, Under the simplifying assumptions µ 0 = · · · = µ n = 1 and ? 0 = · · · = ? n, ?? (1 ? ?)/(1 + ?)}. Proof: Let denote A = A (?,µ)

Y. Boubendir, X. Antoine, and C. Geuzaine, A quasi-optimal non-overlapping domain decomposition algorithm for the Helmholtz equation, J. Comput. Phys, vol.231, issue.2, p.262280, 2012.
URL : https://hal.archives-ouvertes.fr/hal-01094828

X. Claeys, Essential spectrum of local multi-trace boundary integral operators, IMA J. Appl. Math, vol.81, issue.6, p.961983, 2016.
URL : https://hal.archives-ouvertes.fr/hal-01251212

X. Claeys, V. Dolean, and M. J. Gander, An introduction to multi-trace formulations and associated domain decomposition solvers, Appl. Numer. Math, vol.135, p.6986, 2019.

X. Claeys and R. Hiptmair, Multi-trace boundary integral formulation for acoustic scattering by composite structures, Comm. Pure Appl. Math, vol.66, issue.8, p.11631201, 2013.

F. Collino, S. Ghanemi, and P. Joly, Domain decomposition method for harmonic wave propagation: a general presentation, Vistas in domain decomposition and parallel processing in computational mechanics, vol.184, pp.171-211, 2000.
URL : https://hal.archives-ouvertes.fr/inria-00073216

B. Després, Méthodes de décomposition de domaine pour les problèmes de propagation d'ondes en régime harmonique. Le théorème de Borg pour l'équation de Hill vectorielle

, Rocquencourt, 1991.

V. Dolean and M. J. Gander, Multitrace formulations and Dirichlet-Neumann algorithms, Domain decomposition methods in science and engineering XXII, vol.104, p.147155, 2016.
URL : https://hal.archives-ouvertes.fr/hal-00949024

M. J. Gander, Optimized Schwarz methods, SIAM J. Numer. Anal, vol.44, issue.2, p.699731, 2006.

R. Hiptmair and C. Jerez-hanckes, Multiple traces boundary integral formulation for Helmholtz transmission problems, Adv. Comput. Math, vol.37, issue.1, p.3991, 2012.

R. Hiptmair, C. Jerez-hanckes, J. Lee, and Z. Peng, Domain decomposition for boundary integral equations via local multi-trace formulations, Domain decomposition methods in science and engineering XXI, vol.98, p.4357, 2014.

W. Mclean, Strongly elliptic systems and boundary integral equations, 2000.

F. Nataf and F. Rogier, Factorization of the convection-diusion operator and the Schwarz algorithm, Math. Models Methods Appl. Sci, vol.5, issue.1, p.6793, 1995.

J. Nédélec, Integral representations for harmonic problems, Applied Mathematical Sciences, vol.144, 2001.

S. A. Sauter and C. Schwab, Boundary element methods, Springer Series in Computational Mathematics, vol.39, 2011.