二代小波在求解电磁场积分方程中的应用

Application of Second Generation Wavelet Transform to Solution of Electromagnetic Integral Equations

为实现电磁场积分方程的快速求解,对第二代小波变换理论进行了阐述,并给出了适用于矩阵变换的具体公式,从而提出了一种基于第二代小波变换的预处理算法。通过对矩量法生成的稠密阻抗矩阵进行稀疏化预处理,加速了矩阵方程迭代求解中的矩阵矢量积。针对传统小波变换在矩阵方程维数上的限制,构造了一种任意维矩阵方程的预处理算法。对不同目标的电磁散射特性进行了分析,并将结果与解析解、矩量法直接求解等进行了对比,验证了算法的有效性。鉴于其通用性,所提任意维矩阵方程预处理算法可以推广至其他工程计算领域。

The theory of the second generation wavelet transform was described and specific formulas for wavelet matrix transform were deduced, and finally a preprocessing technique based on the second generation wavelet transform was proposed to accelerate the solution of electromagnetic integral equation. By sparsfying the dense impedance matrix obtained by method of moments （MOM）, the matrix-vector-multiplication （MVM） for iteration was sped up. To eliminate the limitation to matrix dimension when the traditional wavelet transform was used, a new preprocessing algorithm for arbitrarily dimensional matrix equations was constructed. The electromagnetic scattering analysis of different objects was completed, and the results were compared with that obtained by the analytical solution or direct MOM solution to validate the effectiveness of the proposed method. Due to its generality, the presented matrix transform technique can also be expanded to other engineering computation areas.