Good Condition Number Of The Electric Field Integral Equation

To realize efficient solution of electromagnetic (EM) scattering from complex target has very practical value for the design of radar system and identify of radar targets. The efficient solver for EM scattering from complex target is more and more important. Hence, it is the important goal of scattering research to find some efficient methods. The method of moments (MoM) based on surface integral equations is one of most efficient numerical approaches for scattering problems. However, if the conventional RWG basis function is used to discretize the EFIE, the numerical solution of the EFIE suffers from instability at low frequencies, since the condition number of the EFIE has an unbounded increase as the discretization interval tends to zero. Hence, a well-conditioned EFIE (WEFIE) to overcome the shortcomings of the EFIE is presented and discussed in this paper.First of all, WEFIE is theoretically analyzed in this paper. Numerical results prove that it can solve the low frequency problem which is always met in traditional EFIE. Then we first proposed a new WEFIE with curve RWG which is named Curve-WEFIE (CWEFIE). By compared with WEFIE based on the plane RWG, CWEFIE needs less unknowns and memory requirement without compromising accuracy and numerical speed. The numerical results validate the stability and efficiency.Secondly, multilevel fast multipole algorithm (MLFMA) is employed in this method for electrically large objects. At the same time, far field is combined with spherical harmonics expansion of the k-space integrals to reduce the memory. Because resulting matrix is well conditioned, the method owns faster solving speed and more stable character compared with the traditional EFIE.Finally, we use SVD to modify the MLFMA to solve the low frequency break down problem when the finest group size is small. At the same time, we combine it with CWEFIE to reduce the solving time. The numerical examples demonstrate the efficiency of our method.