A non-overlapping quasi-optimal optimized Schwarz domain decomposition algorithm for the Helmholtz equation

Yassine Boubendir (1) , Xavier Antoine (2, 3) , Christophe Geuzaine (4)

1 NJIT - Department of Mathematical Sciences [Newark, NJ]
2 CORIDA - Robust control of infinite dimensional systems and applications
3 IECL - Institut Élie Cartan de Lorraine
4 Institut Montefiore - Département d'Electricité, Electronique et Informatique (Liège)

In this paper, we present a new non-overlapping domain decomposition algorithm for the Helmholtz equation. We are particularly interested in the method introduced by P.-L. Lions [6] for the Laplace equation and extended to the Helmholtz equation by B. Després [3]. However, this latest approach provides slow convergence of the iterative method due to the choice of the transmission conditions. Thus, in order to improve the convergence, several methods were developed [4, 5, 9, 10].

Domaines: Analyse numérique [math.NA]; Acoustique [physics.class-ph]

Yassine Boubendir, Xavier Antoine, Christophe Geuzaine. A non-overlapping quasi-optimal optimized Schwarz domain decomposition algorithm for the Helmholtz equation. 2013 - 20th international conference on Domain Decomposition Methods in Science and Engineering, 2013, Rennes, France. pp.519-526, ⟨10.1007/978-3-642-35275-1_61⟩. ⟨hal-01094828⟩