Electromagnetic Scattering by Finite Periodic Arrays Using the Characteristic Basis Function and Adaptive Integral Methods

• Published in: IEEE transactions on antennas and propagation Vol. 58; no. 9; pp. 3086 - 3090
• Main Authors: Li Hu, Le-Wei Li, Mittra, R
• Format: Journal Article
• Language: English
• Published: New York, NY IEEE 01.09.2010; Institute of Electrical and Electronics Engineers; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: Acceleration; Adaptive arrays; Adaptive integral method (AIM); Algorithms; Applied classical electromagnetism; Applied sciences; Arrays; Basis functions; characteristic basis function method (CBFM); characteristic basis functions (CBFs); Computational complexity; Diffraction, scattering, reflection; Electromagnetic scattering; Electromagnetic wave propagation, radiowave propagation; Electromagnetism; electron and ion optics; Exact sciences and technology; Fundamental areas of phenomenology (including applications); Integral equations; Integrals; Mathematical analysis; Mathematical models; Matrix decomposition; periodic array; Periodic structures; Photonic crystals; Physics; Plane waves; Polarization; Radiocommunications; Radiowave propagation; Singular value decomposition; Studies; Telecommunications; Telecommunications and information theory; Unit cell; Electromagnetic wave scattering; Performance evaluation; Singularity; Adaptive integral method (AIM); Algorithm; Adaptive method; characteristic basis function method (CBFM); Characteristic function; Integral method; Accuracy; Electromagnetic wave propagation; Singular vector; periodic array; characteristic basis functions (CBFs); Wave scattering; Plane wave; Numerical simulation; Galerkin method; Singular value decomposition; electromagnetic scattering
• ISSN: 0018-926X; 1558-2221; 1558-2221
• DOI: 10.1109/TAP.2010.2052563

We introduce a novel technique that combines the AIM algorithm with the characteristic basis function method (CBFM) to solve the problem of electromagnetic scattering by large but finite periodic arrays. An important advantage of using the CBFM for this problem is that we only need to analyze a single unit cell to construct the characteristic basis functions (CBFs) for the entire array. The CBFs are generated by illuminating a single unit cell with a plane wave incident from different angles, for both the θ- and φ-polarizations. The initial set of CBFs, generated in the manner described above, are then downselected by applying a singular value decomposition (SVD) procedure and retaining only the left singular vectors whose corresponding singular values fall above a threshold. Next, in the conventional CBFM, we derive a reduced matrix by applying the Galerkin procedure and solve it directly if its size is manageable. However, when solving an array problem, which precludes the direct-solve option, we can utilize the adaptive integral method (AIM) algorithm, detailed below, not only to accelerate the solution but to reduce memory requirements as well. Numerical examples are included in this communication to demonstrate the accuracy and the numerical efficiency of the proposed technique.