Low Order-Singularity Electric-Field Integral Equation Solvable with Pulse Basis Functions and Point Matching

摘要

Unlike the magnetic-field integral equation, the conventional form of the electric-field integral equation (EFIE) cannot be solved accurately with the method of moments (MOM) using pulse basis functions and point matching. The highly singular kernel of the EFIE, rather than the current derivatives, precludes the use of the pulse-basis function point-matching MOM. A new form of the EFIE has been derived whose kernel has no greater singularity than that of the free-space Green's function. This new low-order singularity form of the EFIE, the LEFIE, has been solved numerically for perfectly electrically conducting bodies of revolution (BORs) using pulse basis functions and point- matching. Derivatives of the current are approximated with finite differences using a quadratic Lagrangian interpolation polynomIal. This simple solution of the LEFIE is contingent, however, on the vanishing of a linear integral that appears when the original EFIE is transformed to obtain the LEFIE. This generally restricts the applicability of the LEFIE to smooth closed scatterers. Bistatic scattering calculations performed for a prolate spheroid demonstrate that results comparable in accuracy to the conventional EFIE can be obtained with the LEFIE using pulse basis functions and point matching provided a higher density of points is used close to the ends of the BOR generating curve to compensate for the use of one-sided finite difference approximations of the first and second derivatives of the current.