On the spectrum of the electric field integral equation and the convergence of the moment method
On the spectrum of the electric field integral equation and the convergence of the moment method
复制标题
电场积分方程的谱及矩法的收敛性
DOI：
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发表时间：
2001
影响因子：
2.9
通讯作者：
W. Chew
中科院分区：
文献类型：
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作者：
K. Warnick;W. Chew
现有的基于边界积分方程法的数值散射法的收敛估计在离散长度为零的极限下是渐近的，并且随着问题规模的增大而下降。为了分析计算电磁学中感兴趣的大散射问题的数值方法的效率和精度，我们研究了无限大导电条上TM(弱奇异核)和TE极化(超奇异核)的电场积分方程谱。由于表面波模的自耦合，对于两种极化方式，离散化的积分方程的条件数都随着带电尺寸的平方根而增加。从EFIE的谱，也可以估计由积分方程离散化引入的解的误差。在远离解的边缘奇异性的情况下，对于矩阵元素精确积分的低阶基，其离散化长度误差为二阶，如果采用近似求积规则，则误差为一阶。与数值结果的比较表明，这些条件数和解的误差估计是有效的。频谱理论提供了对计算电磁学中常见的数值方法的行为的见解。版权所有©2001 John Wiley&Sons，Ltd.
Existing convergence estimates for numerical scattering methods based on boundary integral equations are asymptotic in the limit of vanishing discretization length, and break down as the electrical size of the problem grows. In order to analyse the efficiency and accuracy of numerical methods for the large scattering problems of interest in computational electromagnetics, we study the spectrum of the electric field integral equation (EFIE) for an infinite, conducting strip for both the TM (weakly singular kernel) and TE polarizations (hypersingular kernel). Due to the self‐coupling of surface wave modes, the condition number of the discretized integral equation increases as the square root of the electrical size of the strip for both polarizations. From the spectrum of the EFIE, the solution error introduced by discretization of the integral equation can also be estimated. Away from the edge singularities of the solution, the error is second order in the discretization length for low‐order bases with exact integration of matrix elements, and is first order if an approximate quadrature rule is employed. Comparison with numerical results demonstrates the validity of these condition number and solution error estimates. The spectral theory offers insights into the behaviour of numerical methods commonly observed in computational electromagnetics. Copyright © 2001 John Wiley & Sons, Ltd.