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Title of Journal: Comput Mech

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Abbravation: Computational Mechanics

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Springer-Verlag

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10.1016/0304-3800(91)90082-c

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1432-0924

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On evaluation of hypersingular integrals over smoo

Authors: Ilkka Karasalo
Publish Date: 2006/11/03
Volume: 40, Issue: 3, Pages: 617-625
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Abstract

A novel derivation is given of the decomposition of a hypersingular integral over the boundary S of a smooth 3D body into a onedimensional integral and a regular integral over S S is parameterized by a map qθphi of the unit sphere with q0phi at the collocation point The integrand for the normal derivative of the field from a doublelayer density is expanded in powers of a function of θphi and the distance z from S The singularities are contained in the initial terms and give rise to the onedimensional integral in the limit z rightarrow 0+ The remainder is regular in the limit equal to the hypersingular integrand with θ −2 and θ −1 terms removed The decomposition is used to solve a standard and a hypersingular BIE for acoustic scattering by identical highorder discretizations Estimates of the error of the two solutions are computed to verify that their convergence rates are equal


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