基于混合ACA的缺陷钢轨高效电磁建模

提出了一种基于矩量法(MoM)结合多层快速多极子(MLFMA)和自适应交叉近似(ACA)算法计算目标电磁特性的算法，该算法实现了对电大尺寸复合目标散射计算的加速和内存的降低。对于目标自作用的近场区域，多层快速多极子加速矩量法中的矩阵矢量乘运算，降低了计算的存储和复杂度；对于远场区域，根据阻抗矩阵的低秩特性，采用ACA对其压缩，加速矩阵的填充。矩阵填充按照树形结构划分的单元块间的相互作用依次进行存储，对每一块与块之间的求解采用ACA算法，对矩阵做压缩处理。提出的基于ACA的混合算法能够对2个目标耦合作用的阻抗矩阵进行压缩，缩短矩阵的填充时间并降低内存需求，同时也能够减少迭代求解过程中矩阵向量的计算时间，从而极大缩短电磁散射计算的总时间。数值仿真实验表明该算法比传统方法计算更高效，且计算精确度保持一致。

Efficient electromagnetic modeling of defective rail based on hybrid ACA method

The Method of Moments(MoM) combined with Multi-Layer Fast Multipole Algorithm (MLFMA) and Adaptive Cross Approximation(ACA) is proposed to calculate the electromagnetic characteristics of the target. The computation of the scattering of electrically large composite targets is speeded up and the memory requirement is reduced. For the near-field region of self-acting target, MoM and MLFMA are combined to speed up the matrix vector multiplication, reduce the storage and decrease the complexity of calculation. The far-field impedance matrix has a low rank characteristic and can be compressed by ACA to speed-up the filling rate of the matrix. Matrix filling is stored sequentially according to the interaction among the blocks divided by tree structure. ACA algorithm is utilized to solve the problem of the compression of matrix between each block and block. The proposed hybrid algorithm based on ACA can compress the impedance matrix of the coupling between two targets, reduce the filling time and the required memory of the matrix. At the same time, the computation time of matrix vectors can be shortened in the iterative process, thus the total time of electromagnetic scattering calculation can be reduced greatly. Numerical simulation results show that the algorithm is more efficient than the traditional method, and the accuracy of electromagnetic scattering is consistent.