A Multiple-Grid Adaptive Integral Method for Multi-Region Problems

A multiple-grid extension of the adaptive integral method (AIM) is presented for fast analysis of scattering from piecewise homogeneous structures. The proposed scheme accelerates the iterative method-of-moments solution of the pertinent surface integral equations by employing multiple auxiliary Cartesian grids: If the structure of interest is composed of <i>K</i> homogeneous regions, it introduces <i>K</i> different auxiliary grids. It uses the <i>k</i> ^th auxiliary grid first to determine near-zones for the basis functions and then to execute AIM projection, propagation, interpolation, and near-zone pre-correction stages in the <i>k</i> ^th region. Thus, the AIM stages are executed a total of <i>K</i> times using different grids and different groups of basis functions. The proposed multiple-grid AIM scheme requires a total of <i>O</i>(<i>N</i> ^nz,near+?_k <i>N</i> _k ^Clog<i>N</i> _k ^C) operations per iteration, where <i>N</i> ^nz,near denotes the total number of near-zone interactions in all regions and <i>N</i> _k ^C denotes the number of nodes of the <i>k</i> ^th Cartesian grid. Numerical results validate the method's accuracy and reduced complexity for large-scale canonical structures with large numbers of regions (up to ~10⁶ degrees of freedom and ~10³ regions). Moreover, an investigation of HF-band wave propagation in a loblolly pine forest model demonstrates the method's generality and practical applicability. Multiple-grid AIM accelerated simulations with various tree models show that higher fidelity models for the trunk material and branch geometry are needed for accurate calculation of horizontally-polarized field propagation while lower fidelity models can be satisfactory for analyzing vertically-polarized field propagation.