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 easy 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.
Nous nous intéressons au traitement de la condition de rayonnement à lʼinfini pour la résolution numérique dʼun problème posé dans un guide dʼondes non borné. Nous proposons une alternative à lʼapproche classique reposant sur une expression modale dʼopérateurs de type Dirichlet–Neumann (DtN). Cette méthode est particulièrement simple à mettre en œuvre puisquʼelle ne requiert que la résolution de problèmes aux limites dont les conditions aux limites sont locales. La solution approchée correspondante est dʼune précision comparable à celle obtenue en tronquant la série infinie dans les opérateurs DtN.
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Anne-Sophie Bonnet-Ben Dhia 1; Guillaume Legendre 1, 2
@article{CRMATH_2011__349_17-18_1005_0, author = {Anne-Sophie Bonnet-Ben Dhia and Guillaume Legendre}, title = {An alternative to {Dirichlet-to-Neumann} maps for waveguides}, journal = {Comptes Rendus. Math\'ematique}, pages = {1005--1009}, publisher = {Elsevier}, volume = {349}, number = {17-18}, year = {2011}, doi = {10.1016/j.crma.2011.08.006}, language = {en}, }
TY - JOUR AU - Anne-Sophie Bonnet-Ben Dhia AU - Guillaume Legendre TI - An alternative to Dirichlet-to-Neumann maps for waveguides JO - Comptes Rendus. Mathématique PY - 2011 SP - 1005 EP - 1009 VL - 349 IS - 17-18 PB - Elsevier DO - 10.1016/j.crma.2011.08.006 LA - en ID - CRMATH_2011__349_17-18_1005_0 ER -
Anne-Sophie Bonnet-Ben Dhia; Guillaume Legendre. An alternative to Dirichlet-to-Neumann maps for waveguides. Comptes Rendus. Mathématique, Volume 349 (2011) no. 17-18, pp. 1005-1009. doi : 10.1016/j.crma.2011.08.006. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2011.08.006/
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