scholarly journals Fast multipole accelerated singular boundary method for the 3D Helmholtz equation in low frequency regime

2015 ◽  
Vol 70 (4) ◽  
pp. 679-690 ◽  
Author(s):  
Wenzhen Qu ◽  
Wen Chen ◽  
Yan Gu
Keyword(s):  
Helmholtz Equation ◽  
Low Frequency ◽  
Singular Boundary ◽  
Fast Multipole ◽  
Boundary Method ◽  
Frequency Regime ◽  
Singular Boundary Method

scholarly journals Precorrected-FFT Accelerated Singular Boundary Method for High-Frequency Acoustic Radiation and Scattering

Mathematics ◽  
2022 ◽  
Vol 10 (2) ◽  
pp. 238
Author(s):  
Weiwei Li ◽  
Fajie Wang
Keyword(s):  
High Frequency ◽  
Acoustic Radiation ◽  
Low Frequency ◽  
Singular Boundary ◽  
Cpu Time ◽  
Interpolation Matrix ◽  
Collocation Points ◽  
Boundary Method ◽  
Frequency Regime ◽  
Singular Boundary Method

This paper presents a precorrected-FFT (pFFT) accelerated singular boundary method (SBM) for acoustic radiation and scattering in the high-frequency regime. The SBM is a boundary-type collocation method, which is truly free of mesh and integration and easy to program. However, due to the expensive CPU time and memory requirement in solving a fully-populated interpolation matrix equation, this method is usually limited to low-frequency acoustic problems. A new pFFT scheme is introduced to overcome this drawback. Since the models with lots of collocation points can be calculated by the new pFFT accelerated SBM (pFFT-SBM), high-frequency acoustic problems can be simulated. The results of numerical examples show that the new pFFT-SBM possesses an obvious advantage for high-frequency acoustic 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

Singular Boundary Method for Various Exterior Wave Applications

2015 ◽  
Vol 12 (02) ◽  
pp. 1550011 ◽  
Author(s):  
Zhuo-Jia Fu ◽  
Wen Chen ◽  
Ji Lin ◽  
Alexander H.-D. Cheng
Keyword(s):  
Fundamental Solution ◽  
Helmholtz Equation ◽  
Laplace Equation ◽  
International Workshop ◽  
Fundamental Solutions ◽  
Singular Boundary ◽  
Intensity Factors ◽  
Trefftz Method ◽  
Boundary Method ◽  
Singular Boundary Method

This paper presents an improved singular boundary method (ISBM) to various exterior wave applications. The SBM is mathematically simple, easy-to-program, meshless and introduces the concept of source intensity factors to eliminate the singularity of the fundamental solutions. In this study, we first derive the source intensity factors of the exterior Helmholtz equation by means of the source intensity factors of the exterior Laplace equation due to the same order of the singularities on their fundamental solutions. The source intensity factors of the exterior Laplace equation can be determined using the reference technique [Chen, W. and Gu, Y. [2011] "Recent advances on singular boundary method," Joint international workshop on Trefftz method VI and method of fundamental solution II, Taiwan]. Numerical illustrations demonstrate the efficiency and accuracy of the proposed scheme on four benchmark exterior wave examples.

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