A multilevel additive Schwarz method for a hypersingular integral equation on an open curve with graded meshes

2009 ◽  
Vol 59 (9) ◽  
pp. 2195-2202 ◽  
Author(s):  
Matthias Maischak
Keyword(s):  
Integral Equation ◽  
Hypersingular Integral Equation ◽  
Hypersingular Integral ◽  
Schwarz Method ◽  
Additive Schwarz ◽  
Graded Meshes ◽  
Additive Schwarz Method ◽  
Open Curve

scholarly journals Computation of Energy Release Rates for a Nearly Circular Crack

2011 ◽  
Vol 2011 ◽  
pp. 1-17 ◽  
Author(s):  
Nik Mohd Asri Nik Long ◽  
Lee Feng Koo ◽  
Zainidin K. Eshkuvatov
Keyword(s):  
Integral Equation ◽  
Energy Release Rate ◽  
Energy Release ◽  
Release Rate ◽  
Linear Equations ◽  
Circular Crack ◽  
Plane Elasticity ◽  
Hypersingular Integral Equation ◽  
Hypersingular Integral ◽  
Energy Release Rates

This paper deals with a nearly circular crack, in the plane elasticity. The problem of finding the resulting shear stress can be formulated as a hypersingular integral equation over a considered domain, and it is then transformed into a similar equation over a circular region, , using conformal mapping. Appropriate collocation points are chosen on the region to reduce the hypersingular integral equation into a system of linear equations with unknown coefficients, which will later be used in the determination of energy release rate. Numerical results for energy release rate are compared with the existing asymptotic solution and are displayed graphically.

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