Wave Propagation in Vegetation Field by Combining Fast Multiple Scattering Theory and Numerical Electromagnetics in a Hybrid Method

Abstract

To calculate scattering of a vegetation field consisting of a large number of plants, an improved fast version of the hybrid method (FHM) combining fast multiple scattering theory (FMST) and a numerical electromagnetic approach has been developed. In the HM, we use a library of T-matrices and the Foldy–Lax (FL) equation to calculate the electromagnetic field interactions outside of the cylinders enclosing the individual plants. To improve CPU time and memory requirements, the FL equation is solved by a triplet of fast Fourier transforms (FFTs) consisting of two FFTs solving 2-D FFTs of spatial distribution of plants and one 1-D FFT for solving the transformation of the order of cylindrical waves in the translation addition theorem. The triple FFTs minimize the CPU time and the memory requirement for computing translation addition matrix, which has been the bottleneck of large-scale simulations in the HM. To account for nonperiodic distribution of scatterers in a corn field, the premultiplication and the postmultiplication processes were applied to the FHM. The proposed method is validated at L-band (1.4 GHz) for 100 corn plants of height 1.25 m occupying an area of 9.54 by 9.54 <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\text{m}^{2}$ </tex-math></inline-formula> . On a standard laptop, the CPU time is less than 6 min and the memory consumption is less than 710 Mbytes. The CPU time and the memory requirements are orders of magnitude more efficient than those required for solving the problem with a commercial software or using the previous version of the HM.