Diagonal form fast multipole singular boundary method applied to the solution of high-frequency acoustic radiation and scattering

2017 ◽  
Vol 111 (9) ◽  
pp. 803-815 ◽  
Author(s):  
Wenzhen Qu ◽  
Wen Chen ◽  
Changjun Zheng
Keyword(s):  
High Frequency ◽  
Acoustic Radiation ◽  
Diagonal Form ◽  
Singular Boundary ◽  
Fast Multipole ◽  
Boundary Method ◽  
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

The Local Singular Boundary Method for Solution of Two-Dimensional Advection–Diffusion Equation

2021 ◽  
pp. 2150041
Author(s):  
Karel Kovářík ◽  
Juraj Mužík
Keyword(s):  
Diffusion Equation ◽  
Large Scale ◽  
Sparse Matrix ◽  
Singular Boundary ◽  
Tracer Transport ◽  
Advection Diffusion Equation ◽  
Advection Diffusion ◽  
Boundary Method ◽  
Local Variant ◽  
Singular Boundary Method

This work focuses on the derivation of the local variant of the singular boundary method (SBM) for solving the advection-diffusion equation of tracer transport. Localization is based on the combination of SBM and finite collocation. Unlike the global variant, local SBM leads to a sparse matrix of the resulting system of equations, making it much more efficient to solve large-scale tasks. It also allows solving velocity vector variable tasks, which is a problem with global SBM. This paper compares the results on several examples for the steady and unsteady variant of the advection-diffusion equation and also examines the dependence of the accuracy of the solution on the density of the nodal grid and the size of the subdomain.

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