Solution of Helmholtz Equation in the Exterior Domain by Elementary Boundary Integral Methods

1995 ◽  
Vol 118 (2) ◽  
pp. 208-221 ◽  
Author(s):  
S. Amini ◽  
S.M. Kirkup
Keyword(s):  
Helmholtz Equation ◽  
Exterior Domain ◽  
Boundary Integral ◽  
Boundary Integral Methods ◽  
Integral Methods

Multistep and Multistage Boundary Integral Methods for the Wave Equation

2009 ◽  
Author(s):  
Lehel Banjai ◽  
Theodore E. Simos ◽  
George Psihoyios ◽  
Ch. Tsitouras
Keyword(s):  
Wave Equation ◽  
Boundary Integral ◽  
Boundary Integral Methods ◽  
Integral Methods

Error analysis of boundary integral methods

Acta Numerica ◽  
1992 ◽  
Vol 1 ◽  
pp. 287-339 ◽  
Author(s):  
Ian H. Sloan
Keyword(s):  
Approximate Solution ◽  
Partial Differential Equations ◽  
Differential Equations ◽  
Error Analysis ◽  
Boundary Value Problems ◽  
Integral Equations ◽  
Boundary Integral Equations ◽  
Boundary Integral ◽  
Boundary Integral Methods ◽  
Integral Methods

Many of the boundary value problems traditionally cast as partial differential equations can be reformulated as integral equations over the boundary. After an introduction to boundary integral equations, this review describes some of the methods which have been proposed for their approximate solution. It discusses, as simply as possible, some of the techniques used in their error analysis, and points to areas in which the theory is still unsatisfactory.

scholarly journals Approximate methods for modelling cavitation bubbles near boundaries

1990 ◽  
Vol 41 (1) ◽  
pp. 1-44 ◽  
Author(s):  
A. Kucera ◽  
J.R. Blake
Keyword(s):  
Boundary Integral ◽  
Valuable Insight ◽  
Flat Plates ◽  
Confined Geometries ◽  
Rigid Boundary ◽  
Approximate Methods ◽  
Boundary Integral Methods ◽  
Integral Methods ◽  
Cavitation Bubbles ◽  
Insight Into

Approximate methods are developed for modelling the growth and collapse of clouds of cavitation bubbles near an infinite and semi-infinite rigid boundary, a cylinder, between two flat plates and in corners and near edges formed by planar boundaries. Where appropriate, comparisons are made between this approximate method and the more accurate boundary integral methods used in earlier calculations. It is found that the influence of nearby bubbles can be more important than the presence of boundaries. In confined geometries, such as a cylinder, or a cloud of bubbles, the effect of the volume change due to growth or collapse of the bubble can be important at much larger distances. The method provides valuable insight into bubble cloud phenomena.

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