X. Antoine and M. Darbas, Generalized combined field integral equations for the iterative solution of the three-dimensional Helmholtz equation, Mathematical Modelling and Numerical Analysis, vol.41, issue.1, pp.147-167, 2007.
URL : https://hal.archives-ouvertes.fr/hal-00141047

X. Antoine, H. Barucq, and A. Bendali, Bayliss-Turkel-like radiation conditions on surfaces of arbitrary shape, Journal of Mathematical Analysis and Applications, vol.229, issue.1, pp.184-211, 1999.

X. Antoine, M. Darbas, and Y. Y. Lu, An improved surface radiation condition for high-frequency acoustic scattering problems, Computer Methods in Applied Mechanics and Engineering, vol.195, pp.4060-4074, 2006.

A. V. Astaneh and M. N. Guddati, A two-level domain decomposition method with accurate interface conditions for the Helmholtz problem, International Journal for Numerical Methods in Engineering, vol.107, issue.1, pp.74-90, 2016.

A. Bayliss and E. Turkel, Radiation boundary conditions for wave-like equations, Communications on Pure and applied Mathematics, vol.33, issue.6, pp.707-725, 1980.

J. Benamou and B. Desprès, A domain decomposition method for the Helmholtz equation and related optimal control problems, Journal of Computational Physics, vol.136, issue.1, pp.68-82, 1997.
URL : https://hal.archives-ouvertes.fr/inria-00073899

A. Bendali and Y. Boubendir, Non-overlapping domain decomposition method for a nodal finite element method, Numerische Mathematik, vol.103, issue.4, pp.515-537, 2006.

J. Berenger, A perfectly matched layer for the absorption of electromagnetic waves, Journal of computational physics, vol.114, issue.2, pp.185-200, 1994.

A. Bermúdez, L. Hervella-nieto, A. Prieto, and R. Rodriguez, An optimal perfectly matched layer with unbounded absorbing function for time-harmonic acoustic scattering problems, Journal of Computational Physics, vol.223, issue.2, pp.469-488, 2007.

M. Bonazzoli, V. Dolean, I. G. Graham, E. A. Spence, and P. Tournier, Two-level preconditioners for the Helmholtz equation, International Conference on Domain Decomposition Methods, pp.139-147
URL : https://hal.archives-ouvertes.fr/hal-01525424

. Springer, , 2017.

A. Bonnet-ben-dhia, S. Fliss, and A. Tonnoir, The halfspace matching method: A new method to solve scattering problems in infinite media, Journal of Computational and Applied Mathematics, vol.338, pp.44-68, 2018.

Y. Boubendir and A. Bendali, Dealing with cross-points in a non-overlapping domain decomposition solution of the Helmholtz equation, Mathematical and Numerical Aspects of Wave Propagation WAVES 2003, pp.319-324, 2003.

Y. Boubendir and D. Midura, Non-overlapping domain decomposition algorithm based on modified transmission conditions for the Helmholtz equation, Computers & Mathematics with Applications, vol.75, issue.6, pp.1900-1911, 2018.

Y. Boubendir, X. Antoine, and C. Geuzaine, A quasi-optimal non-overlapping domain decomposition algorithm for the Helmholtz equation, Journal of Computational Physics, vol.231, issue.2, pp.262-280, 2012.
URL : https://hal.archives-ouvertes.fr/hal-00573550

O. P. Bruno and L. A. Kunyansky, A sparse matrix arithmetic based on H-matrices. Part I: introduction to H-matrices, computing, Computing, vol.62, issue.2, pp.89-108, 1999.

O. P. Bruno and L. A. Kunyansky, A fast, high-order algorithm for the solution of surface scattering problems: basic implementation, tests, and applications, J. Comput. Phys, vol.169, issue.1, pp.80-110, 2001.

X. Cai and O. B. Widlund, Domain decomposition algorithms for indefinite elliptic problems, SIAM Journal on Scientific and Statistical Computing, vol.13, issue.1, pp.243-258, 1992.

S. Chaillat, M. Darbas, and F. L. Louër, Approximate local Dirichlet-to-Neumann map for three-dimensional time-harmonic elastic waves, Computer Methods in Applied Mechanics and Engineering, vol.297, pp.62-83, 2015.
URL : https://hal.archives-ouvertes.fr/hal-01187242

G. Chen and J. Zhou, Boundary Element Methods, 1992.

S. Christiansen and J. Nédélec, Des préconditionneurs pour la résolution numérique deséquations intégrales de frontière de l'acoustique, C.R. Acad. Sci. Paris Sér. I Math, vol.330, issue.7, pp.617-622, 2000.

X. Claeys, A new variant of the optimised Schwarz method for arbitrary non-overlapping subdomain partitions, 2019.

X. Claeys and E. Parolin, Robust treatment of cross points in optimized Schwarz methods, 2020.

F. Collino, S. Ghanemi, and P. Joly, Domain decomposition method for harmonic wave propagation: a general presentation, Computer methods in applied mechanics and engineering, vol.184, issue.2-4, pp.171-211, 2000.
URL : https://hal.archives-ouvertes.fr/inria-00073216

F. Collino, P. Joly, and M. Lecouvez, Exponentially convergent non overlapping domain decomposition methods for the Helmholtz equation, ESAIM: Mathematical Modelling and Numerical Analysis, vol.54, issue.3, pp.775-810, 2020.

L. Conen, V. Dolean, R. Krause, and F. Nataf, A coarse space for heterogeneous Helmholtz problems based on the Dirichlet-to-Neumann operator, Journal of Computational and Applied Mathematics, vol.271, pp.83-99, 2014.
URL : https://hal.archives-ouvertes.fr/hal-01405536

A. De-la and . Bourdonnaye, Some formulations coupling finite element and integral equation methods for Helmholtz equation and electromagnetism, Numerische Mathematik, vol.69, issue.3, pp.257-268, 1995.

A. De-la-bourdonnaye, C. Farhat, A. Macedo, F. Magoules, and F. Roux, A non-overlapping domain decomposition method for the exterior Helmholtz problem, Contemporary Mathematics, vol.218, pp.42-66, 1998.
URL : https://hal.archives-ouvertes.fr/inria-00073418

B. Després, Domain decomposition method and the Helmholtz problem, Proceedings of the First International Conference on Mathematical and Numerical Aspects of wave Propagation Phenomena, pp.44-52, 1991.

B. Després, A. Nicolopoulos, and B. Thierry, New transmission conditions for corners and cross-points, Proceedings of the 14th International Conference on Mathematical and Numerical Aspects of wave Propagation Phenomena, 2019.

V. Dolean, P. Jolivet, and F. Nataf, An introduction to domain decomposition methods: algorithms, theory, and parallel implementation, vol.144, 2015.
URL : https://hal.archives-ouvertes.fr/cel-01100932

P. Dular, C. Geuzaine, F. Henrotte, and W. Legros, A general environment for the treatment of discrete problems and its application to the finite element method, IEEE Transactions on Magnetics, vol.34, issue.5, pp.3395-3398, 1998.

M. E. Bouajaji, X. Antoine, and C. Geuzaine, Approximate local magnetic-to-electric surface operators for time-harmonic Maxwell's equations, Journal of Computational Physics, vol.279, pp.241-260, 2014.

M. E. Bouajaji, B. Thierry, X. Antoine, and C. Geuzaine, A quasi-optimal domain decomposition algorithm for the time-harmonic Maxwell's equations, Journal of Computational Physics, vol.294, pp.38-57, 2015.

B. Engquist and A. Majda, Absorbing boundary conditions for numerical simulation of waves, Proceedings of the National Academy of Sciences, vol.74, issue.5, pp.1765-1766, 1977.

B. Engquist and L. Ying, Sweeping preconditioner for the Helmholtz equation: moving perfectly matched layers, Multiscale Modeling & Simulation, vol.9, issue.2, pp.686-710, 2011.

Y. A. Erlangga, C. W. Oosterlee, and C. Vuik, A novel multigrid based preconditioner for heterogeneous Helmholtz problems, SIAM Journal on Scientific Computing, vol.27, issue.4, pp.1471-1492, 2006.

C. Farhat, A. Macedo, and M. Lesoinne, A two-level domain decomposition method for the iterative solution of high frequency exterior Helmholtz problems, Numerische Mathematik, vol.85, issue.2, pp.283-308, 2000.

C. Farhat, A. Macedo, M. Lesoinne, F. Roux, F. Magoulés et al., Two-level domain decomposition methods with Lagrange multipliers for the fast iterative solution of acoustic scattering problems, Computer Methods in Applied Mechanics and Engineering, vol.184, issue.2-4, pp.213-239, 2000.
URL : https://hal.archives-ouvertes.fr/hal-00624498

C. Farhat, P. Avery, R. Tezaur, and J. Li, FETI-DPH: a dual-primal domain decomposition method for acoustic scattering, Journal of Computational Acoustics, vol.13, issue.03, pp.499-524, 2005.

M. Gander, F. Magoules, and F. Nataf, Optimized Schwarz methods without overlap for the Helmholtz equation, SIAM Journal on Scientific Computing, vol.24, issue.1, pp.38-60, 2002.
URL : https://hal.archives-ouvertes.fr/hal-00624495

M. J. Gander and F. Kwok, Best Robin parameters for optimized Schwarz methods at cross points, SIAM Journal on Scientific Computing, vol.34, issue.4, pp.1849-1879, 2012.

M. J. Gander and F. Kwok, On the applicability of Lions' energy estimates in the analysis of discrete optimized Schwarz methods with cross points, Domain Decomposition Methods in Science and Engineering XX, pp.475-483, 2013.

M. J. Gander and K. Santugini, Cross-points in domain decomposition methods with a finite element discretization, Electronic Transactions on Numerical Analysis, vol.45, pp.219-240, 2016.
URL : https://hal.archives-ouvertes.fr/hal-00980386

M. J. Gander and H. Zhang, Optimized Schwarz methods with overlap for the Helmholtz equation, SIAM Journal on Scientific Computing, vol.38, issue.5, pp.3195-3219, 2016.

M. J. Gander and H. Zhang, A class of iterative solvers for the Helmholtz equation: Factorizations, sweeping preconditioners, source transfer, single layer potentials, polarized traces, and optimized Schwarz methods, SIAM Review, vol.61, issue.1, pp.3-76, 2019.

M. Ganesh and C. Morgenstern, High-order FEM domain decomposition models for high-frequency wave propagation in heterogeneous media, Computers & Mathematics with Applications, vol.75, issue.6, pp.1961-1972, 2018.

C. Geuzaine and J. Remacle, Gmsh: A 3-D finite element mesh generator with built-in pre-and postprocessing facilities, International journal for numerical methods in engineering, vol.79, issue.11, pp.1309-1331, 2009.

D. Givoli, Non-reflecting boundary conditions, Journal of computational physics, vol.94, issue.1, pp.1-29, 1991.

I. Graham, E. Spence, and E. Vainikko, Domain decomposition preconditioning for high-frequency Helmholtz problems with absorption, Mathematics of Computation, vol.86, issue.307, pp.2089-2127, 2017.

T. Hagstrom, R. P. Tewarson, and A. Jazcilevich, Numerical experiments on a domain decomposition algorithm for nonlinear elliptic boundary value problems, Applied Mathematics Letters, vol.1, issue.3, pp.299-302, 1988.

R. Kechroud, X. Antoine, and A. Soulaimani, Numerical accuracy of a Padé-type non-reflecting boundary condition for the finite element solution of acoustic scattering problems at high-frequency, International Journal for Numerical Methods in Engineering, vol.64, issue.10, pp.1275-1302, 2005.

S. Kim and H. Zhang, Optimized Schwarz method with complete radiation transmission conditions for the Helmholtz equation in waveguides, SIAM Journal on Numerical Analysis, vol.53, issue.3, pp.1537-1558, 2015.

J. Kimn and M. Sarkis, Restricted overlapping balancing domain decomposition methods and restricted coarse problems for the Helmholtz problem, Computer Methods in Applied Mechanics and Engineering, vol.196, issue.8, pp.1507-1514, 2007.

M. Lecouvez, B. Stupfel, P. Joly, and F. Collino, Quasi-local transmission conditions for non-overlapping domain decomposition methods for the Helmholtz equation, Comptes Rendus Physique, vol.15, issue.5, pp.403-414, 2014.
URL : https://hal.archives-ouvertes.fr/hal-01116028

W. Leng and L. Ju, An additive overlapping domain decomposition method for the Helmholtz equation, SIAM Journal on Scientific Computing, vol.41, issue.2, pp.1252-1277, 2019.

S. Loisel, Condition number estimates for the nonoverlapping optimized Schwarz method and the 2-Lagrange multiplier method for general domains and cross points, SIAM Journal on Numerical Analysis, vol.51, issue.6, pp.3062-3083, 2013.

N. Marsic and H. D. Gersem, Convergence of optimized non-overlapping Schwarz method for Helmholtz problems in closed domains, 2020.

V. Mattesi, M. Darbas, and C. Geuzaine, A high-order absorbing boundary condition for 2D time-harmonic elastodynamic scattering problems, Computers & Mathematics with Applications, vol.77, issue.6, pp.1703-1721, 2019.

F. A. Milinazzo, C. A. Zala, and G. H. Brooke, Rational square-root approximations for parabolic equation algorithms, The Journal of the Acoustical Society of America, vol.101, issue.2, pp.760-766, 1997.

A. Modave, A. Atle, J. Chan, and T. Warburton, A GPU-accelerated nodal discontinuous Galerkin method with high-order absorbing boundary conditions and corner/edge compatibility, International Journal for Numerical Methods in Engineering, vol.112, issue.11, pp.1659-1686, 2017.
URL : https://hal.archives-ouvertes.fr/hal-01383074

A. Modave, C. Geuzaine, and X. Antoine, Corner treatments for high-order local absorbing boundary conditions in high-frequency acoustic scattering, Journal of Computational Physics, vol.401, p.109029, 2020.
URL : https://hal.archives-ouvertes.fr/hal-01925160

F. Nataf, F. Rogier, and E. De-sturler, Optimal interface conditions for domain decomposition methods, CMAP (Ecole Polytechnique), vol.301, pp.1-18, 1994.
URL : https://hal.archives-ouvertes.fr/hal-02194208

J. Nédélec, Integral Representations for Harmonic Problems, Applied Mathematical Sciences, 2001.

A. Nicolopoulos, Formulations variationnelles d'équations de Maxwell résonantes et problèmes aux coins en propagation d'ondes, 2019.

A. Piacentini and N. Rosa, An improved domain decomposition method for the 3D Helmholtz equation, Computer Methods in Applied Mechanics and Engineering, vol.162, issue.1-4, pp.113-124, 1998.

A. Quarteroni and A. Valli, Domain decomposition methods for partial differential equations, Numerical Mathematics and Scientific Computation, 1999.

V. Rokhlin, Rapid solution of integral equations of scattering theory in two dimensions, J. Comput. Phys, vol.86, issue.2, pp.414-439, 1990.

A. Schädle and L. Zschiedrich, Additive Schwarz method for scattering problems using the PML method at interfaces, Domain Decomposition Methods in Science and Engineering XVI, pp.205-212, 2007.

C. C. Stolk, A rapidly converging domain decomposition method for the Helmholtz equation, Journal of Computational Physics, vol.241, pp.240-252, 2013.

C. C. Stolk, An improved sweeping domain decomposition preconditioner for the Helmholtz equation, Advances in Computational Mathematics, vol.43, issue.1, pp.45-76, 2017.

B. Stupfel, Improved transmission conditions for a one-dimensional domain decomposition method applied to the solution of the Helmholtz equation, Journal of Computational Physics, vol.229, issue.3, pp.851-874, 2010.

M. Taus, L. Zepeda-núñez, R. J. Hewett, and L. Demanet, L-Sweeps: A scalable, parallel preconditioner for the high-frequency Helmholtz equation, 2019.

B. Thierry, A. Vion, S. Tournier, M. E. Bouajaji, D. Colignon et al., GetDDM: an open framework for testing optimized Schwarz methods for time-harmonic wave problems, Computer Physics Communications, vol.203, pp.309-330, 2016.
URL : https://hal.archives-ouvertes.fr/hal-01244511

A. Toselli and O. Widlund, Domain decomposition methods-algorithms and theory, vol.34, 2006.

E. Turkel and A. Yefet, Absorbing PML boundary layers for wave-like equations, Applied Numerical Mathematics, vol.27, issue.4, pp.533-557, 1998.

A. Vion and C. Geuzaine, Double sweep preconditioner for optimized Schwarz methods applied to the Helmholtz problem, Journal of Computational Physics, vol.266, pp.171-190, 2014.

A. Vion and C. Geuzaine, Improved sweeping preconditioners for domain decomposition algorithms applied to time-harmonic Helmholtz and Maxwell problems, ESAIM: Proceedings and Surveys, vol.61, pp.93-111, 2018.

L. Zepeda-núñez and L. Demanet, The method of polarized traces for the 2D Helmholtz equation, Journal of Computational Physics, vol.308, pp.347-388, 2016.