Broadband Fast Multipole Method For Studying The Electromagnetic Scattering Characteristics Of Ideal Conductor Targets

The integral eqqation method with its high accuracy and robustness for handling the complex boundary condition has been widely used for electromagnetic simulations of the scattering and radiation problems in microwave band and optical band.Using the method of moment to solve integral equations will generate dense impedance matrix,which is the reason why the multilevel fast multipole method was adopted for analyzing problems with big unknowns.As an effective and simply programmable method,the broadband multilevel fast multipole method is studied in this paper,which is used to accelerate the analysis for large targets problems with fine structures.Firstly,the multilevel fast multipole algorithm based on the addition theorem and the principle of plane wave expansion simply introduced.And then an approximate diagonalization of the Green's function is put forward to avoid the low frequency breakdown problem,which will be studied in detail in this paper.The approximate diagonalization needs only minor revise in the existing MLFMM codes and is easy to combine with the high frequency fast multipole algorithm.Secondly,the broadband multilevel fast multipole algorithm is applied to analyze the scattering problems of perfect electric conductor.The magnetic field integral equation(MFIE)which is suited for analyzing closed structures converges fast and does not have low frequency breakdown.The electric field integral equation(EFIE)needs some transformation to avoid low frequency breakdown.The broadband multilevel fast multipole algorithm to expand these two kinds of integral equations is derived in more detail.Finally,the augmented electric field integral equation(AEFIE)which is free of low frequency breakdown includes charges as extra unknowns to separate the contribution of the vector and scalar potentials.In addition,a new augmented combined field integral equation(ACFIE)is developed by adding the magnetic filed operator to AEFIE.Several numerical examples are simulated to verify the accuracy and efficiency of the method.