新型快速高稳定性时域积分方程算法研究

项目名称： 新型快速高稳定性时域积分方程算法研究

项目编号： No.61501085

项目类型： 青年科学基金项目

立项/批准年度： 2016

项目学科： 无线电电子学、电信技术

项目作者： 李金艳

作者单位： 电子科技大学

项目金额： 19万元

中文摘要： 时域积分方程方法具有计算精度高、自动满足辐射边界条件等优势，是解决表面或均匀瞬态散射问题的首选方法。然而该类算法在实现过程中，存在后时稳定性与计算量之间的严重矛盾，一直制约着该类算法的发展。至今仍缺乏有效的后时稳定性定量判断技术，以及平衡后时稳定性与计算量矛盾的理论与实现方法。本项目拟在团队已有研究的基础，着眼于实际应用需求，以解决时域积分方程方法目前存在的关键理论与技术问题为重点，研究实现新型快速高稳定性的时域积分方程算法。首先提出重点采用递推归纳结合数值实验规律的方法，建立与算法核心矩阵相关联的稳定性判别理论；然后，根据该理论，并引入不稳定模式剥离、消除技术，实现算法后时稳定性的自适应改进；之后进一步提出以算法关键矩阵作为中间桥梁建立数学模型，通过最优化理论分析获得快速算法计算量与稳定性的平衡点；最终形成快速高稳定性的时域积分方程新型算法。本项目的研究兼具重要的理论价值与应用意义。

中文关键词： 电磁计算；时域有限积分法；时间步进算法；后时稳定性；快速算法

英文摘要： The time-domain integral equation (TDIE) method, which has the advantages of high computational accuracy and automatic realization of radiation condition, is the preferred method for analyzing homogeneous/surface transient scattering problems. However, the application of the TDIE method has been bottlenecked because of the tradeoff between the late-time stability and high computational expenditure of the method. Even now, there still lack of effective ways to quantitatively predict the late-time stability and to balance the tradeoff between the late-time stability and computational expenditure. This research intends, based on the initial work by our group, to solve these key theoretical and technical problems with the TDIE method, with outcome of the novel fast and stable TDIE algorithms for practical electromagnetic problems. More specifically, we will first use recursive and inductive techniques, discrete mathematics and eigen mode theory to establish the new stability theory and criteria that allow accurate prediction of the late-time stability. Then, based on the developed theory, we will develop the adaptive algorithms free of the late time stability by separating and eliminating unstable modes. After it, by establishing mathematical model on the use of the key matrix and applying optimization theory, we will find a criterion to achieve the best tradeoff between the late-time stability and the computational expenditure. Finally, we will formulate the novel fast and stable TDIE method that is free of the late-time stability with low computational counts for solving real-world problems. In other words, this research will present results of great significance in both theory and applications.

英文关键词： electromagnetic calculation;time-domain integral equation (TDIE) ;marching-on in-time (MOT) scheme;late-time stability;fast algorithm