A fast numerical method for a natural boundary integral equation for the Helmholtz equation

In this paper, we construct Haar wavelet and apply it to investigate the numerical solution of the natural boundary integral equation of the Laplace equation in the concave angle domains. Haar wavelet has better stability and good explicit expression. Moreover, they are mutual orthogonal. We make full use of their mutual orthogonal to cope with the natural boundary integral equation. Taking advantage of Galerkin-wavelet method in discretizing the natural boundary integral equation. Finally, a numerical example is shown and the feasibility and validity of the method are proved.

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A boundary integral equation procedure for the mixed boundary value problem of the vector helmholtz equation

Applicable Analysis ◽

10.1080/00036819008839904 ◽

1990 ◽

Vol 35 (1-4) ◽

pp. 59-74 ◽

Cited By ~ 1

Author(s):

Ernst P. Stephan

Keyword(s):

Integral Equation ◽

Boundary Value Problem ◽

Helmholtz Equation ◽

Boundary Integral Equation ◽

Mixed Boundary ◽

Boundary Value ◽

Boundary Integral ◽

Mixed Boundary Value Problem

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A Spectral Boundary Integral Equation Method for the 2D Helmholtz Equation

Journal of Computational Physics ◽

10.1006/jcph.1995.1169 ◽

1995 ◽

Vol 120 (2) ◽

pp. 340-347 ◽

Cited By ~ 26

Author(s):

Fang Q. Hu

Keyword(s):

Integral Equation ◽

Helmholtz Equation ◽

Boundary Integral Equation ◽

Integral Equation Method ◽

Boundary Integral ◽

Boundary Integral Equation Method ◽

Equation Method

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A meshless numerical method based on the local boundary integral equation (LBIE) to solve linear and non-linear boundary value problems

Engineering Analysis with Boundary Elements ◽

10.1016/s0955-7997(98)00096-4 ◽

1999 ◽

Vol 23 (5-6) ◽

pp. 375-389 ◽

Cited By ~ 63

Author(s):

Tulong Zhu ◽

Jindong Zhang ◽

S.N. Atluri

Keyword(s):

Integral Equation ◽

Boundary Value Problems ◽

Numerical Method ◽

Boundary Integral Equation ◽

Boundary Value ◽

Boundary Integral ◽

Linear Boundary ◽

Local Boundary ◽

Local Boundary Integral Equation ◽

Non Linear

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A numerical method based on the boundary integral equation and dual reciprocity methods for one-dimensional Cahn–Hilliard equation

Engineering Analysis with Boundary Elements ◽

10.1016/j.enganabound.2008.08.008 ◽

2009 ◽

Vol 33 (4) ◽

pp. 522-528 ◽

Cited By ~ 27

Author(s):

Mehdi Dehghan ◽

Davoud Mirzaei

Keyword(s):

Integral Equation ◽

Numerical Method ◽

Boundary Integral Equation ◽

Boundary Integral ◽

One Dimensional ◽

Hilliard Equation ◽

Cahn Hilliard Equation

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On the Burton and Miller Boundary Integral Formulation of the Exterior Acoustic Problem

Journal of Vibration and Acoustics ◽

10.1115/1.2930296 ◽

1992 ◽

Vol 114 (4) ◽

pp. 540-545 ◽

Cited By ~ 11

Author(s):

P. J. Harris ◽

S. Amini

Keyword(s):

Integral Equation ◽

Helmholtz Equation ◽

Boundary Integral Equation ◽

Exterior Domain ◽

Differential Operators ◽

Coupling Parameter ◽

Boundary Integral ◽

Boundary Integral Formulation ◽

Pseudo Differential Operators ◽

Set Up

The direct boundary integral equation due to Burton and Miller (1971) is used for the solution of the Helmholtz equation in the exterior domain. The formulation is complex, involving four integral (pseudo-differential) operators. Here we show that it is possible and advantageous to choose the coupling parameter, η, inherent in the formulation, to depend on the boundary points. By setting the coupling parameter, η(p), to zero, over a large part of the surface, we are able to reduce the set up time without greatly affecting the conditioning of the equation.

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