The Method Of Moments Is A Fast Filling And Solving Algorithm

With the advancement of devices on high frequency,high power,high integration and high complexity in microwave engineering,the problem of ultra large size and multi-scale problems in the electromagnetic field requires us to study new fast methods to improve the efficiency of MoM.In this paper,we research on several problems in the efficient calculation of MoM,focusing on the fast calculation of the impedance matrix,the parallel filling method of the impedance matrix,the wide-band matrix estimation method and the new estimation method.The main contributions of this thesis are as follows:1.A new task distribution method based on parallel moment method is proposed.The method constructs a new matrix block decomposition form by rewriting the moment method impedance matrix.In the shared storage parallel environment,the proposed method implemented the paralleled matrix filling in the fast filling method based on HRWG basis functions and paralleled matrix vector multiplying in the CGS iterative scheme in the manner of chessboard task distribution.Numerical experiments show that the parallel MoM has good parallel efficiency.2.A localized fast multi-frequency matrix-filling method is proposed for fast generating the impedance matrix.The proposed method is based on the retarded 1-ordered Taylor expansion of Green’s functions on each field point,which use shorter series intercepts to get a wider range of Green’s functions,and hence can significantly increase the speed of the multifrequency matrix.Numerical experiments show that this method has good accuracy and computational efficiency.3.An ultra-wide-band rational matrix interpolation method with 4-point samples is proposed.Based on the local expansion technique,this method uses rational polynomial matrix interpolation with few sampling points to obtain a large bandwidth.Different from the traditional rational polynomial function interpolation methods,the method is like the truncation of a Laurent expansion and it is with a very small complexity.The numerical experiment shows that the method has the advantage of calculating the complexity and the performance of the extrapolation.4.A new method of rapid solution for MoM based on sparse representation is studied.By introducing regression training into the moment method solution,the accurate numerical solution is transformed into a machine learning process with different sparsity.In this method,impedance matrix elements with different sparsity are taken as the training set,and obtain an approximate solution with sufficient accuracy by training.