The Dirichlet problem for the propagative Helmholtz equation in a 2-D exterior domain bounded by closed curves and open arcs

@article{Krutitskii2008TheDP,
title={The Dirichlet problem for the propagative Helmholtz equation in a 2-D exterior domain bounded by closed curves and open arcs},
author={P. Krutitskii and N. C. Krutitskaya},
journal={2008 Proceedings of the International Conference Days on Diffraction},
year={2008},
pages={85-91}
}

The Dirichlet problem for the 2-D Helmholtz equation in an exterior domain bounded by closed curves and open arcs is studied. The existence of classical solution is proved by potential theory. The problem is reduced to the Fredholm equation of the second kind and index zero, which is uniquely solvable. It means, that the solution can be computed by standard codes.

Special Functions of Mathematical Physics: A Unified Introduction With Applications

A. F. Nikiforov, V. B. Uvarov

Nauka, Moscow,

1984

1 Excerpt

Elliptic partial differential equations of second order

D. Gilbarg, N. S. Trudinger

(in English). Russian translation: Nauka, Moscow,

1977

I . A course of higher mathematics . Vol . IV . Gostehizdat , Moscow - Leningrad , 1951 ( in Russian )

V. Smirnov

1964

Equations of mathematical physics . GITTL , Moscow , 1951 ( in Russian )

N. TikhonovA., A. SamarskiiA.

1963

A course of higher mathematics

V I.Smirnov

Vol. IV. Gostehizdat, Moscow-Leningrad,

1951

1 Excerpt

Equations of mathematical physics

A. N. Tikhonov, A. A. Samarskii

GITTL, Moscow,

1951

Dirichlet problem for the Helmholtz equation outside cuts in a plane . Zhurnal Vychisl . Matematiki i Matem . Fiziki , 1994 , v . 34 , No . 8 / 9 , pp . 1237 - 1258 ( in Russian )