TY - JOUR
T1 - Precorrected-FFT Accelerated Singular Boundary Method for Large-Scale Three-Dimensional Potential Problems
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 - <p style="text-align: justify;">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.</p>