Volume 22, Issue 2
Precorrected-FFT Accelerated Singular Boundary Method for Large-Scale Three-Dimensional Potential Problems

Weiwei Li, Wen Chen & Zhuojia Fu

Commun. Comput. Phys., 22 (2017), pp. 460-472.

Published online: 2018-04

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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 O(N2 ) 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 O(NlogN). 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.

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@Article{CiCP-22-460, author = {Weiwei Li, Wen Chen and Zhuojia Fu}, title = {Precorrected-FFT Accelerated Singular Boundary Method for Large-Scale Three-Dimensional Potential Problems}, journal = {Communications in Computational Physics}, year = {2018}, volume = {22}, number = {2}, pages = {460--472}, 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 O(N2 ) 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 O(NlogN). 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.

}, issn = {1991-7120}, doi = {https://doi.org/10.4208/cicp.OA-2016-0075}, url = {http://global-sci.org/intro/article_detail/cicp/11306.html} }
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