New Exact Image Methods for Impedance Boundary Half-Space Green’s Function and Their Fast Multipole Expansion

2019 ◽  
Vol 67 (2) ◽  
pp. 1108-1118 ◽  
Author(s):  
Bi-Yi Wu ◽  
Xin-Qing Sheng
Keyword(s):  
Green’S Function ◽  
Half Space ◽  
Green's Function ◽  
Multipole Expansion ◽  
Fast Multipole ◽  
Impedance Boundary

Simulation of Sound Propagation Over an Infinite Impedance Plane by Using a Fast Multipole BEM

2020 ◽  
Vol 28 (02) ◽  
pp. 2050020
Author(s):  
Chang-Jun Zheng ◽  
Wen-Yu Liu ◽  
Yong-Bin Zhang ◽  
Chuan-Xing Bi ◽  
Hai-Feng Gao ◽  
...  
Keyword(s):  
Green’S Function ◽  
Half Space ◽  
Green's Function ◽  
Boundary Integral ◽  
Infinite Plane ◽  
Fast Multipole ◽  
Impedance Boundary ◽  
Image Domain ◽  
Impedance Plane ◽  
Expansion Coefficients

In this paper, a half-space fast multipole BEM is developed for the simulation of three-dimensional acoustic problems above an infinite impedance plane. The half-space impedance Green’s function involving a complex line source is used, so that both mass-like and spring-like impedance boundary conditions on the infinite plane can be explicitly satisfied and the infinite plane is not required to be discretized. The Burton–Miller method is employed to tackle the fictitious eigenfrequency problem involved in the conventional boundary integral equation method. Image relations of the multipole expansion coefficients are used and the half-space impedance Green’s function is modified to apply such relations to avoid calculating, translating and saving the multipole/local expansion coefficients in the image domain. An automatic integrator with adaptive interval subdivision is further adopted to calculate the line integral contained in the M2L translation formula accurately and efficiently. Numerical examples are given to show the validity and potential of the method.

Image Solution for the 3-D Static Green’s Function of a Vertically Stratified Two-Layer Half-Space

2016 ◽  
Vol 64 (10) ◽  
pp. 4336-4342
Author(s):  
Ehsan Zareian-Jahromi ◽  
Seyed Hossein H. Sadeghi ◽  
Reza Sarraf-Shirazi ◽  
Rouzbeh Moini ◽  
Hamidreza Karami
Keyword(s):  
Green’S Function ◽  
Half Space ◽  
Green's Function

A Liouville Type Theorem for Poly-harmonic System with Dirichlet Boundary Conditions in a Half Space

2015 ◽  
Vol 15 (1) ◽  
Author(s):  
Zhao Liu ◽  
Wei Dai
Keyword(s):  
Boundary Conditions ◽  
Green’S Function ◽  
Half Space ◽  
Green's Function ◽  
Dirichlet Boundary ◽  
Type Theorem ◽  
Dirichlet Boundary Conditions ◽  
Liouville Type ◽  
Liouville Type Theorem ◽  
Harmonic System

AbstractIn this paper, we consider the following poly-harmonic system with Dirichlet boundary conditions in a half space ℝwherewhereis the Green’s function in ℝ

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