A Semi-Explicit Solution of Scattering from Dielectric Bodies Using the Method of Moments

This work presents a novel closed-form expression based on the Method of Moments (MoM) for solving the scattering problem in piecewise homogeneous media. Using point-matching with pulse basis functions in MoM, we derive an expression represents the scattered field as an explicit function of the permittivity value of each homogeneous part. The coefficient matrix depends on the permittivity values in the MoM solution to the scattering problem. Therefore, it requires matrix inversion whenever these values change slightly. Here, we propose a new expression where the matrix coefficients are independent of the permittivity values of each homogeneous part. Accordingly, when the geometry does not change, we propose a semi-explicit procedure for updating the solution with less computational complexity. Although the proposed method can be used for all 2D and 3D problems, the formulation details are implemented for 2D problems, TM incidence. Based on this explicit form, we derive some simple approximate expressions for three specific cases of permittivity perturbations. Our proposed solution is appropriate for microwave imaging, particularly when a priori information is utilized.