An analysis of Feng’s and other symmetric local absorbing boundary conditions
Research Center MATHEON, TU Berlin, 10623 Berlin, Germany.
Revised: 8 April 2014
With symmetric local absorbing boundary conditions for the Helmholtz equation scattering problems can be solved on a truncated domain, where the outgoing radiation condition is approximated by a Dirichlet-to-Neumann map with higher tangential derivatives on its outer boundary. Feng’s conditions are symmetric local absorbing boundary conditions, which are based on an asymptotic expansion of the coefficients of the exact Dirichlet-to-Neumann map for large radia of the circular outer boundary. In this article we analyse the well-posedness of variational formulations with symmetric local absorbing boundary conditions in general and show how the modelling error introduced by Feng’s conditions depends on the radius of the truncated domain.
Mathematics Subject Classification: 65N30 / 35J25 / 78M30
Key words: Absorbing boundary conditions / Feng’s conditions / error analysis
© EDP Sciences, SMAI 2015