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Kress, Rainer

A collocation method for a hypersingular boundary integral equation via trigonometric differentiation. (English) Zbl 1310.65169

J. Integral Equations Appl. 26, No. 2, 197-213 (2014).
Summary: Revisiting the author’s paper from 1995 on this topic [J. Comput. Appl. Math. 61, No. 3, 345–360 (1995; Zbl 0839.65119)], a fully discrete collocation method is proposed for the hypersingular integral equation arising from the double-layer approach for the solution of Neumann boundary value problems in two dimensions which is based on trigonometric differentiation to discretize the principal part of the hypersingular operator. Convergence in a Sobolev space setting is proven and the spectral convergence of the method is exhibited by numerical examples.

Cited in 13 Documents

MSC:

65R20 Numerical methods for integral equations
45E05 Integral equations with kernels of Cauchy type

Citations:

Zbl 0839.65119
Cite Review PDF
Full Text: DOI Euclid

References:

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[2] Y. Boubendir and C. Turc, Wave-number estimates for regularized combined field boundary integral operators in acoustic scattering problems with Neumann boundary conditions , IMA J. Numer. Anal. 33 (2013), 1176-1225. · Zbl 1284.65177 · doi:10.1093/imanum/drs038
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[8] —-, Inverse acoustic and electromagnetic scattering theory , 3rd ed., Springer, New York, 2013. · Zbl 1266.35121
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[11] —-, Linear integral equations , 3rd ed., Springer, New York, 2014. · Zbl 1328.45001
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