TDIE-MOT solvers based on PMCHWT and Muller equations for transient scattering by 2D dielectric objects

An accurate numerical procedure for analyses of transient scattering by two-dimensional dielectric objects by using the Time Domain Integral Equation (TDIE) method based on PMCHWT equations and Muller equations is developed. The Marching On-in Time (MOT) scheme is employed to solve the integral equations. Quadratic B-spline function is used as the temporal basis functions, and closed-form integrals with respect to time are derived to calculate the matrix elements precisely. Numerical results demonstrate that both the PMCHWT and Muller approaches are accurate and stable for a range of relative permittivity in comparisons with the frequency domain results via discrete Fourier transforms. The Muller approach may be preferred to the PMCHWT scheme for small relative permittivity; however, the PMCHWT approach seems more dependable in general cases.