基于并行差分法的三维宽角抛物方程电波传播模型研究

Along with the rapid development of modern wireless communication, predicting the radio wave propagation characteristic has become an important research topic.The parabolic equation method has been widely used in modeling radio propagation in troposphere, for it can deal with simultaneously the irregular terrain and in-homogeneous atmosphere. However, the conventional parabolic equation method has the limitation of propagation angles and computational accuracy . .In this project, a new radio propagation model of three-dimensional wide angle parabolic equation based parallel difference algorithms will be designed. Predicting accurately the radio wave propagation characteristic will be realized in complicated environment. Through optimizing parameters of pseudo-differential operator, the propagation angles will be increased. High-order finite difference method will be applied to improve the computational accuracy. By using of parallel algorithm to solve pentadiagonal linear equations, the calculation efficiency will be improved greatly. Finally, we will study the inverse model based on three-dimensional two-way parabolic equation, which provide a new method to target location in complicated environment. And the effects that different environments take on the precision of target localization are analyzed. The research would be benefit to the development of the theory of computational electromagnetics, and to the improvement of practical engineering.

随着无线电技术的迅速发展，复杂环境电波传播预测已经成为一个重要的研究课题。抛物方程法能够同时处理不规则地表和不均匀大气对电波的影响，被广泛的应用于对流层电波传播特性的计算中。然而，传统的抛物方程法具有传播角度偏小、计算精度偏低等缺陷。.本项目提出了一种新型的基于并行差分法的三维宽角抛物方程传播模型，可实现复杂环境中电波传播特性的精确预测。通过优化参数来提高伪微分算子的逼近精度，令抛物方程的传播角度不断增大；采用高阶有限差分法进行数值求解，提高了三维抛物方程的计算精度；通过基于OpenMP的多线程技术，实现了求解五对角线性方程组的并行算法，使三维抛物方程的计算效率显著提高。最后，研究了基于三维双向抛物方程的逆绕射模型，为复杂环境中目标的探测与定位提供了一种新方法，并探讨了不规则地表和不均匀大气等环境因素对定位精度的影响。这些研究不仅对发展计算电磁学理论是非常必要的，还具有极大的工程应用价值。

近些年来，电磁波技术的快速发展不仅给人类的生产与生活带来了诸多便利，还成为现代化电子战中制胜的关键，具有重要的民用和军用价值。如何高效地预测复杂环境中电磁波传播分布特性一直是电磁学领域研究的重点方向。抛物方程法由于其独特的优势被广泛地应用于求解对流层大尺度电波传播问题。然而，现有的抛物方程模型都是基于傅里叶算法的，无法精确地模拟复杂环境中的电磁波传播问题。本项目开展基于并行差分法的三维抛物方程电波传播模型的研究，通过优化伪微分算子提高了三维抛物方程的最大传播角度；通过Sherman-Morrison分解法求解对角矩阵提升了三维抛物方程的计算效率。采用分段线性地形变换法对不规则地表环境进行建模；采用Weierstrass改进分形理论对粗糙海面环境进行建模；采用改进的Debye−Cole双频散模型对森林植被环境进行建模，最终实现了复杂环境中远距离电磁波传播分布特性的高效预测，揭示了地理与气象等环境因素对电磁波传播分布特性的影响机理，研究成果对通信、雷达、遥感、定位等系统具有极大的工程应用价值。

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