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 K homogeneous regions, it introduces different auxiliary grids. It uses the k(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 k(th) region. Thus, the AIM stages are executed a total of times using different grids and different groups of basis functions. The proposed multiple-grid AIM scheme requires a total of O(Nnz,near + Sigma(k) N(k)(C) log N(k)(C)) operations per iteration, where N(nz,near) denotes the total number of near-zone interactions in all regions and N(k)(C) denotes the number of nodes of the k(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 similar to 10(6) degrees of freedom and similar to 10(3) 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.