The goal of this paper is to describe a novel high-resolution 3D numerical method for the solution of high frequency electromagnetic wave propagation. This method will be used later by the author to computationally simulate data for the solution of the inverse problem of imaging mine-like targets. Thus the solution of the forward problem presented in this paper is a necessary prelude to the future solution of a related inverse problem. In this paper, land mines are modeled as small abnormalities imbedded in an otherwise uniform media with an air-ground interface. These abnormalities are characterized by the electrical permittivity and the conductivity, whose values differ from those of the host media. The main challenge in the calculation of the scattered electromagnetic signal in these settings is the requirement of solving the Helmholtz equation for high frequencies which is excessively time consuming using standard direct solution techniques. A high-resolution and rapid numerical procedure for the solution of this equation is described in this paper. The kernel of this algorithm is a combination of a fourth order compact finite-difference scheme and a preconditioned Krylov subspace approach. A fourth order compact approximation for the Helmholtz equation is considered to reduce approximation and pollution errors, thereby softening the point-per-wavelength constraint. The coefficient matrix of the resulting system is not Hermitian and possesses as positive as well as negative eigenvalues so represent a significant challenge for constructing an efficient iterative solver. In our approach this system is solved by a combination of Krylov subspace-type method with a direct FFT-type preconditioner. The resulting numerical method allows efficient implementation on parallel computers. Numerical results for realistic ranges of parameters in soil and mine-like targets confirm the high efficiency of the proposed iterative algorithm.

Date Published: 31 May 2013
PDF: 8 pages
Proc. SPIE 8714, Radar Sensor Technology XVII, 87141B (31 May 2013); doi: 10.1117/12.2017982

Published in SPIE Proceedings Vol. 8714:
Radar Sensor Technology XVII
Kenneth I. Ranney; Armin Doerry, Editor(s)