This article is cited in 1 paper

Dirichlet and Neumann boundary value problems for Helmholtz equation in unbounded domains with piecewise smooth part of boundary

E. K. Lipachev

Kazan State University

Abstract: In this paper we study the boundary value problems modelling scattering waves by a domain with the rough boundary. We assume that a domain is the half plane and a finite part of boundary is characterized by a piecewise smooth function. We also assumed that singularities of boundaries are the edges. We prove the theorems of existence and uniqueness of solution of the boundary value problems. We find the integral equations of second kind and we show that these equations are equivalent to the boundary value problems. We propose the numerical algorithms for scattering problems. They are based on the spline-subdomains method for integral equations. We establish the convergence of this numerical algorithm.

UDC: 517.958:537.8

Received: 09.10.2006

Bibliographic databases:

•