Improved Model-Based Parameter Estimation Approach for Accelerated Periodic Method of Moments Solutions With Application to the Analysis of Convoluted Frequency Selected Surfaces and Metamaterials

• Published in: IEEE transactions on antennas and propagation Vol. 58; no. 1; pp. 122 - 131
• Main Authors: Xiande Wang, Werner, D.H.
• Format: Journal Article
• Language: English
• Published: New York, NY IEEE 01.01.2010; Institute of Electrical and Electronics Engineers; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: Acceleration; Applied sciences; Artificial magnetic conductors (AMC); Diffraction, scattering, reflection; Exact sciences and technology; fast Fourier transform (FFT); Filters; Frequency estimation; Frequency selective surfaces; frequency selective surfaces (FSS); impedance matrix interpolation; Incidence; Interpolation; Magnetic separation; Mathematical analysis; Mathematical models; Matrices; Matrix methods; Metamaterials; Method of moments; model-based parameter estimation (MBPE); Moment methods; multiband FSS; Parameter estimation; periodic moment method (PMM); Radiocommunications; Radiowave propagation; space-filling Hilbert curves; spectral-domain periodic method of moments (PMM); Studies; Surface impedance; Telecommunications; Telecommunications and information theory; Performance evaluation; Frequency selective surfaces; Parameter estimation; Fast Fourier transformation; Oblique incidence; Iterative method; spectral-domain periodic method of moments (PMM); impedance matrix interpolation; Accuracy; Wide band; Multilevel system; Conjugate gradient method; Spectral method; Moment method; periodic moment method (PMM); Matrix product; metamaterials; fast Fourier transform (FFT); Algorithm; multiband FSS; space-filling Hilbert curves; Interpolation; frequency selective surfaces (FSS); Artificial magnetic conductors (AMC); model-based parameter estimation (MBPE); Impedance matrix; Metamaterial; Normal incidence
• ISSN: 0018-926X; 1558-2221
• DOI: 10.1109/TAP.2009.2036196

An improved ¿smart¿ interpolation approach known as model-based parameter estimation (MBPE) is applied to the wide-band interpolation of periodic method of moments (PMM) impedance matrices for normal and oblique incidence cases. Prior to interpolation, easy to calculate but hard to interpolate, phase terms are removed from the impedance matrices. An efficient spectral-domain PMM formulation is introduced for the accelerated analysis of frequency selective surface (FSS) problems with a large number of unknowns, employing a one dimensional O(N log N) FFT-based method to speed up the computation of matrix-vector products within the bi-conjugate gradient (BCG) iterative solver, which is made possible by the asymmetric multilevel block-Toeplitz structure of the impedance-matrix. The MBPE interpolation algorithm provides a faster matrix fill time than the brute force method and is comparable or even faster than the 2-D FFT-based method for a large number of unknowns. It also has the advantage that it can be applied to non-uniform gridding cases. The accuracy and efficiency of the proposed techniques for large FSS problems are demonstrated by several design examples for both the normal and oblique incidence cases. We also apply this efficient analysis tool to the design of multiband single-layer FSS filters and artificial magnetic conductors (AMC) comprised of a 2-D periodic arrangement of convoluted metallic strips in the shape of a Hilbert curve. The multiband properties of the Hilbert curve FSS filters are studied for different iteration orders (i.e., different degrees of space-filling).