UMA Home page for Sonia Fliss
Teaching activities
MA 103 : Introduction to the discretization for PDEs
ANN201 : Finite element method
AMS-X01 : Periodic homogenization
ANN201 : Finite element method
AMS-X01 : Periodic homogenization
Publications
Papers in peer-reviewed journals
Submitted
- Guided modes in a hexagonal periodic graph like domain
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submitted
2023
- DISCRETE HONEYCOMBS, RATIONAL EDGES AND EDGE STATES
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Communications on Pure and Applied Mathematics, sep, 2023 
- Scattering in a partially open waveguide: the forward problem
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IMA Journal of Applied Maths, feb, 2023 [
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- The Half-Space Matching method for elastodynamic scattering problems in unbounded domains
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Journal of Computational Physics, vol. 490, oct, 2023 - Wave propagation in one-dimensional quasiperiodic media
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COT, apr, 2023
2022
- Edge states in rationally terminated honeycomb structures
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Proceedings of the National Academy of Sciences, 2022 - On the Half-Space Matching method for real wavenumbers
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SIAM Journal on Applied Mathematics, vol. 82(4), 2022 
- The Complex-Scaled Half-Space Matching Method
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SIAM Mathematical Analysis, vol. 54, pp. 512-557, jan, 2022
2021
- A DtN approach to the mathematical and numerical analysis in waveguides with periodic outlets at infinity
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Pure and Applied Analysis, vol. 3-3, pp. 487--526, 2021 - On a surprising instability result of Perfectly Matched Layers for Maxwell's equations in 3D media with diagonal anisotropy
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Comptes Rendus. Mathématique, vol. 3, pp. 249-256, 2021
2020
- Time harmonic wave propagation in one dimensional weakly randomly perturbed periodic media
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SN Partial Differential Equations and Applications, vol. 1(40), oct, 2020
2019
- On well-posedness of time-harmonic problems in an unbounded strip for a thin plate model
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Communications in Mathematical Sciences, vol. 17/6, pp. 1487 – 1529, dec, 2019 [ ] - Trapped modes in thin and infinite ladder like domains. Part 2 : asymptotic analysis and numerical application
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Asymptotic analysis, nov, 2019 [ ]
2018
- On well-posedness of time-harmonic problems in an unbounded strip for a thin plate model
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sep, 2018 [ ] - The Halfspace Matching Method: a New Method to Solve Scattering Problem in Infinite Media
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JCAM, vol. 338, pp. 44-68, jul, 2018 [ ]
2017
- On the Approximation of Electromagnetic Fields by Edge Finite Elements. Part 2: A Heterogeneous Multiscale Method for Maxwell's equations
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Computers & Mathematics with Applications, vol. 73(9), pp. 1900-1919, may, 2017 - Trapped modes in thin and infinite ladder like domains. Part1: Existence results
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Asymptotic Analysis, vol. 103(3), pp. 103-134, jun, 2017
2016
- A Rellich type theorem for the Helmholtz equation in a conical domain
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C. R. Acad. Sci. Paris, Ser. I, vol. 354, pp. 27-32, 2016 - Iterative methods for scattering problems in isotropic and anisotropic elastic waveguides
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Wave Motion, vol. 64, pp. 13-33, jul, 2016 [ ] - Solutions of the time-harmonic wave equation in periodic waveguides : asymptotic behaviour and radiation condition
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Archive for rational mechanics and analysis, vol. 219(1), pp. 349-386, jan, 2016 [ ]
2015
- Robin-to-Robin transparent boundary conditions for the computation of guided modes in photonic crystal waveguides
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BIT Numerical Mathematics, vol. 55(1), pp. 81-115, mar, 2015
2014
- Numerical realisation of Dirichlet-to-Neumann transparent boundary conditions for photonic crystal waveguides
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Comput. Math. Appl., vol. 67(4), pp. 918-943, 2014 - On the identification of defects in a periodic waveguide from far field data
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Inverse Problems, vol. 30, pp. 095004, 2014 [ ]
2013
- A Dirichlet-to-Neumann approach for the exact computation of guided modes in photonic crystal waveguides
SiAM J. Sci. Comp., vol. 35(2), pp. B438-B461, mar, 2013 [ ] - Transparent boundary conditions for locally perturbed infinite hexagonal periodic media
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Communications in Mathematical Sciences, vol. 11 (4), pp. 907-938, 2013 [ ]
2012
- Wave propagation in locally perturbed periodic media (case with absorption): Numerical aspects
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Journal of Computational Physics, vol. 231(4), pp. 1244-1271, feb, 2012
2010
- Computation of light refraction at the surface of a photonic crystal using DtN approach
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JOSA B, vol. 27 (7), pp. 1492-1503, jul, 2010 [ ]
2009
- Exact boundary conditions for time-harmonic wave propagation in locally perturbed periodic media
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Applied Numerical Mathematics, vol. 59 (9), pp. 2155-2178, sep, 2009
2006
- Exact boundary conditions for periodic waveguides containing a local perturbation
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Communications in Computational Physics, vol. 1(6), pp. 945-973, 2006
Chapters
2019
- Numerical analysis of the Half-Space Matching method with Robin traces on a convex polygonal scatterer, in Maxwell's Equations: Analysis and Numerics
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Radon Series on Computational and Applied Mathematics 24, De Gruyter, may, 2019
2009
- Exact boundary conditions for wave propagation in periodic media containing a local perturbation
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E-Book Series Progress in Computational Physics (PiCP), Volume 1, dec, 2009 [ ]
International conferences with proceedings
2022
- The Half-space Matching method and the Perfectly Matched Layers for scattering problem in anisotropic elastic media
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pp. 402, 15th International Conference on Mathematical and Numerical Aspects of Wave Propagation, 2022
2007
- Computation of harmonic wave propagation in infinite periodic media
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Report No.5/2007 of Mathematisches Forschungsinstitut Oberwolfach "Computational Electromagnetism and Acoustics, Oberwolfach., 2007
Conferences without proceedings
2018
- Coupling BEMs in overlapping domains when a global Green’s function is not available
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IABEM 2018, Paris, may, 2018 - The Half-Space Matching method for Lamb wave scattering in anisotropic plates
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2nd International Conference on Advanced Modelling of Wave Propagation in Solids, Prague, sep, 2018 - The Half-Space Matching method for guided wave scattering in anisotropic elastic plates
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AFPAC 2018, Surrey, jan, 2018
2017
- The Half-Space Matching method for the diffraction by polygonal scatterers
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Waves 2017, Minneapolis, may, 2017
2015
- Absence of trapped modes for a class of unbounded propagative media
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Waves 2015, Karlsruhe, Allemagne, 2015
2014
- Inverse scattering in a periodic waveguide from far field data
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Recent progress in theoretical and numerical aspects of inverse problems, CIRM, Marseille, 19-23/5/2014, may, 2014
2013
- Decomposition domain methods for scattering problems in elastic waveguides
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Waves 2013, Tunis, jun, 2013 - New transparent boundary condition for time harmonic acoustic di raction in anisotropic media.
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Waves 2013, Tunis, jun, 2013 - On sampling methods to identify defects in a periodic waveguide from far field data
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Inverse Problems: Scattering, Tomography and Parameter Identification, Conference honoring Andreas Kirsch for his 60th birthday, Bad Herrenalb - Germany, 8-11/4/2013, apr, 2013 - On the far field of scattering solutions in a periodic waveguide. Part II : The inverse problem
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Waves conference, Gammarth, Tunisie, 3-7/6/2013, jun, 2013
2012
- Dirichlet-to-Neumann operators in periodic waveguides. Application to the computation of trapped modes
Days on Diffraction, may, 2012 - Iterative methods to solve scattering problems in elastic waveguides
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Seventh GDR conference, 2012
2011
- A Dirichlet-to-Neumann approach for the exact computation of guided modes in photonic crystal waveguides
10th International Conference on Mathematical and Numerical Aspects of Waves, waves 2011, Vancouver, jul, 2011 [ ]
2009
- Exact boundary conditions for locally perturbed 2d periodic plane : Numerical Aspects
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9th International Conference on Mathematical and Numerical Aspects of Waves (WAVES'09), Pau, jun, 2009
2008
- Transparent boundary conditions, Wave propagation and Periodic media
Séminaire du Cermics (ENPC), apr, 2008 - Wave propagation in locally perturbed periodic media
Conférence "EDP et applications 2008", Hammamet (Tunisie), mar, 2008
2007
- Exact boundary conditions for locally perturbed 2d-periodic plane
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Mathematical and numerical aspects of wave propagation, Reading, 2007
2005
Habilitation these
2019
- Wave propagation in periodic media : mathematical analysis and numerical simulation
Université Paris Sud (Paris 11), jan, 2019
Doctoral these
2009
- Analyse mathématique et numérique de problèmes de propagation des ondes dans des milieux périodiques infinis localement perturbés
Ecole doctorale de l'Ecole Polytechnique (EDX) - ED 447, mai 2009 [ ]
Research report
2016
- Trapped modes in thin and infinite ladder like domains: existence and asymptotic analysis
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Rapport de Recherche INRIA, mar, 2016 [ ]
Preprint
2022
- The Half-Space Matching method for elastodynamic scattering problems in unbounded domains
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2022