Efficient evaluation of Sommerfeld integrals for TM wave scattering by buried objects

Abstract

Unlike the scattering problem in homogeneous space, intensive computations of Sommerfeld integrals are involved in the EM scattering of buried scatterers. There are mainly three bottlenecks of the CPU time for such problem: matrix filling, matrix inversion and calculation of the scattered fields. For moderately sized problems, extensive numerical experience shows that the CPU time used in the first and third items (concerned with the Sommerfeld integrals) is much more than that used in the matrix inversion. Therefore an efficient method for solving such buried object problems requires the fast evaluation of such Sommerfeld integrals. In this paper, several efficient methods are presented to evaluate the integrals that appear in the TM wave scattering by two-dimensional buried dielectric and conducting cylinders. In the numerical integration method, the original integrating path is deformed to the steepest-descent paths to expedite the numerical integration and yield a more stable computation result. In the method of steepest descent, the leading and higher-order approximation of the saddle point, and the contribution of the branch point are formulated. However these formulations are invalid near the so called critical angles. In the uniform asymptotic expansion method, we improve the approximations near such critical angles to yield satisfactory results. Finally, numerous numerical examples are given by using the fast evaluation methods. Numerical results show that the leading-order approximation and the uniform asymptotic solution can expedite the buried object scattering problem, and the CPU time will be reduced several thousands times.