A Research Of Skeletonization-Scheme-Based Integral Operator Compression Method And Its Applications

An integral operator of integral equation,which reveals the relationship between field and source,is a critical factor in electromagnetic radiation analysis.The integral operator compression can be used for electromagnetic radiation model simplication.The thesis will propose a skeletonization-scheme-based integral operator compression method,which is used for studying radiation field sample compression and antenna array synthesis.The process of proposed integral operator compression can be briefed as follow.First,the integral operator can be dispersed into an interaction matrix when the integral equation is dispersed into a matrix equation.A skeletonization-scheme of the interaction matrix is then obtained by using the proposed integral operator compression method.The skeletonization-scheme can be divided into two parts,which are row skeletonization-scheme and column skeletonization-scheme,respectively.The thesis will study and analyze these skeletonization-schemes as follow.Each row of the interaction matrix corresponds to a field point,so the row skeletonization is the compression of the radiation field,essentially.According to the row-skeletonization-scheme-based compression,radiation near-field and far-field adaptive sampling method is proposed,which effectively reduces the samples in radiation near-field and far-field measurement with little accuracy loss.From the numerical results,the proposed skeletonization-scheme-based adaptive sampling method is effectively saving the samples in the near field measurement.For example,the saving rate of near-field sample can reach 60% and more.After combining with the de-noise method(truncated singular value decomposition),the performance of the proposed adaptive sampling method is effectively improved when the noise is existing at the near field.In addition,according to the distribution of skeleton sample points obtained by the row-skeletonization-scheme,the reason for the distribution of skeleton sample points is then analyzed.Each column of the interaction matrix corresponds to a source point,so column skeletonization of the interaction matrix can achieve the compression of the radiation source.According to the column-skeletonization-scheme-based compression method,the sampling of continuous aperture source is compressed and a multiple pattern antenna array synthesis is proposed,where the obtained antenna array can reproduce the radiation pattern of continuous aperture sources.The numerical results show that the proposed antenna synthesis method will transform a continuous source into an antenna array and does not need to optimize the structure of the antenna array when the continuous aperture source is changing,which is effective in multiple pattern antenna synthesis.After considering the mutual coupling matrix by using post-compensation method,the performance of the antenna array with mutual coupling is investigated.At the same time,a convex optimization method is further used for enlarging the minimum spacing of antenna array elements and reducing the number of samples,which reduce the cost and difficulty in experiment effectively.Furthermore,the thesis will present the experimental scheme and analyze the existing experimental results.According to the analysis results,solutions for experiment improvement are then proposed.Numerical results show that the skeletonization-scheme-based integral operator compression method achieves the adaptive sampling of radiation field and the continuous-aperture-sources-based antenna array synthesis,effectively.The row-skeletonization-scheme-based adaptive sampling method can reduce the number of samples effectively(the sampling saving rate is more than 60%)with little error.And the column-skeletonization-scheme-based antenna array synthesis method can transform a continuous aperture source into an antenna array,where the multiple pattern antenna array synthesis method is achieved.It is worth to mention that the proposed compression method is iteration-free method.The proposed iteration-free method avoids the nonconvergence problem that may occur in an iteration-based method.In addition,the proposed compression method is based on radiation source-field relationship and independent of the source/field distribution.The performance of proposed compression method is not affected by the spatial distribution of radiation source/field.Therefore,the skeletonization-scheme obtained by proposed compression method will be fixed if the radiation source-field relationship is fixed,which can save the time cost effectively in calculation of skeletonization-scheme.