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
K
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
K
times using different grids and different groups of basis functions. The proposed multiple-grid AIM scheme requires a total of
O
(
N

^nz,near
+?
_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 ~10
⁶
degrees of freedom and ~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.