An efficient and robust solution to time domain integral equations of electromagnetics and their implementation for homogeneous and inhomogeneous dielectric scatterers.

摘要

Recent developments in the areas of high-resolution radar technology, electromagnetics pulse (EMP) simulation studies, target identification techniques, and singularity expansion method (SEM) related problems where the transient response plays a vital role have increased the need for a reliable and robust time domain integral equation (TDIE) solver. Numerical methods based on TDIEs are needed for their geometrical flexibility, lack of numerical dispersion, efficiency for broadband, time-varying, and nonlinear problems, and intrinsic incorporation of radiation condition.; Despite these advantages and the multiplying need for a TDIE solver, the issues of instability and inaccuracy encountered in their execution still continue to haunt them and hamper their widespread implementation. This work aims at developing a stable and accurate TDIE technique based on the marching-on-in-time (MOT) method using special temporal basis functions and bandlimited extrapolation. The work developed here uses a method called AMBLE: Accurate Marching by Band-Limited Extrapolation.; AMBLE was initially implemented for PECs using bandlimited interpolatory functions (BLIFs) and higher-order vector basis functions to effect the temporal and spatial discretization of the surface integral equations, respectively. Since the basis functions used for the temporal representation are noncausal, an extrapolation scheme was employed to recover the ability to solve the problem by marching on in time. Early results of AMBLE showed that it rendered stable and accurate results for closed scatterers but went unstable for open scatterers. The instability witnessed was a slow growing, low frequency type that occurred due to the existence of solenoidal currents.; The work presented here overcomes this low frequency instability using two novel stabilization techniques. The first method augments the commonly used tangential field integral equations with additional integral equations that impose conditions on the temporal derivative of the normal magnetic field. The next method developed here is based on the same idea, but with an entirely different implementation. Specifically, it uses a loop-tree decomposition of the space of spatial basis functions and treats the equations tested with solenoidal testing functions differently than the other equations. Numerical results show that the modified methods are stable and accurate retaining the superlinear and exponential convergence with regard to spatial and temporal discretizations respectively, observed in early AMBLE implementations. (Abstract shortened by UMI.)