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求解电大尺寸目标的电磁问题的关键是计算量和存储量。本文分析了共轭梯度法解基于分层基层次型(H2)矩阵快速算法的电磁散射问题时单步迭代的计算量。一方面临时存储部分矩阵向量积而避免层间及同层同一矩矢积的重复计算,以较小的存储增量为代价明显加快了计算速度;另一方面根据均匀Lagrange插值退化核函数矩阵的多层Toeplitz矩阵特性,压缩存储退化核函数矩阵,并用快速傅里叶变换加速该矩阵与向量的乘积。算例结果显示了本文方法在减少内存占用量和缩短单步迭代时间方面的有效性。
The key to solving the electromagnetic problem of large size targets is the amount of computation and storage. This paper analyzes the computational complexity of single-step iteration when the conjugate gradient method is used to solve the electromagnetic scattering problem based on the fast algorithm of the hierarchical matrix (H2) matrix. On the one hand, partial matrix vector product is stored temporarily to avoid repeated calculation of the same moment product between layers and the same layer, and the calculation speed is obviously accelerated at the expense of smaller storage increment; on the other hand, according to the uniform Lagrange interpolation degenerated kernel function matrix Multi-layer Toeplitz matrix features compress the degenerated kernel matrix and store the product of the matrix and vector using Fast Fourier Transform. The results of the example show the effectiveness of our method in reducing the memory footprint and shortening the single-step iteration time.