论文标题
时间指数积分器傅立叶伪谱法具有高精度和多个保护法的三维麦克斯韦方程
Time exponential integrator Fourier pseudospectral methods with high accuracy and multiple conservation laws for three-dimensional Maxwell's equations
论文作者
论文摘要
麦克斯韦方程描述了电磁波的传播，因此是理解天线和电磁学研究中遇到的许多问题的基础。本文的目的是提出和分析一个有效的完全离散方案，以解决三维麦克斯韦方程。这是通过结合时间指数积分器和傅立叶伪光谱方法来完成的。通过使用快速傅立叶变换算法在科学计算中众所周知，该方案中实现了快速计算。建立了不受CFL条件限制的最佳误差估计，并证明所得方案在空间和无限级别准确度上具有光谱精度。此外，该方案被证明具有多种保护定律，包括离散能量，螺旋，动量，符号性和无差异场保护。精度和保护的所有理论结果通过两个数值测试在数值上进行了说明。
Maxwell equations describe the propagation of electromagnetic waves and are therefore fundamental to understanding many problems encountered in the study of antennas and electromagnetics. The aim of this paper is to propose and analyse an efficient fully discrete scheme for solving three-dimensional Maxwell's equations. This is accomplished by combining time exponential integrator and Fourier pseudospectral methods. Fast computation is implemented in the scheme by using the Fast Fourier Transform algorithm which is well known in scientific computations. An optimal error estimate which is not encumbered by the CFL condition is established and the resulting scheme is proved to be of spectral accuracy in space and infinite-order accuracy in time. Furthermore, the scheme is shown to have multiple conservation laws including discrete energy, helicity, momentum, symplecticity, and divergence-free field conservations. All the theoretical results of the accuracy and conservations are numerically illustrated by two numerical tests.
