Journal article
Artificial boundary conditions for an exterior boundary value problem with a cylindrical inhomogeneity
Publication Details
Authors: | Specovius-Neugebauer, M.; Nazarov, S. |
Publication year: | 2004 |
Journal: | Computational Mathematics and Mathematical Physics |
Pages range : | 2087–2103 |
Volume number: | 44 |
ISSN: | 0965-5425 |
eISSN: | 1555-6662 |
Abstract
Local artificial boundary conditions are constructed in exterior Dirichlet and Neumannboundary value problems for a fairly general formally self-adjoint system of second-orderdifferential equations with piecewise constant coefficients. The coefficients have jumps at an infinitecylindrical surface with an arbitrary smooth cross section, and the shape of a truncationsurface-the boundary of a circular cylinder with a height and diameter of 2R-is 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
Local artificial boundary conditions are constructed in exterior Dirichlet and Neumannboundary value problems for a fairly general formally self-adjoint system of second-orderdifferential equations with piecewise constant coefficients. The coefficients have jumps at an infinitecylindrical surface with an arbitrary smooth cross section, and the shape of a truncationsurface-the boundary of a circular cylinder with a height and diameter of 2R-is 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
