计算电磁学积分方程的数值精度研究与改进

项目名称： 计算电磁学积分方程的数值精度研究与改进

项目编号： No.61201012

项目类型： 青年科学基金项目

立项/批准年度： 2013

项目学科： 电子学与信息系统

项目作者： 颜溯

作者单位： 电子科技大学

项目金额： 27万元

中文摘要： 在计算电磁学积分方程方法中被广泛使用的面积分方程可以被分为第一类和第二类Fredholm积分方程。长期以来，计算电磁学界对这两类方程的普遍认识是，第一类积分方程具有很高的数值求解精度，但是迭代收敛性能很差；而第二类积分方程具有很快的迭代收敛速度，但是数值精度却很差。近十余年来，国际学术界一直致力于研究有效提高第二类积分方程数值精度的方法。然而，对于这一问题，至今仍然没有有效的处理方法，第二类积分方程至今仍然无法达到第一类积分方程的求解精度。同时，对于影响第二类积分方程数值求解精度的原因也仍然众说纷纭，没有公认的结论性认识。本项研究，将从积分方程的算子特性出发，通过分析各个算子的数值误差来源，找到限制积分方程求解精度的瓶颈，并对其进行改进，以使第二类积分方程的数值精度与第一类积分方程相当。同时也对第一类积分方程的求解精度进行改进，并提出稳定的误差检验方案。

中文关键词： 第二类积分方程；数值精度；电磁散射与辐射；积分方程快速算法；GPU并行

英文摘要： In computational electromagnetics, the widely used surface integral equations can be categorized into the Fredholm integral equations of the first and the second kinds. It is a common observation among the international academia that the first-kind integral equations always have a very good numerical accuracy, but a rather poor convergence in an iterative solution; while the second-kind integral equations usually have a fast convergence rate in an iterative solution, but far less accurate numerical solutions than their first-kind counterparts. In the past decade, much effort has been made to improve the numerical accuracy of the second-kind integral equations world widely. However, there is still no effective resolution to this accuracy issue, and no conclusive understandings on the numerical accuracy of these two kinds of integral equations are achieved. In this research, we will start our investigation from the mathematical properties of the integral equation operators. By the thorough analysis of the error sources of the numerical solutions to the integral equations, we will locate and systematically remove the bottlenecks which limit the improvement of the numerical accuracy. The objective of this research is to improve the numerical accuracy of the second-kind integral equations in both the perfect electr

英文关键词： Second Kind Integral Equation；Numerical Accuracy；Electromagnetic Radiation and Scattering；Fast Algorithms in Integral Equations；GPU Parallelization