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

Norimasa NAKASHIMA  Mitsuo TATEIBA  

Publication
IEICE TRANSACTIONS on Electronics   Vol.E86-C   No.11   pp.2158-2166
Publication Date: 2003/11/01
Online ISSN: 
DOI: 
Print ISSN: 0916-8516
Type of Manuscript: Special Section PAPER (Special Issue on Analytical and Simulation Methods for Electromagnetic Wave Problems)
Category: 
Keyword: 
electromagnetic wave scattering,  boundary element method,  Greengard-Rokhlin's algorithm,  fast multipole method,  

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Summary: 
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.