Multiple-grid adaptive integral method for general multi-region problems

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Wu, Mingfeng

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Efficient electromagnetic solvers based on surface integral equations (SIEs) are developed for the analysis of scattering from large-scale and complex composite structures that consist of piecewise homogeneous magnetodielectric and perfect electrically/magnetically conducting (PEC/PMC) regions. First, a multiple-grid extension of the adaptive integral method (AIM) is presented for multi-region problems. The proposed method accelerates the iterative method-of-moments solution of the pertinent SIEs 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/anterpolation, 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}+sum({N_k}^Clog{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). Then, a Green function modification approach and a scheme of Hankel- to Teoplitz-matrix conversions are efficiently incorporated to the multiple-grid AIM method to account for a PEC/PMC plane. Theoretical analysis and numerical examples show that, compared to a brute-force imaging scheme, the Green function modification approach reduces the simulation time and memory requirement by a factor of (almost) two or larger if the structure of interest is terminated on or resides above the plane, respectively. In addition, the SIEs are extended to cover structures composed of metamaterial regions, PEC regions, and PEC-material junctions. Moreover, recently introduced well-conditioned SIEs are adopted to achieve faster iterative solver convergence. Comprehensive numerical tests are performed to evaluate the accuracy, computational complexity, and convergence of the novel formulation which is shown to significantly reduce the number of iterations and the overall computational work. Lastly, the efficiency and capabilities of the proposed solvers are demonstrated by solving complex scattering problems, specifically those pertinent to analysis of wave propagation in natural forested environments, the design of metamaterials, and the application of metamaterials to radar cross section reduction.



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