LABORATOIRE J.A. DIEUDONNE

UMR CNRS-UNS N°7351
 
Publications - Stéphane Descombes
  1. Christophe A., Descombes S., Lanteri S., An implicit hybridized discontinuous Galerkin method for the 3D time-domain Maxwell equations, to appear in Applied Mathematics and Computation.
  2. Descombes S., Duarte M., Dumont T., Guillet T., Louvet V., Massot M, Task-based adaptive multiresolution for time-space multi-scale reaction-diffusion systems on multi-core architectures, SMAI Journal of Computational Mathematics, Volume 3, pp 29-51 (2017).
  3. Descombes S., Lanteri S., Moya L., Temporal convergence analysis of a locally implicit discontinuous Galerkin time domain method for electromagnetic wave propagation in dispersive media, Journal of Computational and Applied Mathematics, Volume 316, pp 122–132 (2017).
  4. Descombes S., Lanteri S., Moya L., Locally implicit discontinuous Galerkin time domain method for electromagnetic wave propagation in dispersive media applied to numerical dosimetry in biological tissues, SIAM Journal of Scientific Computing, Volume 38, no. 5, pp. A2611-A2633 (2016).
  5. Descombes, Stéphane; Duarte, Max; Dumont, Thierry; Laurent, Frédérique; Louvet, Violaine; Massot, Marc, Analysis of operator splitting in the non-asymptotic regime for nonlinear reaction diffusion equations. Application to the dynamics of premixed flames, SIAM Journal on Numerical Analysis, Volume 52, no. 3, 1311–1334 (2014).
  6. S. Descombes C. Durochat. S. Lanteri, L. Moya, C. Scheid and J. Viquerat, Recent advances on a DGTD method for time-domain electromagnetics, Photonics and Nanostructures, Volume 11, issue 4, 291-302 (2013).
  7. Max Duarte, Stéphane Descombes, Christian Tenaud, Sébastien Candel, Marc Massot, Time-space adaptive numerical methods for the simulation of combustion fronts, Combustion and Flame, volume 160, Issue 6 (2013), Pages 1083–1101.
  8. Stéphane Descombes, Stéphane Lanteri, Ludovic Moya, Locally implicit time integration strategies in a discontinuous Galerkin method for Maxwell's equations, Journal Of Scientific Computing (2013) Volume 56, Issue 1, pp 190-218.
  9. S. Descombes, M. Thalhammer,  An exact local error representation of exponential operator splitting methods for evolutionary problems and applications to linear Schrödinger equations in the semi-classical regime, IMA J Numer Anal (2013) 33 (2): 722-745.
  10. Thierry Dumont, Max Duarte, Stéphane Descombes, Marie-Aimée Dronne, Marc Massot, Violaine Louvet,  Simulation of human ischemic stroke in realistic 3D geometry, Communications in Nonlinear Science and Numerical Simulation 18 (2013) , no. 6, 1539-1557.
  11. Duarte, Max; Bonaventura, Zdeněk; Massot, Marc; Bourdon, Anne; Descombes, Stéphane; Dumont, Thierry A new numerical strategy with space-time adaptivity and error control for multi-scale streamer discharge simulations. J. Comput. Phys. 231 (2012), no. 3, 1002–1019. 
  12. Duarte, Max; Massot, Marc; Descombes, Stéphane; Tenaud, Christian; Dumont, Thierry; Louvet, Violaine; Laurent, Frédérique New resolution strategy for multiscale reaction waves using time operator splitting, space adaptive multiresolution, and dedicated high order implicit/explicit time integrators. SIAM J. Sci. Comput. 34 (2012), no. 1, A76–A104.
  13. Descombes, Stéphane; Duarte, Max; Dumont, Thierry; Louvet, Violaine; Massot, Marc Adaptive time splitting method for multi-scale evolutionary partial differential equations. Confluentes Math. 3 (2011), no. 3, 413–443.
  14. Duarte, Max; Massot, Marc; Descombes, Stéphane Parareal operator splitting techniques for multi-scale reaction waves: numerical analysis and strategies. ESAIM Math. Model. Numer. Anal. 45 (2011), no. 5, 825–852.
  15. S. Descombes, M. Thalhammer, An exact local error representation of exponential operator splitting methods for evolutionary problems and applications to linear Schrödinger equations in the semi-classical regime, BIT. Numerical Mathematics, 50, no. 4, p.729-749 (2010).
  16. P. Chartier, F. Castella, S. Descombes, G. Vilmart, Splitting methods with complex times for parabolic equations, BIT. Numerical Mathematics, 49, no. 3, p.487-508 (2009).
  17. M. A. Dronne, E. Grenier, S. Descombes, H. Gilquin, Examples of the influence of the geometry on the propagation of progressive waves, Math. Comput. Modelling, 49, no. 11-12, p.2138--2144 (2009).
  18. E. Grenier, M.A. Dronne, S. Descombes, H. Gilquin, A. Jaillard, M. Hommel, J.P. Boissel, A numerical study of the blocking of migraine by Rolando sulcus, Progress in Biophysics and Molecular Biology, 97 (1), p.54-59 (2008).
  19. S. Descombes, T. Dumont, Numerical simulation of a stroke: Computational problems and methodology, Progress in Biophysics and Molecular Biology, 97 (1), p.40-53, (2008).
  20. S. Descombes, T. Dumont, V. Louvet, M. Massot, On the local and global errors of splitting approximations of reaction-diffusion equations with high spatial gradients, International Journal of Computer Mathematics 84 (2007), no. 6, 749--765.
  21. S. Benzoni-Gavage, R. Danchin, S. Descombes, Well-posedness of one-dimensional Korteweg models, Electronic Journal of Differential Equations, 59 (2006), 1 - 35.
  22. S. Benzoni-Gavage, R. Danchin, S. Descombes, On the well-posedness of the Euler-Korteweg model in several space dimensions, Indiana University Mathematics Journal 56 (2007), no. 4, 1499--1579.
  23. X. Antoine, C. Besse, S. Descombes, Artificial boundary conditions for one-dimensional cubic nonlinear Schrödinger equations, SIAM J. Numer. Anal., 43 (2006), no. 6, 2272 - 2293.
  24. S. Benzoni-Gavage, R. Danchin, S. Descombes, D. Jamet, Structure of Korteweg models and stability of diffuse interfaces, Interfaces and Free Boundaries. Modelling, Analysis and Computation, 7 (2005), no. 4, 371--414.
  25. S. Descombes, M. Massot, Operator splitting for nonlinear reaction-diffusion systems with an entropic structure : singular perturbation and order reduction, Numerische Mathematik (2004) Volume 97, Number 4, pp. 667 - 698.
  26. A.B. Iskakov, S. Descombes, E. Dormy, An integro-differential formulation for magnetic induction in bounded domains: boundary element--finite volume method, J. Comput. Phys. 197 (2004), no. 2, pp. 540-554.
  27. S. Descombes, M. Ribot, Convergence of the Peaceman-Rachford approximation for reaction-diffusion systems, Numerische Mathematik (2003) Volume 95, Number 3, pp. 503 - 525.
  28. C. Besse, B. Bidégaray, S. Descombes, Order estimates in time of splitting methods for the nonlinear Schrödinger equation, SIAM J. Numer. Anal. 40 (2002), no. 5, 26--40.
  29. S. Descombes, M. Schatzman, Strang's formula for holomorphic semi-groups, J. Math. Pures Appl. 81 (2002), no. 1, 93--114
  30. S. Descombes, Convergence of a splitting method of high order for reaction-diffusion systems, Math. Comp. 70 (2001), no. 236, 1481--1501.
  31. S. Descombes, B. O. Dia, An operator theoretic proof of an estimate on the transfer operator, J. Funct. Anal. 165 (1999), no. 2, 240--257.
  32. S. Descombes, M. Moussaoui, Global existence and regularity of solutions for complex Ginzburg-Landau equations, Boll. Unione Mat. Ital. Sez. B Artic. Ric. Mat. (8) 3 (2000), no. 1, 193--211.
  33. S. Descombes, M. Schatzman, On Richardson Extrapolation of Strang's Formula for Reaction-Diffusion Equations, Equations aux Dérivées Partielles et Applications, articles dédiés à Jacques-Louis Lions, p. 429-452, Gauthier-Villars Elsevier, Paris, 1998.
  34. S. Descombes, M. Schatzman, Directions alternées d'ordre élevé en réaction-diffusion, C.R. Acad. Sci. Paris, t.321, Série I, p 1521-1524, 1995.
  35. S. Descombes, M. Moussaoui, Existence globale et régularité de solutions d'équations de Ginzburg-Landau complexes, C.R. Acad. Sci. Paris, t.329, Série I, p 189-192, 1999.
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Chapitres de livres/Book chapters
  1. Duarte M., Massot M., Descombes S., Tenaud C., Candel S, Time-space adaptive numerical methods for the simulation of combustion fronts
    Annual Research Briefs of the Center for Turbulence Research, Center for Turbulence Research - Stanford University (Ed.) (2012) 347-358.
  2. S. Descombes, M. Duarte, M. Massot, Operator splitting methods with error estimator and adaptive time–stepping. Application to the simulation of combustion phenomena
    3. Splitting Method in Communication and Imaging, Science and Engineering, Editors: Glowinski, Roland, Osher, Stanley J., Yin, Wotao, Springer 2016.
Proceedings
  1. Wang H., Xu L., Li B., Descombes S., Lanteri S., Numerical study of a family of IMEX-DGTD methods for the 3D time-domain Maxwell's equations, International Applied Computational Electromagnetics Society (ACES) Symposium, At Firenze (2017).
  2. Moya, Ludovic; Descombes, Stéphane; Lanteri, Stéphane; High-order locally implicit time integration strategies in a discontinuous Galerkin method for Maxwell’s equations, Selected papers from the ICOSAHOM conference, June 25-29, 2012, Gammarth, Tunisia, Series: Lecture Notes in Computational Science and Engineering, Vol. 95 (2013).
  3. Massot, Marc; Duarte, Max; Descombes, Stéphane; Méthodes numériques adaptatives pour la simulation de la dynamique de fronts de réaction multi-échelles en temps et en espace, Actes du colloque Edp-Normandie, Le Havre 2012 pp. 93-109 (2013).
  4. Bonaventura, Zdeněk; Duarte, Max; Bourdon, Anne; Massot, Marc; Descombes, Stéphane; Dumont, Thierry; Numerical simulation of the interaction of two streamer discharges in air, ESCAMPIG XXI, Viana do Castelo, Portugal, July 10-14 (2012).
  5. Duarte, Max; Massot, Marc; Descombes, Stéphane; Tenaud, Christian; Dumont, Thierry; Louvet, Violaine; Laurent, Frédérique New resolution strategy for multi-scale reaction waves using time operator splitting and space adaptive multiresolution: application to human ischemic stroke. Summer School on Multiresolution and Adaptive Mesh Refinement Methods, 277–290, ESAIM Proc., 34, EDP Sci., Les Ulis, 2011
  6. Duarte, Max; Massot, Marc; Descombes, Stéphane; Dumont, Thierry Adaptive time-space algorithms for the simulation of multi-scale reaction waves. Finite volumes for complex applications. VI. Problems & perspectives. Volume 1, 2, 379–387, Springer Proc. Math., 4, Springer, Heidelberg, 2011.
  7. Descombes, Stéphane; Dolean, Victorita; Gander, Martin J. Schwarz waveform relaxation methods for systems of semi-linear reaction-diffusion equations. Domain decomposition methods in science and engineering XIX, 423–430, Lect. Notes Comput. Sci. Eng., 78, Springer, Heidelberg, 2011.
  8. Benzoni, Sylvie; Descombes, Stéphane; Poignard, Claire; Ribot, Magali, Michelle Schatzman (1949–2010).  Gaz. Math. No. 127 (2011), 79–82. 
  9. Benzoni, Sylvie; Descombes, Stéphane; Poignard, Clair; Ribot, Magali, Michelle Schatzman, 1949–2010. (French) Matapli No. 93 (2010), 53–58.
  10. Duarte M., Massot M., Laurent F., Descombes S., Tenaud C., Dumont T., Louvet V.
    New Resolution Strategies for Multi-scale Reaction Waves: Optimal Time Operator Splitting and Space Adaptive Multiresolution
    XXXVI Latin American Conference on Informatics (CLEI 2010) 14 (2010) Paper 6, 14 pages.
  11. Benzoni-Gavage, Sylvie; Danchin, Raphaël; Descombes, Stéphane; Jamet, Didier Stability issues in the Euler-Korteweg model. Control methods in PDE-dynamical systems, 103–127, Contemp. Math., 426, Amer. Math. Soc., Providence, RI, 2007.
  12. Benzoni-Gavage, Sylvie; Danchin, Raphaël; Descombes, Stéphane; Jamet, Didier On Korteweg models for fluids exhibiting phase changes. Hyperbolic problems: theory, numerics and applications. I, 311–318, Yokohama Publ., Yokohama, 2006
  13. Descombes, S.; Dumont, T.; Massot, M. Operator splitting for stiff nonlinear reaction-diffusion systems: order reduction and application to spiral waves. Patterns and waves (Saint Petersburg, 2002), 386–482, AkademPrint, St. Petersburg
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Prépublications/Preprint
  1. Wang H., Xu L., Li B., Descombes S., Lanteri S., A new family of exponential-based high order DGTD  methods for modelling 3D transient multiscale electromagnetic problems.