Numerical 3D Solutions of Maxwell Equations Based on Hybrid Method Combining Generalized T Matrix and Foldy-Lax Multiple Scattering Theory for Vegetation/Trees Scattering

In this paper, we develop a hybrid method based on Foldy-Lax multiple scattering theory (FL) and generalized T matrix of a single object, for full wave simulations of vegetation/trees. The hybrid method of solving the Maxwell equations has three steps: (1) extracting the T matrix of every single object, (2) wave transformations and (3) solving the coupled wave interaction equations. To calculate the generalized T matrix of a single object, we use HFSS which is a 3D full-wave electromagnetic field simulation tool. The method of T matrix extraction from HFSS is verified by comparing with the analytical solution of a sphere. The method is applicable to find the T matrix for the complicated object where the analytical solutions are not available. Then, the wave transformations are performed based on the translation addition theorem. Numerical methods of calculating the transformation coefficients are developed. Finally, the wave interactions among the single objects are accounted for by FL. The results of the hybrid method agree with those of the HFSS brute force method. In comparison, the hybrid method is much more efficient than HFSS for vegetation scattering and applicable to large problems such as full wave simulations of a tree.