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Efficient iterative solution of electromagnetic scattering using adaptive cross approximation enhanced characteristic basis function method

机译:自适应交叉逼近增强特征基函数方法的电磁散射有效迭代解

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摘要

A new hybrid adaptive cross approximation-characteristic basis function method (ACA-CBFM) is proposed to efficiently solve the electromagnetic scattering problems. In the conventional ACA-CBFM, the ACA is only applied to speed up the construction of the reduced matrix that is directly solved and stored. However, with the increase of the size of the targets under analysis, the reduced matrix will become so large that it is difficult to directly solve and store. In this study, the reduced matrix is further compressed by the adaptive cross approximation-singular value decomposition (ACA-SVD) and solved by an iterative method, which leads to reduced storage and accelerated matrix vector product. Furthermore, the ACA-SVD is adapted to efficiently generate the characteristic basis functions (CBFs), which reduces both the time of generating initial CBFs and the SVD time of initial CBFs. Numerical results about the electromagnetic scattering from perfect electric conducting targets are given to demonstrate the merits of the proposed methods.
机译:为了有效地解决电磁散射问题,提出了一种新的混合自适应交叉逼近特征基函数方法(ACA-CBFM)。在传统的ACA-CBFM中,ACA仅用于加速直接求解和存储的简化矩阵的构建。但是,随着分析对象的大小增加,缩小后的矩阵将变得很大,以至于难以直接求解和存储。在这项研究中,通过自适应交叉逼近奇异值分解(ACA-SVD)对压缩后的矩阵进行进一步压缩,并通过迭代方法对其进行求解,从而减少了存储量并加速了矩阵矢量积。此外,ACA-SVD适于有效地生成特征基函数(CBF),这减少了生成初始CBF的时间和初始CBF的SVD时间。给出了来自理想导电目标的电磁散射的数值结果,以证明所提出方法的优点。

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