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

Weiwei Li, Wen Chen & Zhuojia Fu

DOI: 10.4208/cicp.OA-2016-0075

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 $\mathcal{O}$($N^2$) 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 $\mathcal{O}$($N$log$N$). 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 $\mathcal{O}$($N^2$) 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 $\mathcal{O}$($N$log$N$). 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} }
TY - JOUR T1 - Precorrected-FFT Accelerated Singular Boundary Method for Large-Scale Three-Dimensional Potential Problems AU - Weiwei Li, Wen Chen & Zhuojia Fu JO - Communications in Computational Physics VL - 2 SP - 460 EP - 472 PY - 2018 DA - 2018/04 SN - 22 DO - http://doi.org/10.4208/cicp.OA-2016-0075 UR - https://global-sci.org/intro/article_detail/cicp/11306.html KW - AB -

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 $\mathcal{O}$($N^2$) 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 $\mathcal{O}$($N$log$N$). 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.

Weiwei Li, Wen Chen and Zhuojia Fu. (2018). Precorrected-FFT Accelerated Singular Boundary Method for Large-Scale Three-Dimensional Potential Problems. Communications in Computational Physics. 22 (2). 460-472. doi:10.4208/cicp.OA-2016-0075
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