新型缩减矩阵构造加快特征基函数法迭代求解

New reduced matrix construction accelerated iterative solution of characteristic basis function method

针对特征基函数法在分析电大目标电磁散射特性时存在缩减矩阵方程迭代求解收敛慢的问题,提出一种新型缩减矩阵构造方法提高特征基函数法的迭代求解效率.首先,应用奇异值分解技术压缩激励源,求解出新激励源下各子域的特征基函数;其次,将新激励源和特征基函数作为构造缩减矩阵的检验函数和基函数新方法构造的缩减矩阵的对角子矩阵均为单位矩阵,缩减矩阵条件数得到了优化.与传统方法相比,新方法构造的缩减矩阵方程迭代求解效率得到了显著提高;另外,由于矩阵方程求解次数减少,特征基函数的构造效率也得到了提高,数值结果证明了新方法的精确性和有效性.

The characteristic basis function method is known as an effective method to solve the electromagnetic scattering problems,but the convergence of the iterative solution of the reduced matrix equation is slow when the characteristic basis function method is used to analyze the electromagnetic scattering characteristics of the electrically large target.In order to mitigate this problem,a new reduced matrix construction method is proposed to improve the iterative solution efficiency of characteristic basis function method in this paper.Firstly,the singular value decomposition technique is used to compress the incident excitations,and the characteristic basis functions of each sub-domain under the new excitations are solved.Then,the new excitations and the characteristic basis functions are defied as the testing and basis functions to construct the reduced matrix.The diagonal sub-matrices of the reduced matrix constructed by the new testing and basis functions are all identity matrices,thereby improving the condition of reduced matrix.Thus,the total number of iterations to achieve reasonable results is significantly reduced.Numerical simulations are conducted to validate the performance of the proposed method.The results demonstrate that the efficiency of the iterative solution of the reduced matrix equation constructed by the new method is significantly improved.Furthermore,the characteristic basis functions’ generation time required by the proposed method is noticeably less than that by the traditional characteristic basis function method due to the reduced number of matrix equation solutions.