Ernst O., Gander M. Why it is difficult to solve Helmholtz problems with classical iterative methods. Lecture Notes in Computational Science and Engineering 2012, vol. 83:325-363. Springer, Berlin, Heidelberg. 10.1007/978-3-642-22061-6_10. I.G. Graham, T.Y. Hou, O. Lakkis, R. Scheichl (Eds.).
Schwarz H.A. Über einen grenzübergang durch alternierendes verfahren. Vierteljahrsschr. Nat.forsch. Ges. Zür. 1870, 15:272-286.
Collino F., Ghanemi S., Joly P. Domain decomposition method for harmonic wave propagation: a general presentation. Comput. Methods Appl. Mech. Eng. 2000, 184(2-4):171-211.
Toselli A., Widlund O. Domain Decomposition Methods - Algorithms and Theory. Ser. Comput. Math. 2005, Springer.
Gander M., Magoulès F., Nataf F. Optimized Schwarz methods without overlap for the Helmholtz equation. SIAM J. Sci. Comput. 2002, 24(1):38-60.
Y. Boubendir, X. Antoine, C. Geuzaine, A quasi-optimal non-overlapping domain decomposition algorithm for the Helmholtz equation, J. Comput. Phys. 231 (2).
Smith B.F., Bjorstad P.E., Gropp W.D. Domain Decomposition: Parallel Multilevel Methods for Elliptic Partial Differential Equations 1996, Cambridge University Press.
Roux F.X., Magoulès F., Series L., Boubendir Y. Approximation of optimal interface boundary conditions for two-Lagrange multiplier FETI method. Lecture Notes in Computational Science and Engineering 2005, vol. 40:283-290.
Farhat C., Tezaur R., Toivanen J. A domain decomposition method for discontinuous Galerkin discretizations of Helmholtz problems with plane waves and Lagrange multipliers. Int. J. Numer. Methods Eng. 2009, 78:1513-1531.
Dubois O., Gander M.J., Loisel S., St-cyr A., Szyld D.B. The optimized Schwarz method with a coarse grid correction. SIAM J. Sci. Comput. 2012, 34(2):421-458. 10.1137/090774434.
Gander M., Zhang H. Domain decomposition methods for the Helmholtz equation: a numerical investigation. Lecture Notes in Computational Science and Engineering 2013, vol. 91:215-222. Springer, Berlin, Heidelberg. R. Bank, M. Holst, O. Widlund, J. Xu (Eds.).
Engquist B., Ying L. Sweeping preconditioner for the Helmholtz equation: moving perfectly matched layers. Multiscale Model. Simul. 2011, 9(2):686-710.
Engquist B., Ying L. Sweeping preconditioner for the Helmholtz equation: hierarchical matrix representation. Commun. Pure Appl. Math. 2011, 64(5):697-735.
Stolk C.C. A rapidly converging domain decomposition method for the Helmholtz equation. J. Comput. Phys. 2013, 241:240-252.
Lions P.-L. On the Schwarz alternating method III: a variant for non overlapping subdomains. Third International Symposium on Domain Decomposition Methods for Partial Differential Equations 1990, 202-223. SIAM, Philadelphia, PA. T. Chan, R. Glowinski, J. Périaux, O. Widlund (Eds.).
Després Décomposition de domaine pour les problèmes de propagation d'ondes en régime harmonique. Le théorème de Borg pour l'equation de Hill vectorielle 1991, Ph.D. thesis, Paris VI University, France.
Boubendir Y., Bendali A. Dealing with cross-points in a non-overlapping domain decomposition solution of the Helmholtz equation. Mathematical and Numerical Aspects of Wave Propagation WAVES 2003 2003, 319-324. Springer, Berlin, Heidelberg.
Nataf F. Interface connections in domain decomposition methods. NATO Sci. Ser. II Math. Phys. Chem. 2002, vol. 75:323-364. Kluwer Acad. Publ., Dordrecht.
Greenbaum A. Iterative Methods for Solving Linear Systems. Frontiers in Applied Mathematics 1997, vol. 17. Society for Industrial and Applied Mathematics (SIAM), Philadelphia, PA.
Saad Y. Iterative Methods for Sparse Linear Systems 2003, Society for Industrial and Applied Mathematics. 2nd edition.
Nataf F., Nier F. Convergence rate of some domain decomposition methods for overlapping and nonoverlapping subdomains. Numer. Math. 1997, 75:357-377.
Strang G. Linear Algebra and Its Applications 1988, Thomson Brooks/Cole learning. 3rd edition.
Chen N. Inverse iteration on defective matrices. Math. Comput. 1977, 31(139):726-732.
Zhongxiao J. The convergence of Krylov subspace methods for large unsymmetric linear systems. Acta Math. Sin. 1998, 14(4):507-518.
Ihlenburg F., Babuska I. Finite element solution to the Helmholtz equation with high wavenumber. Part I: The h-version of the FEM. Comput. Math. Appl. 1995, 39:9-37.
Vion A., Geuzaine C. Parallel double sweep preconditioner for the optimized Schwarz algorithm applied to high frequency Helmholtz and Maxwell equations. Proceedings of the 22nd International Conference on Domain Decomposition Methods (DD22) 2013.
Dryja M., Widlund O. Some domain decomposition algorithms for elliptic problems. Iterative Methods for Large Linear Systems 1989, 273-291. Academic Press, San Diego, CA. L. Hayes, D. Kincaid (Eds.).
Poulson J., Engquist B., Li S., Ying L. A parallel sweeping preconditioner for heterogeneous 3D Helmholtz equations. SIAM J. Sci. Comput. 2013, 35(3):194-212. 10.1137/090774434.
Roux F.-X., Magoulès F., Salmon S., Series L. Optimization of interface operator based on algebraic approach. Domain Decomposition Methods in Sci. Engrg. 2002, 297-304.
Farhat C., Macedo A., Lesoinne M. A two-level domain decomposition method for the iterative solution of high frequency exterior Helmholtz problems. Numer. Math. 2000, 85(2):282-303.
Farhat C., Macedo A., Lesoinne M., Roux F., Magoulès F., Bourdonnaye A.D.L. Two-level domain decomposition methods with Lagrange multipliers for the fast iterative solution of acoustic scattering problems. Comput. Methods Appl. Mech. Eng. 2000, 184:213-239.
Bourdonnaye A.D.L., Farhat C., Macedo A., Magoulès F., Roux F. A non overlapping domain decomposition method for the exterior Helmholtz problem. Contemp. Math. 1998, 218(2):42-66.
Boubendir Y. An analysis of the BEM-FEM non-overlapping domain decomposition method for a scattering problem. J. Comput. Appl. Math. 2007, 204(2):282-291.
Boubendir Y., Bendali A., Fares M.B. Coupling of a non-overlapping domain decomposition method for a nodal finite element method with a boundary element method. Int. J. Numer. Methods Eng. 2008, 73:1624-1650.
Bendali A., Boubendir Y., Fares M. A FETI-like domain decomposition method for coupling FEM and BEM in large-size problems of acoustic scattering. Comput. Struct. 2007, 85:526-535.
Givoli D. Numerical Methods for Problems in Infinite Domains. Studies in Applied Mechanics 1992, vol. 33. Elsevier Scientific Publishing Co., Amsterdam.
Després B. Domain decomposition method and the Helmholtz problem. Mathematical and Numerical Aspects of Wave Propagation Phenomena 1991, 44-52. SIAM, Philadelphia, PA. G. Cohen, L. Halpern, P. Joly (Eds.).
Bélanger-Rioux R., Demanet L. Compressed absorbing boundary conditions via matrix probing ArXiv e-prints. arxiv:1401.4421.
Vion A., Bélanger-Rioux R., Demanet L., Geuzaine C. A DDM double sweep preconditioner for the Helmholtz equation with matrix probing of the DtN map. Mathematical and Numerical Aspects of Wave Propagation WAVES 2013 2013.
Ihlenburg F., Babuska I. Dispersion analysis and error estimation of Galerkin finite element methods for the Helmholtz equation. Int. J. Numer. Methods Eng. 1995, 38:3745-3774.
Pinçon B., Ramdani K. Selective focusing on small scatterers in acoustic waveguides using time reversal mirrors. Inverse Probl. 2007, 23(1):1-25.
Plessix R., Mulder W. Separation-of-variables as a preconditioner for an iterative Helmholtz solver. Appl. Numer. Math. 2003, 44:385-400.
Erlangga Y.A., Vuil C., Oosterlee C.W. Comparison of multigrid and incomplete LU shifted-Laplace preconditioners for the inhomogeneous Helmholtz equation. Appl. Numer. Math. 2006, 56:648-666.
Chiu J., Demanet L. Matrix probing and its conditioning. SIAM J. Numer. Anal. 2012, 50:171-193.