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Precorrected-FFT Accelerated Singular Boundary Method for Large-Scale Three-Dimensional Potential Problems

Part of: Partial differential equations, boundary value problems Numerical methods in Fourier analysis Partial differential equations, initial value and time-dependent initial-boundary value problems

Published online by Cambridge University Press:  21 June 2017

Weiwei Li ,
Wen Chen  and
Zhuojia Fu
Weiwei Li*
Affiliation:
State Key Laboratory of Hydrology-Water Resources and Hydraulic Engineering, International Center for Simulation Software in Engineering and Sciences, College of Mechanics and Materials, Hohai University, Nanjing 210098, P.R. China State Key Laboratory of Acoustics, Institute of Acoustics, Chinese Academy of Sciences, Beijing 100190, P.R. China
Wen Chen*
Affiliation:
State Key Laboratory of Hydrology-Water Resources and Hydraulic Engineering, International Center for Simulation Software in Engineering and Sciences, College of Mechanics and Materials, Hohai University, Nanjing 210098, P.R. China State Key Laboratory of Acoustics, Institute of Acoustics, Chinese Academy of Sciences, Beijing 100190, P.R. China
Zhuojia Fu*
Affiliation:
State Key Laboratory of Hydrology-Water Resources and Hydraulic Engineering, International Center for Simulation Software in Engineering and Sciences, College of Mechanics and Materials, Hohai University, Nanjing 210098, P.R. China State Key Laboratory of Acoustics, Institute of Acoustics, Chinese Academy of Sciences, Beijing 100190, P.R. China
*
*Corresponding author. Email addresses:liweiwei_hhu@163.com (W. Li), chenwen@hhu.edu.cn (W. Chen), paul212063@hhu.edu.cn (Z. Fu)
*Corresponding author. Email addresses:liweiwei_hhu@163.com (W. Li), chenwen@hhu.edu.cn (W. Chen), paul212063@hhu.edu.cn (Z. Fu)
*Corresponding author. Email addresses:liweiwei_hhu@163.com (W. Li), chenwen@hhu.edu.cn (W. Chen), paul212063@hhu.edu.cn (Z. Fu)
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Abstract

This study makes the first attempt to accelerate the singular boundary method (SBM) by the precorrected-FFT (PFFT) for large-scale three-dimensional potential problems. The SBM with the GMRES solver requires computational complexity, where N is the number of the unknowns. To speed up the SBM, the PFFT is employed to accelerate the SBM matrix-vector multiplication at each iteration step of the GMRES. Consequently, the computational complexity can be reduced to . Several numerical examples are presented to validate the developed PFFT accelerated SBM (PFFT-SBM) scheme, and the results are compared with those of the SBM without the PFFT and the analytical solutions. It is clearly found that the present PFFT-SBM is very efficient and suitable for 3D large-scale potential problems.

Keywords

Singular boundary methodprecorrected-FFTfast matrix algorithmthree-dimensional potential problemslarge-scale

MSC classification

Secondary: 65M70: Spectral, collocation and related methods 65N35: Spectral, collocation and related methods 65T50: Discrete and fast Fourier transforms
Type
Research Article
Information
Communications in Computational Physics , Volume 22 , Issue 2 , August 2017 , pp. 460 - 472
Copyright
Copyright © Global-Science Press 2017 

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