Transient Electromagnetic Analysis of Complex Penetrable Scatterers using Volume Integral Equations

Abstract

Simulation tools capable of analyzing electromagnetic (EM) field/wave interactions on complex penetrable scatterers have applications in various areas of engineering ranging from the design of integrated antennas to the subsurface imaging. EM simulation tools operating in the time domain can be formulated to directly solve the Maxwell equations or the integral equations obtained by enforcing fundamental field relations or boundary conditions. Time domain integral equation (TDIE) solvers offer several benefits over differential equation solvers: They require smaller number discretization elements/sampling points (both in space and time). Despite the advantages, TDIE solvers suffer from increased computational cost, stability issues of the time-marching algorithms, and limited applicability to complex scatterers. This thesis is focused on addressing the last two issues associated with time domain volume integral equation (TD-VIE) solvers, as the issue of increased computational cost has been addressed by recently developed acceleration methods. More specifically, four new closely-related, but different marching on-in-time (MOT) algorithms are formulated and implemented to solve the time domain electric and magnetic field volume integral equations (TD-EFVIE and TD-MFVIE). The first algorithm solves the TD-EFVIE to analyze EM wave interactions on high-contrast dielectric scatterers. The stability of this MOT scheme is ensured by using two-sided approximate prolate spherical wave (APSW) functions to discretize the time dependence of the unknown current density as well as an extrapolation scheme to restore the causality of matrix system resulting from this discretization. The second MOT scheme solves the TDMFVIE to analyze EM wave interactions on dielectric scatterers. The TD-MFVIE is cast in the form of an ordinary differential equation (ODE) and the unknown magnetic field is expanded using spatial basis functions. The time-dependent coefficients of this expansion are found by integrating the resulting ODE system using a linear multistep method. The third method is formulated and implemented to analyze EM wave interactions on scatterers with Kerr nonlinearity. The former scheme integrates in time a coupled of system of the TD-EFVIE and the nonlinear constitutive relation, which is cast in the form of an ODE system, for the expansion coefficients of the electric field and flux using a linear multistep method. The last method described in this thesis is developed to analyze EM wave interactions on ferrite scatterers.