Free Access
Issue
ESAIM: M2AN
Volume 55, Number 2, March-April 2021
Page(s) 429 - 448
DOI https://doi.org/10.1051/m2an/2020083
Published online 16 March 2021
  1. G. Allaire and S.M. Kaber, Numerical linear algebra. In: Vol. 55 of Texts in Applied Mathematics. Springer, New York (2008). [CrossRef] [Google Scholar]
  2. X. Antoine and C. Geuzaine, Optimized Schwarz domain decomposition methods for scalar and vector Helmholtz equations. In: Modern Solvers for Helmholtz Problems. Birkhäuser/Springer, Basel (2017) 189–213. [Google Scholar]
  3. X. Antoine, Y. Boubendir and C. Geuzaine, A quasi-optimal non-overlapping domain decomposition algorithm for the Helmholtz equation. J. Comput. Phys. 231 (2012) 262–280. [Google Scholar]
  4. X. Antoine, C. Geuzaine and A. Modave, Corner treatment for high-order local absorbing boundary conditions in high-frequency acoustic scattering. J. Comput. Phys. 401 (2020). [Google Scholar]
  5. X. Antoine, C. Geuzaine, A. Modave and A. Royer, A non-overlapping domain decomposition method with high-order transmission conditions and cross-point treatment for Helmholtz problems. Comput. Methods Appl. Mech. Eng. 368 (2020). [Google Scholar]
  6. M. Bebendorf, A means to efficiently solve elliptic boundary value problems. In: Vol. 63 of Hierarchical Matrices. Lecture Notes in Computational Science and Engineering. Springer-Verlag, Berlin (2008). [Google Scholar]
  7. A. Bendali and Y. Boubendir, Non-overlapping domain decomposition method for a nodal finite element method. Numer. Math. 103 (2006) 515–537. [Google Scholar]
  8. S. Börm, Efficient numerical methods for non-local operators: H2-matrix compression, algorithms and analysis. In: Vol. 14 of EMS Tracts in Mathematics. European Mathematical Society (EMS), Zürich (2010). [Google Scholar]
  9. Y. Boubendir, Techniques de Décomposition de Domaine et Méthodes d’Equations Intégrales. Ph.D. thesis, INSA of Toulouse (2002). [Google Scholar]
  10. X. Claeys, A single trace integral formulation of the second kind for acoustic scattering. Technical Report 2011-14, Seminar for Applied Mathematics, ETH Zürich, Switzerland (2011). [Google Scholar]
  11. X. Claeys, Quasi-local multitrace boundary integral formulations. Numer. Methods Part. Differ. Equ. 31 (2015) 2043–2062. [Google Scholar]
  12. X. Claeys and R. Hiptmair, Electromagnetic scattering at composite objects: a novel multi-trace boundary integral formulation. ESAIM:M2AN 46 (2012) 1421–1445. [EDP Sciences] [Google Scholar]
  13. X. Claeys and R. Hiptmair, Integral equations on multi-screens. Integral Equ. Oper. Theory 77 (2013) 167–197. [Google Scholar]
  14. X. Claeys and R. Hiptmair, Multi-trace boundary integral formulation for acoustic scattering by composite structures. Comm. Pure Appl. Math. 66 (2013) 1163–1201. [Google Scholar]
  15. X. Claeys and E. Parolin, Robust treatment of cross points in Optimized Schwarz Methods. Preprint arXiv:2003.06657 (2020). [Google Scholar]
  16. X. Claeys, R. Hiptmair and C. Jerez-Hanckes, Multitrace boundary integral equations. In: Direct and Inverse Problems in Wave Propagation and Applications. Selected Papers of the Workshop on Wave Propagation and Scattering, Inverse Problems and Applications in Energy and the Environment, Linz, Austria, November 21–25, 2011. de Gruyter, Berlin (2013) 51–100. [Google Scholar]
  17. X. Claeys, R. Hiptmair and E. Spindler, A second-kind Galerkin boundary element method for scattering at composite objects. BIT 55 (2015) 33–57. [Google Scholar]
  18. X. Claeys, R. Hiptmair and E. Spindler, Second kind boundary integral equation for multi-subdomain diffusion problems. Adv. Comput. Math. 43 (2017) 1075–1101. [Google Scholar]
  19. X. Claeys, R. Hiptmair and E. Spindler, Second-kind boundary integral equations for electromagnetic scattering at composite objects. Comput. Math. Appl. 74 (2017) 2650–2670. [Google Scholar]
  20. X. Claeys, B. Thierry and F. Collino, Integral equation based optimized schwarz method for electromagnetics. In: Domain Decomposition Methods in Science and Engineering XXIV, edited by P.E. Bjørstad, S.C. Brenner, L. Halpern, H.H. Kim, R. Kornhuber, T. Rahman and O.B. Widlund. Springer International Publishing, Cham (2018) 187–194. [Google Scholar]
  21. F. Collino, S. Ghanemi and P. Joly, Domain decomposition method for harmonic wave propagation: a general presentation. Comput. Methods Appl. Mech. Engrg. 184 (2000) 171–211. [Google Scholar]
  22. D. Colton and R. Kress, Inverse acoustic and electromagnetic scattering theory, 2nd edition. In: Vol. 93 of Applied Mathematical Sciences. Springer, New York (2013). [CrossRef] [Google Scholar]
  23. D. Colton and R. Kress, Integral equation methods in scattering theory. In: Vol. 72 of Classics in Applied Mathematics. Society for Industrial and Applied Mathematics (SIAM), Philadelphia, PA (2013). [Google Scholar]
  24. M. Costabel, Boundary integral operators on Lipschitz domains: elementary results. SIAM J. Math. Anal. 19 (1988) 613–626. [CrossRef] [MathSciNet] [Google Scholar]
  25. E. Darve, The fast multipole method: numerical implementation. J. Comput. Phys. 160 (2000) 195–240. [Google Scholar]
  26. B. Després, Décomposition de domaine et problème de Helmholtz. C. R. Acad. Sci. Paris Sér. I Math. 311 (1990) 313–316. [Google Scholar]
  27. B. Després, Domain decomposition method and the Helmholtz problem. In: Mathematical and Numerical Aspects of Wave Propagation Phenomena (Strasbourg, 1991). SIAM, Philadelphia, PA (1991) 44–52. [Google Scholar]
  28. B. Després, Méthodes de décomposition de domaine pour les problèmes de propagation d’ondes en régime harmonique. Thèse, Institut National de Recherche en Informatique et en Automatique (INRIA), Rocquencourt, 1991, Université de Paris IX (Dauphine), Paris (1991). [Google Scholar]
  29. B. Després, Domain decomposition method and the Helmholtz problem. II. In: Second International Conference on Mathematical and Numerical Aspects of Wave Propagation (Newark, DE, 1993). SIAM, Philadelphia, PA (1993) 197–206. [Google Scholar]
  30. B. Després, A. Nicolopoulos and B. Thierry, Corners and stable optimized domain decomposition methods for the Helmholtz problem. Preprint https://hal.archives-ouvertes.fr/hal-02612368 (2020). [Google Scholar]
  31. V. Dolean, P. Jolivet and F. Nataf, An Introduction to Domain Decomposition Methods. Algorithms, Theory, and Parallel Implementation. Society for Industrial and Applied Mathematics (SIAM), Philadelphia, PA (2015). [Google Scholar]
  32. M. El Bouajaji, X. Antoine and C. Geuzaine, Approximate local magnetic-to-electric surface operators for time-harmonic Maxwell’s equations. J. Comput. Phys. 279 (2014) 241–260. [Google Scholar]
  33. M. El Bouajaji, B. Thierry, X. Antoine and C. Geuzaine, A quasi-optimal domain decomposition algorithm for the time-harmonic Maxwell’s equations. J. Comput. Phys. 294 (2015) 38–57. [Google Scholar]
  34. M. Gander and F. Kwok, On the applicability of Lions’ energy estimates in the analysis of discrete optimized Schwarz methods with cross points. In: Vol. 91 of Domain Decomposition Methods in Science and Engineering. Springer, Heidelberg (2013) 475–483. [Google Scholar]
  35. M. Gander and K. Santugini, Cross-points in domain decomposition methods with a finite element discretization. Electron. Trans. Numer. Anal. 45 (2016) 219–240. [Google Scholar]
  36. 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 Rev. 61 (2019) 3–76. [Google Scholar]
  37. L. Greengard and J.-Y. Lee, Stable and accurate integral equation methods for scattering problems with multiple material interfaces in two dimensions. J. Comput. Phys. 231 (2012) 2389–2395. [Google Scholar]
  38. L. Greengard and V. Rokhlin, A new version of the fast multipole method for the Laplace equation in three dimensions. In: Vol. 6 of Acta Numer. Cambridge Univ. Press, Cambridge (1997) 229–269. [Google Scholar]
  39. W. Hackbusch, Hierarchical matrices: algorithms and analysis. In: Vol. 49 of Springer Series in Computational Mathematics. Springer, Heidelberg (2015). [Google Scholar]
  40. U. Langer and O. Steinbach, Boundary element tearing and interconnecting methods. Computing 71 (2003) 205–228. [CrossRef] [MathSciNet] [Google Scholar]
  41. M. Lecouvez, Iterative methods for domain decomposition without overlap with exponential convergence for the Helmholtz equation. Ph.D thesis, Ecole Polytechnique (2015). [Google Scholar]
  42. M. Lecouvez, B. Stupfel, P. Joly and F. Collino, Quasi-local transmission conditions for non-overlapping domain decomposition methods for the Helmholtz equation. C. R. Phys. 15 (2014) 403–414. [Google Scholar]
  43. R. Leis, Initial-Boundary Value Problems in Mathematical Physics, edited by B.G. Teubner, Stuttgart. John Wiley & Sons Ltd, Chichester (1986). [Google Scholar]
  44. P.-L. Lions, On the Schwarz alternating method III. A variant for nonoverlapping subdomains. In: Vol. 22 of Third International Symposium on Domain Decomposition Methods for Partial Differential Equations. SIAM (1989). [Google Scholar]
  45. W. McLean, Strongly Elliptic Systems and Boundary Integral Equations. Cambridge University Press, Cambridge (2000). [Google Scholar]
  46. A. Moiola and E.A. Spence, Is the Helmholtz equation really sign-indefinite? SIAM Rev. 56 (2014) 274–312. [Google Scholar]
  47. F.W.J. Olver, D.W. Lozier, R.F. Boisvert and C.W. Clark, NIST handbook of mathematical functions. In: U.S. Department of Commerce, National Institute of Standards and Technology. Cambridge University Press, Cambridge, Washington, DC (2010). [Google Scholar]
  48. C. Pechstein, Finite and boundary element tearing and interconnecting solvers for multiscale problems. In: Vol. 90 of Lecture Notes in Computational Science and Engineering. Springer, Heidelberg (2013). [Google Scholar]
  49. Z. Peng, K.-H. Lim and J.-F. Lee, Computations of electromagnetic wave scattering from penetrable composite targets using a surface integral equation method with multiple traces. IEEE Trans. Antennas Propag. 61 (2013) 256–270. [Google Scholar]
  50. Z. Peng, K.-H. Lim and J.-F. Lee, A boundary integral equation domain decomposition method for electromagnetic scattering from large and deep cavities. (English summary). J. Comput. Phys. 280 (2015) 626–642. [Google Scholar]
  51. Y. Saad, Iterative Methods for Sparse Linear Systems, 2nd edition. SIAM Society for Industrial and Applied Mathematics, Philadelphia, PA (2003). [Google Scholar]
  52. S. Sauter and C. Schwab, Boundary element methods. In: Vol. 39 of Springer Series in Computational Mathematics. Springer-Verlag, Berlin (2011). [Google Scholar]
  53. O. Steinbach, Numerical Approximation Methods for Elliptic Boundary Value Problems. Finite and Boundary Elements. Springer, New York (2008). [Google Scholar]
  54. A. Toselli and O. Widlund, Domain decomposition methods – algorithms and theory. In: Vol. 34 of Springer Series in Computational Mathematics. Springer-Verlag, Berlin (2005). [Google Scholar]
  55. A. Vion and C. Geuzaine, Improved sweeping preconditioners for domain decomposition algorithms applied to time-harmonic Helmholtz and Maxwell problems. ESAIM: Proc. Surv. 61 (2018) 93–111. [Google Scholar]
  56. T. von Petersdorff, Boundary integral equations for mixed Dirichlet, Neumann and transmission problems. Math. Methods Appl. Sci. 11 (1989) 185–213. [Google Scholar]

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