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Application of multilevel directional adaptive cross approximation technique for electromagnetic problems

机译:多级方向自适应交叉逼近技术在电磁问题中的应用

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摘要

In this paper, a novel scheme is presented for forming the matrix equations of multilevel adaptive cross approximation (MLACA) algorithm. The main idea of the proposed technique is to use the directional grouping scheme to subdivide the far-field domain of MLACA algorithm. By using the grouping scheme, the far-field interaction domain can be divided into many cone structures. The matrix between the observation group and far-field group in the cone structure is low-rank, which meets the directional far-field requirement. At the same time, the near-field interaction matrices are formed by the SVD(T) method to further reduce the total memory requirements. With the given techniques, the memory requirement of the novel grouping scheme for the far-field is much less than half of traditional MLACA algorithm. Meanwhile, the memory requirement of the SVD(T) method for the near-field is only about one-third of direct filling.
机译:本文提出了一种新的形成多层自适应交叉逼近(MLACA)算法矩阵方程的方案。提出的技术的主要思想是使用方向分组方案细分MLACA算法的远场域。通过使用分组方案,可以将远场交互作用域划分为许多圆锥结构。圆锥结构中观测组与远场组之间的矩阵为低秩,满足定向远场要求。同时,通过SVD(T)方法形成近场交互矩阵,以进一步减少总存储需求。使用给定的技术,针对远场的新颖分组方案的存储需求远小于传统MLACA算法的一半。同时,SVD(T)方法对近场的存储需求仅为直接填充的三分之一。

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