A weakly singular form of the hypersingular boundary integral equation applied to 3-D acoustic wave problems

1992 ◽  
Vol 96 (2) ◽  
pp. 271-287 ◽  
Author(s):  
Yijun Liu ◽  
F.J. Rizzo
Keyword(s):  
Integral Equation ◽  
Acoustic Wave ◽  
Boundary Integral Equation ◽  
Boundary Integral ◽  
Weakly Singular ◽  
Singular Form ◽  
Hypersingular Boundary Integral Equation ◽  
Wave Problems

scholarly journals Regularization of the Divergent Integrals. I. General Consideration.

2007 ◽  
Vol 4 (2) ◽  
Author(s):  
Vladimir Zozulya
Keyword(s):  
Integral Equation ◽  
Boundary Integral Equation ◽  
Boundary Integral ◽  
General Consideration ◽  
Science And Engineering ◽  
Hypersingular Integrals ◽  
Weakly Singular ◽  
Easy Calculation ◽  
Multidimensional Integrals

This article considers weakly singular, singular and hypersingular integrals, which arise when the boundary integral equation (BIE) methods are used to solve problems in science and engineering. For their regularization, an approach based on the theory of distribution and application of the Green theorem has been used. The expressions, which allow an easy calculation of the weakly singular, singular and hypersingular integrals, have been constructed. Such approach may be easily generalized and applied to the calculation of multidimensional integrals with singularities of various types.

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