A single-level low rank IE-QR algorithm for PEC scattering problems using EFIE formulation
A single-level low rank IE-QR algorithm for PEC scattering problems using EFIE formulation
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DOI：
10.1109/tap.2004.832367
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发表时间：
2004-08
影响因子：
5.7
通讯作者：
S. Seo;Jin-Fa Lee
中科院分区：
文献类型：
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作者：
S. Seo;Jin-Fa Lee
本文提出了一种基于低秩近似的单级矩阵压缩算法，称为IE-QR，以加快电场积分方程（EFIE）的计算速度。如图所示，选择的组数与N/sup 1/2/成正比，其中N为未知数，结果算法的内存和CPU时间均为0 （N/sup 1.5/）。该算法的独特之处在于：a. IE-QR算法基于分离良好的组的近秩缺乏性。这种近秩缺陷假设适用于许多积分方程方法，如电磁学（EM）中的拉普拉斯、辐射和散射问题。同样的算法可以适用于EM以外的其他应用，只需很少或不需要修改；b.通过对发送组和接收组分别进行排序的双排序过程实现秩估计。因此，IE-QR算法可以在不组装整个系统矩阵的情况下实现矩阵压缩。此外，本文还提出了一种“几何邻近”预条件。当与GMRES结合使用时，这种“几何邻近”预条件被证明是求解压缩矩阵方程的高效和有效的。
This paper presents a single-level matrix compression algorithm, termed IE-QR, based on a low-rank approximation to speed up the electric field integral equation (EFIE) formulation. It is shown, with the number of groups chosen to be proportional to N/sup 1/2/, where N is the number of unknowns, the memory and CPU time for the resulting algorithm are both O(N/sup 1.5/). The unique features of the algorithm are: a. The IE-QR algorithm is based on the near-rank-deficiency property for well-separated groups. This near-rank-deficiency assumption holds true for many integral equation methods such as Laplacian, radiation, and scattering problems in electromagnetics (EM). The same algorithm can be adapted to other applications outside EM with few or no modifications; and, b. The rank estimation is achieved by a dual-rank process, which ranks the transmitting and receiving groups, respectively. Thus, the IE-QR algorithm can achieve matrix compression without assembling the entire system matrix. Also, a "geometric-neighboring" preconditioner is presented in this paper. This "geometric-neighboring" preconditioner when used in conjunction with GMRES is proven to be both efficient and effective for solving the compressed matrix equations.