Fast Solution of Low-Frequency Problems Using Efficient Form of MLACA with Loop-Tree Basis Functions - Zhaoneng Jiang; Xiaoyan Zhao; Ye Jiang; Xuguang Qiao; Quanquan Wang (Applied Computational Electromagnetics Society Journal (ACES), 2019)
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).