Green’s Function for the Helmholtz Equation in a Polygonal Domain of Special Form with Ideal Boundary Conditions
A formal approach for the construction of the Green’s function in a polygonal domain with the Dirichlet boundary conditions is proposed. The complex form of the Kontorovich–Lebedev transform and the reduction to a system of integral equations is employed. The far-field asymptotics of the wave field is discussed.
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- 1.V. M. Babich, M. A. Lyalinov, and V. E. Grikurov, Diffraction Theory. The Sommerfeld–Malyuzhinets Technique, Alpha Science Ser. Wave Phenom., Alpha Science, Oxford (2008).Google Scholar
- 2.M. A. Lyalinov and N. Y. Zhu, Scattering of Waves by Wedges and Cones with Impedance Boundary Conditions (Mario Boella Series on Electromagnetism in Information & Communication), SciTech-IET Edison, NJ (2012).Google Scholar
- 6.A. D. Avdeev and S. M. Grudsky, “On a modified Kontorovich–Lebedev transform and its application to the diffraction problem of cylindrical wave by a perfeclty conducting wedge,” Radiotekh. Electr., 39, No. 7, 1081–1089 (1994).Google Scholar
- 7.J.-M. L. Bernard and M. A. Lyalinov, “Diffraction of acoustic waves by an impedance cone of an arbitrary cross-section,” Wave Motion, 33, 155–181 (2001). (erratum : p. 177 replace O(1/ cos(π(ν − b))) by O(ν d sin(πν)/ cos(π(ν − b)))).Google Scholar
- 8.I. S. Gradstein and I. M. Ryzhik, Tables of Integrals, Series and Products, 4th ed., Academic Press, Orlando (1980).Google Scholar