Block-Toeplitz Fast Integral Equation Solver for Large Finite Periodic and Partially Periodic Array Systems

Elizabeth H. BLESZYNSKI; Marek K. BLESZYNSKI; Thomas JAROSZEWICZ

Block-Toeplitz Fast Integral Equation Solver for Large Finite Periodic and Partially Periodic Array Systems

Elizabeth H. BLESZYNSKI, Marek K. BLESZYNSKI, Thomas JAROSZEWICZ

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We describe elements of a fast integral equation solver for large periodic and partly periodic finite array systems. A key element of the algorithm is utilization (in a rigorous way) of a block-Toeplitz structure of the impedance matrix in conjunction with either conventional Method of Moments (MoM), Fast Multipole Method (FMM), or Fast Fourier Transform (FFT)-based Adaptive Integral Method (AIM) compression techniques. We refer to the resulting algorithms as the (block-)Toeplitz-MoM, (block-)Toeplitz-AIM, or (block-)Toeplitz-FMM algorithms. While the computational complexity of the Toeplitz-AIM and Toeplitz-FMM algorithms is comparable to that of their non-Toeplitz counterparts, they offer a very significant (about two orders of magnitude for problems of the order of five million unknowns) storage reduction. In particular, our comparisons demonstrate, that the Toeplitz-AIM algorithm offers significant advantages in problems of practical interest involving arrays with complex antenna elements. This result follows from the more favorable scaling of the Toeplitz-AIM algorithm for arrays characterized by large number of unknowns in a single array element and applicability of the AIM algorithm to problems requiring strongly sub-wavelength resolution.

Publication: IEICE TRANSACTIONS on Electronics Vol.E87-C No.9 pp.1586-1594

Publication Date: 2004/09/01

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Type of Manuscript: Special Section PAPER (Special Section on Wave Technologies for Wireless and Optical Communications)

Category: Basic Electromagnetic Analysis

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Elizabeth H. BLESZYNSKI, Marek K. BLESZYNSKI, Thomas JAROSZEWICZ, "Block-Toeplitz Fast Integral Equation Solver for Large Finite Periodic and Partially Periodic Array Systems" in IEICE TRANSACTIONS on Electronics, vol. E87-C, no. 9, pp. 1586-1594, September 2004, doi: .
Abstract: We describe elements of a fast integral equation solver for large periodic and partly periodic finite array systems. A key element of the algorithm is utilization (in a rigorous way) of a block-Toeplitz structure of the impedance matrix in conjunction with either conventional Method of Moments (MoM), Fast Multipole Method (FMM), or Fast Fourier Transform (FFT)-based Adaptive Integral Method (AIM) compression techniques. We refer to the resulting algorithms as the (block-)Toeplitz-MoM, (block-)Toeplitz-AIM, or (block-)Toeplitz-FMM algorithms. While the computational complexity of the Toeplitz-AIM and Toeplitz-FMM algorithms is comparable to that of their non-Toeplitz counterparts, they offer a very significant (about two orders of magnitude for problems of the order of five million unknowns) storage reduction. In particular, our comparisons demonstrate, that the Toeplitz-AIM algorithm offers significant advantages in problems of practical interest involving arrays with complex antenna elements. This result follows from the more favorable scaling of the Toeplitz-AIM algorithm for arrays characterized by large number of unknowns in a single array element and applicability of the AIM algorithm to problems requiring strongly sub-wavelength resolution.
URL: https://globals.ieice.org/en_transactions/electronics/10.1587/e87-c_9_1586/_p

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@ARTICLE{e87-c_9_1586,
author={Elizabeth H. BLESZYNSKI, Marek K. BLESZYNSKI, Thomas JAROSZEWICZ, },
journal={IEICE TRANSACTIONS on Electronics},
title={Block-Toeplitz Fast Integral Equation Solver for Large Finite Periodic and Partially Periodic Array Systems},
year={2004},
volume={E87-C},
number={9},
pages={1586-1594},
abstract={We describe elements of a fast integral equation solver for large periodic and partly periodic finite array systems. A key element of the algorithm is utilization (in a rigorous way) of a block-Toeplitz structure of the impedance matrix in conjunction with either conventional Method of Moments (MoM), Fast Multipole Method (FMM), or Fast Fourier Transform (FFT)-based Adaptive Integral Method (AIM) compression techniques. We refer to the resulting algorithms as the (block-)Toeplitz-MoM, (block-)Toeplitz-AIM, or (block-)Toeplitz-FMM algorithms. While the computational complexity of the Toeplitz-AIM and Toeplitz-FMM algorithms is comparable to that of their non-Toeplitz counterparts, they offer a very significant (about two orders of magnitude for problems of the order of five million unknowns) storage reduction. In particular, our comparisons demonstrate, that the Toeplitz-AIM algorithm offers significant advantages in problems of practical interest involving arrays with complex antenna elements. This result follows from the more favorable scaling of the Toeplitz-AIM algorithm for arrays characterized by large number of unknowns in a single array element and applicability of the AIM algorithm to problems requiring strongly sub-wavelength resolution.},
keywords={},
doi={},
ISSN={},
month={September},}

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TY - JOUR
TI - Block-Toeplitz Fast Integral Equation Solver for Large Finite Periodic and Partially Periodic Array Systems
T2 - IEICE TRANSACTIONS on Electronics
SP - 1586
EP - 1594
AU - Elizabeth H. BLESZYNSKI
AU - Marek K. BLESZYNSKI
AU - Thomas JAROSZEWICZ
PY - 2004
DO -
JO - IEICE TRANSACTIONS on Electronics
SN -
VL - E87-C
IS - 9
JA - IEICE TRANSACTIONS on Electronics
Y1 - September 2004
AB - We describe elements of a fast integral equation solver for large periodic and partly periodic finite array systems. A key element of the algorithm is utilization (in a rigorous way) of a block-Toeplitz structure of the impedance matrix in conjunction with either conventional Method of Moments (MoM), Fast Multipole Method (FMM), or Fast Fourier Transform (FFT)-based Adaptive Integral Method (AIM) compression techniques. We refer to the resulting algorithms as the (block-)Toeplitz-MoM, (block-)Toeplitz-AIM, or (block-)Toeplitz-FMM algorithms. While the computational complexity of the Toeplitz-AIM and Toeplitz-FMM algorithms is comparable to that of their non-Toeplitz counterparts, they offer a very significant (about two orders of magnitude for problems of the order of five million unknowns) storage reduction. In particular, our comparisons demonstrate, that the Toeplitz-AIM algorithm offers significant advantages in problems of practical interest involving arrays with complex antenna elements. This result follows from the more favorable scaling of the Toeplitz-AIM algorithm for arrays characterized by large number of unknowns in a single array element and applicability of the AIM algorithm to problems requiring strongly sub-wavelength resolution.
ER -