分析表明，该格式是无条件稳定的，无耗散的，时间上具有一阶精度，空间上具有二阶精度。作为一种简化，我们还考虑了LOD-MS在二维麦克斯韦方程组中的应用。数值实验与理论结果吻合较好。这些结果表明，LOD-MS不仅编码简单，而且具有多辛积分器的几乎所有性质。(C)2010年爱思唯尔公司All rights reserved.
In the paper, we describe a novel kind of multisymplectic method for three-dimensional (3-D) Maxwell's equations. Splitting the 3-D Maxwell's equations into three local one-dimensional (LOD) equations, then applying a pair of symplectic Runge-Kutta methods to discretize each resulting LOD equation, it leads to splitting multisymplectic integrators. We say this kind of schemes to be LOD multisymplectic scheme (LOD-MS). The discrete conservation laws, convergence, dispersive relation, dissipation and stability are investigated for the schemes. Theoretical analysis shows that the schemes are unconditionally stable, non-dissipative, and of first order accuracy in time and second order accuracy in space. As a reduction, we also consider the application of LOD-MS to 2-D Maxwell's equations. Numerical experiments match the theoretical results well. They illustrate that LOD-MS is not only efficient and simple in coding, but also has almost all the nature of multisymplectic integrators. (C) 2010 Elsevier Inc. All rights reserved.