Mixed-Form Nested Approximation for Wideband Multiscale Simulations
Mixed-Form Nested Approximation for Wideband Multiscale Simulations
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DOI：
10.1109/tap.2018.2864334
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发表时间：
2018-11
影响因子：
5.7
通讯作者：
Mengmeng Li;M. Francavilla;D. Ding;Rushan Chen;G. Vecchi
中科院分区：
文献类型：
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作者：
Mengmeng Li;M. Francavilla;D. Ding;Rushan Chen;G. Vecchi
本文提出了一种混合“骨架”和“等价”的嵌套近似方法来压缩矩量法的阻抗矩阵，并用于宽带多尺度模拟。我们首先介绍一种嵌套骨架近似，其中阻抗矩阵通过对主导基函数（e.例如，在一个实施例中，骨架）与一个完整的代数实现从原来的基础功能。其思想是在近场和远场区域之间的界面周围引入自动构造的测试表面，对于每组，利用自适应交叉近似递归地对主导RWG进行采样，以压缩测试表面上的矩阵。其次，提出了一种“骨架”和“等价”嵌套逼近的混合形式算法，在低层采用嵌套骨架逼近，在高层平滑地转换为标准宽带嵌套等价逼近（WNESA）。相对于WNESA，总是可以在预定阈值处于低水平的情况下找到精确数量的骨架，这将提高计算效率。该算法的计算复杂度为$\mathcal {O}（N\log {N}）$，$N$为未知数的个数。宽带多尺度数值仿真结果表明了该算法的有效性。
We propose a mixed “skeleton” and “equivalence” nested approximation method to compress the impedance matrix of the method of moments for the wideband multiscale simulations. We first introduce a nested skeleton approximation, where the impedance matrix is expressed recursively by sampling the dominant basis functions (e. g., skeletons) with a fully algebraic implementation from the original basis functions. The idea is to introduce the automatically constructed test surface around the interface between near- and far-field regions, for each group the dominant RWGs are sampled recursively with the adaptive cross approximation to compress the matrix against the test surface. Second, we introduce a mixed-form algorithm of “skeleton” and “equivalence” nested approximation method, at low levels, the nested skeleton approximation is employed, and it is smoothly transferred to standard wideband nested equivalence approximation (WNESA) at high levels. An accurate number of skeletons can be always found with a predetermined threshold at a low level, which will improve computation efficiency, with respect to WNESA. The computational complexity of the proposed algorithm is $\mathcal {O}(N\log {N})$ , $N$ is the number of unknowns. Numerical wideband multiscale simulations demonstrate the efficiency of the proposed algorithm.