A domain decomposition for a hybrid computation of the Helmholtz equation. (Décomposition de domaine pour un calcul hybride de l’équation de Helmholtz.) (French. Abridged English version) Zbl 0879.35010
Summary: We prove an estimate for the Dirichlet-Neumann operator, and for the \(H^1\) local norm for solutions of the Helmholtz equation outside an obstacle without trapping rays. We give an algorithm solving the Helmholtz equation outside a union of such obstacles. Convergence follows from this estimate. At each step of the resolution, only one obstacle is considered for itself; this defines a decomposition domain technique fitting this equation. One can use different numerical schemes, one at each step, adapted to the considered component of the obstacle; therefore, this algorithm is a hybrid computation. The results are given for two obstacles, and the generalization is straightforward.
MSC:
65M99 | Numerical methods for partial differential equations, initial value and time-dependent initial-boundary value problems |
65N99 | Numerical methods for partial differential equations, boundary value problems |
35J05 | Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation |
65Z05 | Applications to the sciences |