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A Fast Numerical Solution Of Scattering By A Cylinder Spectral Method For The Boundary Integral Equations
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Author :National Aeronautics and Space Administration (NASA) Publisher :Createspace Independent Publishing Platform ISBN 13 :9781721999552 Total Pages :38 pages Book Rating :4.9/5 (995 download)
Book Synopsis A Fast Numerical Solution of Scattering by a Cylinder by : National Aeronautics and Space Administration (NASA)
Download or read book A Fast Numerical Solution of Scattering by a Cylinder written by National Aeronautics and Space Administration (NASA) and published by Createspace Independent Publishing Platform. This book was released on 2018-06-28 with total page 38 pages. Available in PDF, EPUB and Kindle. Book excerpt: It is known that the exact analytic solutions of wave scattering by a circular cylinder, when they exist, are not in a closed form but in infinite series which converges slowly for high frequency waves. In this paper, we present a fast number solution for the scattering problem in which the boundary integral equations, reformulated from the Helmholtz equation, are solved using a Fourier spectral method. It is shown that the special geometry considered here allows the implementation of the spectral method to be simple and very efficient. The present method differs from previous approaches in that the singularities of the integral kernels are removed and dealt with accurately. The proposed method preserves the spectral accuracy and is shown to have an exponential rate of convergence. Aspects of efficient implementation using FFT are discussed. Moreover, the boundary integral equations of combined single and double-layer representation are used in the present paper. This ensures the uniqueness of the numerical solution for the scattering problem at all frequencies. Although a strongly singular kernel is encountered for the Neumann boundary conditions, we show that the hypersingularity can be handled easily in the spectral method. Numerical examples that demonstrate the validity of the method are also presented. Hu, Fang Q. Unspecified Center NAS1-19480; RTOP 505-90-52-01...
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