Greengard-Rokhlin's Fast Multipole Algorithm for Numerical Calculation of Scattering by <I>N</I> Conducting Circular Cylinders

Norimasa NAKASHIMA; Mitsuo TATEIBA

Greengard-Rokhlin's Fast Multipole Algorithm for Numerical Calculation of Scattering by N Conducting Circular Cylinders

Norimasa NAKASHIMA, Mitsuo TATEIBA

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The boundary element method (BEM), a representative method of numerical calculation of electromagnetic wave scattering, has been used for solving boundary integral equations. Using BEM, however, we finally have to solve a linear system of L equations expressed by dense coefficient matrix. The floating-point operation is O(L²) due to a matrix-vector product in iterative process. Greengard-Rokhlin's fast multipole algorithm (GRFMA) can reduce the operation to O(L). In this paper, we describe GRFMA and its floating-point operation theoretically. Moreover, we apply the fast Fourier transform to the calculation processes of GRFMA. In numerical examples, we show the experimental results for the computation time, the amount of used memory and the relative error of matrix-vector product expedited by GRFMA. We also discuss the convergence and the relative error of solution obtained by the BEM with GRFMA.

Publication: IEICE TRANSACTIONS on Electronics Vol.E86-C No.11 pp.2158-2166

Publication Date: 2003/11/01

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Type of Manuscript: Special Section PAPER (Special Issue on Analytical and Simulation Methods for Electromagnetic Wave Problems)

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Norimasa NAKASHIMA, Mitsuo TATEIBA, "Greengard-Rokhlin's Fast Multipole Algorithm for Numerical Calculation of Scattering by N Conducting Circular Cylinders" in IEICE TRANSACTIONS on Electronics, vol. E86-C, no. 11, pp. 2158-2166, November 2003, doi: .
Abstract: The boundary element method (BEM), a representative method of numerical calculation of electromagnetic wave scattering, has been used for solving boundary integral equations. Using BEM, however, we finally have to solve a linear system of L equations expressed by dense coefficient matrix. The floating-point operation is O(L²) due to a matrix-vector product in iterative process. Greengard-Rokhlin's fast multipole algorithm (GRFMA) can reduce the operation to O(L). In this paper, we describe GRFMA and its floating-point operation theoretically. Moreover, we apply the fast Fourier transform to the calculation processes of GRFMA. In numerical examples, we show the experimental results for the computation time, the amount of used memory and the relative error of matrix-vector product expedited by GRFMA. We also discuss the convergence and the relative error of solution obtained by the BEM with GRFMA.
URL: https://global.ieice.org/en_transactions/electronics/10.1587/e86-c_11_2158/_p

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@ARTICLE{e86-c_11_2158,
author={Norimasa NAKASHIMA, Mitsuo TATEIBA, },
journal={IEICE TRANSACTIONS on Electronics},
title={Greengard-Rokhlin's Fast Multipole Algorithm for Numerical Calculation of Scattering by N Conducting Circular Cylinders},
year={2003},
volume={E86-C},
number={11},
pages={2158-2166},
abstract={The boundary element method (BEM), a representative method of numerical calculation of electromagnetic wave scattering, has been used for solving boundary integral equations. Using BEM, however, we finally have to solve a linear system of L equations expressed by dense coefficient matrix. The floating-point operation is O(L²) due to a matrix-vector product in iterative process. Greengard-Rokhlin's fast multipole algorithm (GRFMA) can reduce the operation to O(L). In this paper, we describe GRFMA and its floating-point operation theoretically. Moreover, we apply the fast Fourier transform to the calculation processes of GRFMA. In numerical examples, we show the experimental results for the computation time, the amount of used memory and the relative error of matrix-vector product expedited by GRFMA. We also discuss the convergence and the relative error of solution obtained by the BEM with GRFMA.},
keywords={},
doi={},
ISSN={},
month={November},}

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TY - JOUR
TI - Greengard-Rokhlin's Fast Multipole Algorithm for Numerical Calculation of Scattering by N Conducting Circular Cylinders
T2 - IEICE TRANSACTIONS on Electronics
SP - 2158
EP - 2166
AU - Norimasa NAKASHIMA
AU - Mitsuo TATEIBA
PY - 2003
DO -
JO - IEICE TRANSACTIONS on Electronics
SN -
VL - E86-C
IS - 11
JA - IEICE TRANSACTIONS on Electronics
Y1 - November 2003
AB - The boundary element method (BEM), a representative method of numerical calculation of electromagnetic wave scattering, has been used for solving boundary integral equations. Using BEM, however, we finally have to solve a linear system of L equations expressed by dense coefficient matrix. The floating-point operation is O(L²) due to a matrix-vector product in iterative process. Greengard-Rokhlin's fast multipole algorithm (GRFMA) can reduce the operation to O(L). In this paper, we describe GRFMA and its floating-point operation theoretically. Moreover, we apply the fast Fourier transform to the calculation processes of GRFMA. In numerical examples, we show the experimental results for the computation time, the amount of used memory and the relative error of matrix-vector product expedited by GRFMA. We also discuss the convergence and the relative error of solution obtained by the BEM with GRFMA.
ER -