Research On Direct Solution To System Equation Of Method Of Moments Using Low-rank Matrix Compression

The method of moments in electromagnetic field is one of common methods to solve electromagnetic scattering.The system matrix of the method of moments is dense,and there are direct solutions to the system equation of the traditional method of moments,including Gauss elimination method,LU decomposition method and so on.For the direct solutions,the storage complexity and computational complexity are very high.In the past very long time,the system equation of the method of moments is mainly solved by an iterative solver.The convergence of an iterative solver depends on the condition number of system matrix.Therefore,when the condition number of system matrix is very high,the iterative solver is not suitable for solving.In recent years,more and more attention has been paid to the direct solution to the system equation of the method of moments,which is mainly focused on the introduction of low-rank matrix compression to reduce storage requirement and improve computational efficiency.In this dissertation,direct solutions to the system equation of the method of moments using low-rank matrix compression are researched.The specific works is as follows:1.A binary tree-based scheme for fast grouping basis functions is proposed.The system matrix of the method of moments built by using this scheme has a block structure,and each sub-block has almost the same size,which is very conducive to the balance between storage requirement and computational efficiency at each level of a multilevel algorithm.At each level,a non-diagonal sub-block is decided,according to the far-field condition,to be directly compressed or to be subdivided.All sub-matrices to be compressed will be compressed by using U-ACA algorithm instead of using ACA algorithm and QR algorithm one after another as in the existing literature.2.A recursive algorithm for the inverse of the system matrix of method of moments based on the traditional blocked Gaussian elimination method is established.The algorithm is both simple and intuitive,and can be applied to directly solve the system equation of method of moments whose system matrix is not very large in size.3.A recursive algorithm for the inverse of the H-matrix is proposed for directly solving the system equation of the method of moments based on the combined-field integral equation.The algorithm adopts the idea of divide and conquer,and partitions the system matrix into four recursively until proper bottom size is reached,greatly reducing the computational complexity of the recursive process for the inverse matrix.