zbMATH — the first resource for mathematics

Integral equation methods for scattering from an impedance crack. (English) Zbl 1041.65094
The authors investigate the uniqueness and existence for the scattering problem for time-harmonic waves from an impedance crack in two dimensions. They combine a single and double layer potential approach in a Hölder space setting leading to a system of integral equations that contains a hypersingular operator. Its numerical solution via a fully discrete collocation method based on trigonometric and interpolatory quadrature rules is investigated.

65N38 Boundary element methods for boundary value problems involving PDEs
35J05 Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation
78A45 Diffraction, scattering
78M15 Boundary element methods applied to problems in optics and electromagnetic theory
Full Text: DOI
[1] Cakoni, F.; Colton, D., The linear sampling method for cracks, Inverse problems, 19, 279-295, (2003) · Zbl 1171.35487
[2] Capobianco, M.R.; Criscuolo, G.; Junghanns, P., A fast algorithm for Prandtl’s integro-differential equation, J. comput. appl. math., 77, 103-128, (1997) · Zbl 0870.65135
[3] Chapko, R.; Kress, R.; Mönch, L., On the numerical solution of a hypersingular integral equation for elastic scattering from a planar crack, IMA J. numer. anal., 20, 601-619, (2000) · Zbl 0995.74080
[4] Colton, D.; Kress, K., Inverse acoustic and electromagnetic scattering theory, (1998), Springer Berlin · Zbl 0893.35138
[5] Costabel, M.; Dauge, M., Crack singularities for general elliptic systems, Math. nachr., 235, 29-49, (2002) · Zbl 1094.35038
[6] Kress, R., A Nyström method for boundary integral equations in domains with corners, Numer. math., 58, 145-161, (1990) · Zbl 0707.65078
[7] Kress, R., Inverse scattering from an open arc, Math. methods appl. sci., 18, 267-293, (1995) · Zbl 0824.35030
[8] Kress, R., On the numerical solution of a hypersingular integral equation in scattering theory, J. comput. appl. math., 61, 345-360, (1995) · Zbl 0839.65119
[9] Kress, R., Inverse elastic scattering from a crack, Inverse problems, 12, 667-684, (1996) · Zbl 0864.35118
[10] Kress, R., Linear integral equations, (1999), Springer New York
[11] Mönch, L., On the numerical solution of the direct scattering problem for a sound-hard open arc, J. comput. appl. math., 71, 343-356, (1996) · Zbl 0854.65106
[12] Multhopp, H., Die berechnung der auftriebsverteilung von tragflügeln, Luftfahrt-forschung, 4, 153-169, (1938) · JFM 64.0863.04
[13] Osipov, A.V.; Norris, A.N., The malyuzhinets theory for scattering from wedge boundariesa review, Wave motion, 29, 313-340, (1999) · Zbl 1074.76611
[14] S. Prössdorf, B. Silbermann, Numerical Analysis for Integral and Related Operator Equations, Akademie-Verlag, Berlin, Birkhäuser-Verlag, Basel, 1991.
[15] Yan, Y.; Sloan, I.H., On integral equations of the first kind with logarithmic kernels, J. integral equations appl., 1, 549-579, (1988) · Zbl 0682.45001
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.