The boundary knot method is an inherently meshless, integration-free, boundary-type, radial basis function collocation technique for the solution of partial differential equations. In this paper, the method is applied to the solution of some inverse problems for the Helmholtz equation, including the
An inverse problem for the helmholtz equation in a domain with unknown boundary
β Scribed by A.S. Barashkov
- Publisher
- Elsevier Science
- Year
- 1984
- Weight
- 414 KB
- Volume
- 24
- Category
- Article
- ISSN
- 0041-5553
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## Abstract In this paper we shall define an inverse problem for the Helmholtz equation with imaginary part of the wave number being positive. The Cauchy data are known on the boundary of the half plane, but it is not known where the half axis, lying vertically in the upper half plane, is situated.
Based on the two-dimensional stationary Oseen equation we consider the problem to determine the shape of a cylindrical obstacle immersed in a #uid #ow from a knowledge of the #uid velocity on some arc outside the obstacle. First, we obtain a uniqueness result for this ill-posed and non-linear invers
A novel approach to the development of inΓΏnite element formulations for exterior problems of time-harmonic acoustics is presented. This approach is based on a functional which provides a general framework for domainbased computation of exterior problems. Special cases include non-re ecting boundary
Dedicated to Professor George C. Hsiao on the occasion of his 60th birthday