Open Access
Issue |
ESAIM: M2AN
Volume 54, Number 3, May-June 2020
|
|
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Page(s) | 775 - 810 | |
DOI | https://doi.org/10.1051/m2an/2019050 | |
Published online | 01 April 2020 |
- R.A. Adams and J.J.F. Fournier, Sobolev spaces, In: Vol. 140 of Pure and Applied Mathematics. Elsevier Science (2003). [Google Scholar]
- J.M. Ball, Y. Capdeboscq and B.T. Xiao, On uniqueness for time harmonic anisotropic Maxwell’s equations with piecewise regular coefficients. Math. Models Methods Appl. Sci. 22 (2012) 1–9. [Google Scholar]
- Y. Boubendir, X. Antoine and C. Geuzaine, A quasi-optimal non-overlapping domain decomposition algorithm for the Helmholtz equation. J. Comput. Phys. 231 (2012) 262–280. [Google Scholar]
- Y. Boubendir, C. Jerez-Hanckes, C. Pérez-Arancibia and C. Turc, Domain Decomposition Methods based on quasi-optimal transmission operators for the solution of Helmholtz transmission problems. Preprint arXiv:1710.02694 (2017) [Google Scholar]
- F. Collino, S. Ghanemi and P. Joly, Domain decomposition method for harmonic wave propagation: a general presentation. Comput. Methods Appl. Math. 184 (2000) 171–211. [Google Scholar]
- F. Demengel and G. Demengel, Functional Spaces for the Theory of Elliptic Partial Differential Equations. Springer-Verlag, London (2012). [CrossRef] [Google Scholar]
- B. Després, Domain decomposition method and the Helmholtz problem (Part II)In: Second international conference on mathematical and numerical aspects of wave propagation. SIAM (1993) 197–206. [Google Scholar]
- E. Di Nezza, G. Palatucci and E. Valdinoci, Hitchhiker’s guide to the fractional sobolev spaces. Preprint arXiv:1104.4345 (2011). [Google Scholar]
- 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, Preprint arXiv:1610.02270 (2016). [Google Scholar]
- M. Gander, L. Halpern and F. Magoulès, An optimized Schwarz method with two-sided Robin transmission conditions for the Helmholtz equation. Int. J. Numer. Methods Fluids 55 (2007) 163–175. [Google Scholar]
- M. Gander, F. Magoulès and F. Nataf, Optimized Schwarz methods without overlap for the Helmholtz equation. SIAM J. Sci. Comput. 24 (2002) 38–60. [Google Scholar]
- P. Grisvard, Elliptic Problems in Nonsmooth Domains. Society for Industrial and Applied Mathematics (2011). [Google Scholar]
- S.P. Han, A globally convergent method for nonlinear programming. J. Optim. Theory and Appl. 22 (1977) 297–309. [CrossRef] [Google Scholar]
- P. Joly, F. Collino, M. Lecouvez and B. Stupfel, Quasi-local transmission conditions for non-overlapping domain decomposition methods for the helmholtz equation. C.R. Phys. 4310 (2014) 385–478. [Google Scholar]
- M. Lecouvez, Méthodes itératives de décomposition de domaine sans recouvrement avec convergence géométrique pour l’équation de Helmholtz, Ph.D. thesis, Mathématiques appliquées Palaiseau, Ecole polytechnique, Thèse de doctorat dirigée par Joly Patrick (2015). [Google Scholar]
- W. McLean, Strongly Elliptic Systems and Boundary Integral Equations. Cambridge University Press (2000). [Google Scholar]
- J.-C. Nedelec, Acoustic and Electromagnetic Equations: Integral Representations for Harmonic Problems. Springer-Verlag (2001). [CrossRef] [Google Scholar]
- Z. Peng, V. Rawat and J.-F. Lee, One way domain decomposition method with second order transmission conditions for solving electromagnetic wave problems, J. Comput. Phys. 229 (2010) 1181–1197. [Google Scholar]
- M.J.D. Powell, A fast algorithm for nonlinearly constrained optimization calculations, edited by G.A. Watson. In: Numerical Analysis, Vol. 630 of Lecture Notes in Mathematics. Springer, Berlin Heidelberg (1978) 144–157. [CrossRef] [Google Scholar]
- E.M. Stein, Singular integrals and differentiability properties of functions. In Princeton mathematical series. Princeton University Press (1970). [Google Scholar]
- O. Steinbach and M. Windisch, Stable boundary element domain decomposition methods for the helmholtz equation. Numer. Mathematik 118 (2011) 171–195. [CrossRef] [Google Scholar]
- L.N. Trefethen and L. Halpern, Well-posedness of one-way wave equations and absorbing boundary conditions, Math. Computation 47 (1986) 421–435. [CrossRef] [Google Scholar]
- M. Vouvakis, K. Zhao, S.-M. Seo and J.-F. Lee, A domain decomposition approach for non-conformal couplings between finite and boundary elements for unbounded electromagnetic problems in R3. J. Comput. Phys. 225 (2007) 975–994. [Google Scholar]
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