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首页> 外文期刊>Applied Computational Electromagnetics Society journal >Fast Solution of Low-Frequency Problems Using Efficient Form of MLACA with Loop-Tree Basis Functions
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Fast Solution of Low-Frequency Problems Using Efficient Form of MLACA with Loop-Tree Basis Functions

机译：使用带有回路树基函数的有效形式的MLACA快速解决低频问题

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摘要

In this paper, an efficient scheme of numerical method is proposed to solve the low frequency (LF) problems, which combines the loop-tree basis functions with an efficient form of multilevel adaptive cross approximation (EFMLACA) algorithm. It utilizes the loop-tree basis functions to divide the vector part and scalar part of the impedance matrix. Meanwhile, the scalar part is frequency normalized Through this operation, it can avoid the low frequency breakdown problem. In order to accelerate the matrix vector multiplication, the EFMLACA algorithm is applied. Meanwhile, the compressed block decomposition (CBD) preconditioner is applied to improve the condition number of poor convergence problems. The numerical results demonstrate that the memory requirement and computation time required for a matrix vector multiplication of EFMLACA algorithm is much less than that of MLACA and ACA-SVD. Moreover, the matrix vector multiplication of EFMLACA algorithm is also much more efficient than that of low-frequency multilevel fast multipole algorithm (LF-MLFMA).
机译：本文提出了一种有效的数值方法来解决低频问题，该方法将回路树基函数与一种有效形式的多级自适应交叉逼近（EFMLACA）算法相结合。它利用循环树基函数来划分阻抗矩阵的矢量部分和标量部分。同时，对标量部分进行频率归一化，可以避免低频击穿问题。为了加快矩阵矢量的乘法运算，应用了EFMLACA算法。同时，使用压缩块分解（CBD）预处理器来改善收敛性较差问题的条件数。数值结果表明，EFLMACA算法的矩阵向量乘法所需的存储空间和计算时间远小于MLACA和ACA-SVD。此外，EFLMACA算法的矩阵矢量乘法也比低频多级快速多极算法（LF-MLFMA）高效得多。

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