An alternative to Dirichlet-to-Neumann maps for waveguides

Anne-Sophie Bonnet-Ben Dhia (1) , Guillaume Legendre (2)

1 POEMS - Propagation des Ondes : Étude Mathématique et Simulation
2 CEREMADE - CEntre de REcherches en MAthématiques de la DEcision

We are interested by the treatment of the radiation condition at infinity for the numerical solution of a problem set in an unbounded waveguide. We propose an alternative to the classical approach involving a modal expression of Dirichlet-to-Neumann (DtN) operators. This method is particularly simple to implement since it only requires the solution of boundary value problems with local boundary conditions. The corresponding approximate solution is comparable in accuracy to the one obtained by truncating the infinite series in the DtN maps.

Domaines: Analyse numérique [math.NA]

Anne-Sophie Bonnet-Ben Dhia, Guillaume Legendre. An alternative to Dirichlet-to-Neumann maps for waveguides. 2011. ⟨hal-00585361v1⟩