Research On Optimization Algorithm Of Wideband Frequency Sweeping Moment Method

The integral equations for electromagnetic scattering from a perfectly conductive surface include the electric field integral equation(EFIE),the magnetic field integral equation(MFIE)and the combined field integral equation(CFIE).CFIE is a linear combination of EFIE and MFIE.The numerical accuracy of EFIE moment method is higher when no internal resonance is encountered,but the convergence speed of its iteration solution is very slow.The numerical accuracy of MFIE moment method and CFIE moment method is lower than EFIE,but their corresponding coefficient matrices have better condition numbers,and the convergence speed of their iterative solutions is faster.When using EFIE Moment Method or CFIE Moment Method in a broadband,the latter takes much less time than the former,but its numerical accuracy is obviously worse than the former.The main reason is that MFIE is used in CFIE.In theory,the analytical solution of EFIE also satisfies MFIE,but the solution from the method of moments is discrete solution rather than analytical solution.In the method of moments,the discretization of the target surface destroys the continuity of the surface normal vector,which results in that the solution of EFIE moment method does not satisfy the matrix equation of MFIE moment method.In this paper,we abandon the traditional MFIE matrix equation as the companion of EFIE matrix equation,and find a new companion for EFIE matrix equation(a non-traditional companion)by means of mathematical optimization method,so as to establish an optimized CFIE matrix equation of non-traditional meaning and apply it to swept-frequency moment method.The main works are as follows:1.A new companion for EFIE matrix equation of moment method is proposed,which is used to establish an optimized CFIE matrix equation of non-traditional meaning.The mathematical principle and implementation steps of the method are described.The numerical accuracy and convergence speed of the iterative solution are verified by numerical examples.2.The optimized CFIE matrix equation of moment method is applied to sweeping-frequency moment method,and is combined with matrix interpolation method to improve the speed of generating matrices.The implementation steps of the method are described,and the feasibility and efficiency of the method are verified by numerical examples.3.The optimized CFIE matrix equation of moment method is combined with FG-FFT fast algorithm(with matrix interpolation method)for sweeping-frequency moment method.The implementation steps of this method are described,and numerical examples show that the method can significantly reduce the computing time and memory requirements.