A Weakly Singular Boundary Integral Formulation of the External Helmholtz Problem Valid for All Wavenumbers

2006 ◽  
pp. 79-87 ◽  
Author(s):  
Paul J. Harris ◽  
Ke Chen ◽  
Jin Cheng
Keyword(s):  
Boundary Integral ◽  
Integral Formulation ◽  
Singular Boundary ◽  
Weakly Singular ◽  
Boundary Integral Formulation ◽  
Helmholtz Problem

scholarly journals Meshless acoustic analysis using a weakly singular Burton-Miller boundary integral formulation

2020 ◽  
Vol 41 (12) ◽  
pp. 1897-1914
Author(s):  
Linchong Chen ◽  
Xiaolin Li
Keyword(s):  
Complex Variable ◽  
Solid Angle ◽  
Normal Derivative ◽  
Boundary Integral ◽  
Least Square ◽  
Integral Formulation ◽  
Variable Boundary ◽  
Moving Least Square ◽  
Weakly Singular ◽  
Boundary Integral Formulation

AbstractThe Burton-Miller boundary integral formulation is solved by a complex variable boundary element-free method (CVBEFM) for the boundary-only meshless analysis of acoustic problems with arbitrary wavenumbers. To regularize both strongly singular and hypersingular integrals and to avoid the computation of the solid angle and its normal derivative, a weakly singular Burton-Miller formulation is derived by considering the normal derivative of the solid angle and adopting the singularity subtraction procedures. To facilitate the implementation of the CVBEFM and the approximation of gradients of the boundary variables, a stabilized complex variable moving least-square approximation is selected in the meshless discretization procedure. The results show the accuracy and efficiency of the present CVBEFM and reveal that the method can produce satisfactory results for all wavenumbers, even for extremely large wavenumbers such as κ = 10 000.

Boundary Integral Formulation for Inelastic Problems

1984 ◽  
pp. 237-276
Author(s):  
C. A. Brebbia ◽  
J. C. F. Telles ◽  
L. C. Wrobel
Keyword(s):  
Boundary Integral ◽  
Integral Formulation ◽  
Boundary Integral Formulation
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