Research On Fast Algorithm Of Target Electromagnetic Scattering Based On Wavelet-MoM

With the increasingly wider application of electromagnetic fields,the discipline computational electromagnetics has been gradually developed,thereinto,it is available to accurately solve all kind of electromagnetic problems with the method of moments(Mo M)which is widely used especially in radiation and scattering of target.However,as a solving method for integral equation,in the solving process,Green's functions are introduced,the Mo M makes it necessary to solve a complicated matrix equation.In the calculation of electromagnetic scattering by the electrically large conducting objects,a big non-singular and dense impedance matrix will be formed,the inversion of which is of complexity requiring more computation,more time consuming and also liable to give fault.Under this condition,this paper carries out in-depth exploration of the solving process of electromagnetic scattering of target with the Mo M and the detailed research is as follows:1.Firstly,this paper introduces the theory of surface integral equation,deduces the integral equation based on ideal conductor surface,then discusses the basic principle of the Mo M,emphatically illustrates the selection of basis functions,and deduces the general formula of solving the electric field integral equation with the Mo M,and also carries out verification of the relevant solving correctness based on the specific examples.2.It carries out detailed analysis of singularities existing in the solution of the Mo M based discrete electric field integral equation,puts forward a high efficiency method of impedance matrix completion-barycentric subdivision by considering the problems of low efficiency and computational complexity in impedance matrix completion with traditional methods,which also solves the singularities above mentioned at the same time and completes the formula derivation for its relevant application.3.To carry out sparsification of dense impedance matrix and rapidly solving the matrix equation,wavelet analysis is introduced in the Mo M based solution of electromagnetic scattering of target,the discrete wavelet sequence is deduced with Mallat algorithm and Haar wavelet basis,and then analysis of the transformation principle of wavelet into the sparse matrix is carried out.It is available to realize the sparsification of dense matrix through wavelet transformation and thresholding.4.By combining the restarted Generalized Minimum Residual method and ILU preconditioning technique,the transformed impedance matrix equation from wavelet is solved,then visualization analysis of the relevant transformation principle is carried out,convergence analysis of the Generalized Minimum Residual method used also carried out,and finally aiming at target scattering characteristics,the algorithm's high efficiency and correctness put forward in this paper is proved based on simulation examples.