Journal article
Artificial boundary conditions for an exterior boundary value problem with a cylindrical inhomogeneity
Publication Details
Authors:  SpecoviusNeugebauer, M.; Nazarov, S.

Journal:  Computational Mathematics and Mathematical Physics / Zhurnal Vychislitel'noi Matematiki i Matematicheskoi Fiziki 
Journal acronym:  Comput. Math. Math. Phys.

Abstract
Local artificial boundary conditions are constructed in exterior Dirichlet and Neumannboundary value problems for a fairly general formally selfadjoint system of secondorderdifferential equations with piecewise constant coefficients. The coefficients have jumps at an infinitecylindrical surface with an arbitrary smooth cross section, and the shape of a truncationsurfacethe boundary of a circular cylinder with a height and diameter of 2Ris adapted to suchinhomogeneity. The artificial boundary conditions are constructed without using explicit formulasfor the fundamental matrix. Existence and uniqueness theorems are proved for the original andapproximating problems, and an asymptotically sharp error estimate is derived