Fast forward solver for buried dielectric targets at low frequencies

摘要

Fast solutions of the electromagnetic scattering and inverse scattering by dielectric objects buried in the lossy earth are very important for near-surface geophysical exploration problems, environmental applications, and demining, detection and characterization of unexploded ordnance. Usually, a ground penetrating radar (GPR) is the electromagnetic tool of choice for such detection problems because it can provide high resolution. Unfortunately, when the electrical conductivity is high, GPR cannot penetrate far enough for many applications due to the high-frequency components. In order to achieve greater penetration in conductive earth, much lower frequencies are often used **************************************************************************************************************************************************************************************************************************************************************** **************************************************************************************************************************************************************************************************************************************************************** ques have been proposed to speed up the evaluation of matrix-vector multiply in the iterative solvers of method of moments. The fast multipole method (FMM) [1] and its multilevel cousin, the multilevel fast multipole algorithm (MLFMA) [2], rely on a multilevel geometrical partitioning of the problem space and an expansion of the scattered field in spherical harmonics. The conjugate-gradient fast-Fourier-transform (CG-FFT) method [3] is a powerful fast algorithm but it works only when the object is modeled with uniform rectangular grids which necessitates a staircase approximation in the modeling of an arbitrary geometry. The adaptive integral method (ATM) [4] projects triangular elements onto uniform grids with the aid of auxiliary basis functions and then carries out the matrix-vector multiplication by the fast Fourier transforms (FFT). The precorrected-FET method was originally proposed by Philips and White [5] to solve the electrostatic problems. It was extended by the authors recently to solve 3-D scattering problems in flee space [6] and to analyze large-scale microstrip structures [7]. In [6], the precorrected-FFT formulations for only the electric field integral equation (EFIE) are presented. As we know, a combination of the EFIE and MEW, namely the combined field integral equation (CFIE), has been found to be able to eliminate the interior resonance problem suffered by both EFIE and MFIE and to converge much faster than EFIE and MEW [8]. In comparison with the AIM, the present method can achieve good results of the same accuracy, but with a grid spacing at least two to three times larger than that of AIM. So in normal cases, the number of the grids is of a level of O(N), the precorrected-FFT method is at best an approach of O(N) (memory requirement) and O(NlogN) (computational complexity) requirements [6]. It should be also noted that in this paper, the algorithm is implemented in a way that no eatra computational expense is required as compared with those in EFIE, which leads to another advantage over the AIM based method reported in [8].