FDTD coeffcient modification schemes of the wave and Maxwell’s equations for controlling order of accuracy and dispersion errors

B. Finkelstein, R. Kastner
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引用次数: 3

Abstract

Recently, a general methodology for generating FDTD dispersion relation preserving (DRP) schemes of the wave equation (WE) was introduced. These schemes can be designed to accommodate arbitrary requirements for phase and group velocity dispersion characteristics over the operating frequency range. In this work, the methodology is further generalized to include specification of both dispersion behavior and the orders of accuracy (OoAs) by minimizing the local truncation error [4, Ch. 5.1] for both the WE and Maxwell's equations (MEs). While the increase in OoA leads, in general, to a lower overall dispersion error, additional improvements of dispersion characteristics at certain frequencies can be accomplished at the expense of reduced OoA. This tradeoff affords flexibility in designing an FDTD algorithm for a wide range of applications. The OoA for a given stencil size is analyzed in this work by a Taylor expansion of the dispersion relationship in powers of the normalized frequency. This equation serves as a starting point for the methodology for the analysis and control of the OoA and dispersion errors, that encompasses both the customary analysis with Taylor expansion of the field in terms of At and Ax and the derivative-swapping approach.
波的FDTD系数修正方案和麦克斯韦方程用于控制精度和色散误差的阶数
本文介绍了一种生成波动方程时域有限差分色散关系保持格式的一般方法。这些方案可以设计成适应在工作频率范围内对相位和群速度色散特性的任意要求。在这项工作中,该方法被进一步推广到包括色散行为和精度阶数(OoAs)的规范,通过最小化WE和Maxwell方程(MEs)的局部截断误差[4,第5.1章]。虽然OoA的增加通常会导致总体色散误差降低,但在某些频率下,色散特性的进一步改善可以以降低OoA为代价来实现。这种权衡为设计广泛应用的FDTD算法提供了灵活性。本文通过对归一化频率的幂次色散关系进行泰勒展开,分析了给定模板尺寸的OoA。该方程可作为OoA和色散误差分析和控制方法的起点,该方法包括使用At和Ax的泰勒展开场的习惯分析和导数交换方法。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
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