A Regularized Singular Boundary Method for Inverse Cauchy Problem in Three-Dimensional Elastostatics

2018 ◽  
Vol 10 (6) ◽  
pp. 1459-1477 ◽  
Author(s):  
Aixia Zhang
Keyword(s):  
Cauchy Problem ◽  
Three Dimensional ◽  
Singular Boundary ◽  
Boundary Method ◽  
Singular Boundary Method

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

2017 ◽  
Vol 22 (2) ◽  
pp. 460-472 ◽  
Author(s):  
Weiwei Li ◽  
Wen Chen ◽  
Zhuojia Fu
Keyword(s):  
Computational Complexity ◽  
Large Scale ◽  
Three Dimensional ◽  
Iteration Step ◽  
Singular Boundary ◽  
Matrix Vector Multiplication ◽  
Boundary Method ◽  
Potential Problems ◽  
Speed Up ◽  
Singular Boundary Method

AbstractThis 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.

A wideband fast multipole accelerated singular boundary method for three-dimensional acoustic problems

2018 ◽  
Vol 206 ◽  
pp. 82-89 ◽  
Author(s):  
Wenzhen Qu ◽  
Changjun Zheng ◽  
Yaoming Zhang ◽  
Yan Gu ◽  
Fajie Wang
Keyword(s):  
Three Dimensional ◽  
Singular Boundary ◽  
Fast Multipole ◽  
Boundary Method ◽  
Singular Boundary Method
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