Precorrected-FFT Accelerated Singular Boundary Method for Large-Scale Three-Dimensional Potential Problems (Communications in Computational Physics, 2018)
This study makes the first attempt to accelerate the singular boundarymethod (SBM) by the precorrected-FFT (PFFT) for large-scale three-dimensional potentialproblems. The SBM with the GMRES solver requires $\mathcal{O}$($N^2$) computationalcomplexity, where N is the number of the unknowns. To speed up the SBM, thePFFT is employed to accelerate the SBM matrix-vector multiplication at each iterationstep of the GMRES. Consequently, the computational complexity can be reducedto $\mathcal{O}$($N$log$N$). Several numerical examples are presented to validate the developedPFFT accelerated SBM (PFFT-SBM) scheme, and the results are compared with thoseof the SBM without the PFFT and the analytical solutions. It is clearly found that thepresent PFFT-SBM is very efficient and suitable for 3D large-scale potential problems.