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

• Published in: IEEE transactions on antennas and propagation Vol. 58; no. 5; pp. 1601 - 1613
• Main Authors: Ming-Feng Wu, Kaur, Guneet, Yilmaz, Ali E
• Format: Journal Article
• Language: English
• Published: New York, NY IEEE 01.05.2010; Institute of Electrical and Electronics Engineers; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: Acceleration; Adaptive integral method (AIM); Algorithms; Analytical models; Antennas; Applied classical electromagnetism; Basis functions; Cartesian; Electromagnetic wave propagation, radiowave propagation; Electromagnetism; electron and ion optics; Exact sciences and technology; Fundamental areas of phenomenology (including applications); Geometry; Hafnium; Integral equations; Integrals; Interpolation; Iterative methods; Large-scale systems; Mathematical models; method of moments (MoM); Moment methods; multiple region problem; Physics; Pine; Propagation; Scattering; Solid modeling; Studies; wave propagation; wave scattering; multiple region problem; Moments method; Digital simulation; Adaptive integral method (AIM); method of moments (MoM); Horizontal polarization; Vertical polarization; Large-scale structure; Adaptive method; Integral method; Interpolation; Accuracy; Wave propagation; Electromagnetic wave propagation; Integral equations; Wave scattering; High frequency; Iterative methods; Polarized field
• ISSN: 0018-926X; 1558-2221
• DOI: 10.1109/TAP.2010.2044340

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.