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An FFT Based Fast Poisson Solver on Spherical Shells

Published online by Cambridge University Press:  20 August 2015

Yin-Liang Huang ,
Jian-Guo Liu  and
Wei-Cheng Wang
Yin-Liang Huang*
Affiliation:
Department of Applied Mathematics, National University of Tainan, Tainan 70005, Taiwan
Jian-Guo Liu*
Affiliation:
Department of Physics and Department of Mathematics, Duke University, Durham, NC 27708, USA
Wei-Cheng Wang*
Affiliation:
Department of Mathematics, National Tsing Hua University, Hsinchu 30013, Taiwan
*
Corresponding author.Email:[email protected]
Email:[email protected]
Email:[email protected]
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Abstract

We present a fast Poisson solver on spherical shells. With a special change of variable, the radial part of the Laplacian transforms to a constant coefficient differential operator. As a result, the Fast Fourier Transform can be applied to solve the Poisson equation with operations. Numerical examples have confirmed the accuracy and robustness of the new scheme.

Keywords

35Q8665N0665N1565N2265T50Poisson equationspherical coordinateFFTspectral-finite difference methodfast diagonalizationhigh order accuracyerror estimatetrapezoidal ruleEuler-Maclaurin formulaBernoulli numbers
Type
Research Article
Information
Communications in Computational Physics , Volume 9 , Issue 3 , March 2011 , pp. 649 - 667
Copyright
Copyright © Global Science Press Limited 2011

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