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主要研究了低频条件下目标的散射问题,详细给出了基于Loop-Tree矩量法的多层低频快速多极子方法基本原理。通过对自由空间格林函数进行多极子展开,避免了传统快速多极子方法通过平面波展开格林函数遇到的低频崩溃问题。改进的对角预条件技术显著地减少了预条件矩阵的构造时间和矩阵的迭代求解时间。数值算例证明了算法的有效性。
The scattering of the target under low frequency is mainly studied. The principle of multilayer low frequency fast multipole method based on Loop-Tree method is given in detail. The multi-dipole expansion of free space Green’s function is avoided, which avoids the low-frequency collapse problem encountered by the traditional fast multipole method by expanding the Green’s function by plane wave. The improved diagonal preconditioning technique significantly reduces the construction time of the preconditioned matrix and the iterative solution time of the matrix. Numerical examples demonstrate the effectiveness of the algorithm.