* Habilitation à diriger des recherches en mathématiques, du laboratoire Jacques
Louis-Lions (LJLL) de l'Université Pierre et Marie Curie, Paris VI.
* Thèse de doctorat en mathématiques appliquées, mention très honorable, du laboratoire d'analyse numérique de l'Université Pierre et Marie Curie, Paris VI.
* DEA analyse numérique de l'École Polytechnique (Palaiseau 1994).
3- Responsabilités administratives à la faculté des sciences de l'Université Saint-Joseph.
* Depuis septembre 2014 à la FS-USJ : Directeur de l'unité de recherche "UR-MM : Mathématiques et modélisation".
* 2012 - 2014 à la FS-USJ : Responsable du master "Sciences actuarielle et financière".
* 2006 - 2012 : directeur du département de mathématiques.
* 2005 - 2006 : responsable des masters "Sciences actuarielle et financière" et "Analyse numérique : option équations aux dérivées partielles".
* 2002 - 2005 : responsable du master "Mathématiques et informatique pour la nance".
Domaine d’expertise
• Ingénierie et technologie; Sciences
Thématiques de recherche
Discrétisation des équations aux dérivées partielles et analyse numérique correspondante, avec applications en :
1. Ondes électromagnétiques : -Méthodes des équations intégrales pour l'étude des problèmes de diffraction des ondes électromagnétiques par différents types d'obstacles (obstacle conducteur parfait, obstacle avec conditions d'impédances, obstacle diélectrique, . . .) -Propagation des ondes électromagnétiques dans des guides d'ondes et étude des jonctions.
2. Mécanique des fluides : -Etudes des estimations d'erreur a priori et a posteriori pour différents types de problèmes de fluide (Stokes, Navier-Stokes, Fluide de grade deux, Problème de type convection diffusion réaction. . .) stationnaires et instationnaires. -Méthode de deux grilles pour les équations de Navier-Stokes.
+ Publications et communications
1- Rim Aldbaissy, Frédéric HECHT, Gihane Mansour, Toni SAYAH and Pierre Henri Tournier, Scalable domain decomposition preconditioner for Navier-Stokes equations coupled with the heat equation, International Journal of Computer Mathematics, https ://doi.org/10.1080/00207160.2021.1925888, (2021).
2- Nancy Chalhoub, Pascal Omnes, Toni Sayah and Rebecca El Zahlaniyeh, A Posteriori error estimates for the time dependent convection-diusion-reaction equation coupled with the Darcy system, "Numerical Algorithms", https ://doi.org/10.1007/s11075-021-01152-3, (2020).
3- Toufic El Arwadi and Toni Sayah, A new regularization of the D-bar Method with complex conductivity, to Complex Variables and Elliptic Equations, 66(5), pp. 826-842, DOI : 10.1080/17476933.2020.1747056, (2021).
4- Jad Dacroub, Joanna Faddoul and Toni Sayah, A posteriori analysis of the Newton method applied to the Navier-Stokes problem, Journal of applied mathematics and computing, 63, pp. 411-437, DOI : 10.1007/s12190-020-01323-w, (2020).
5- Dayana Dib, Séréna Dib and Toni Sayah, A new numerical scheme for Darcy's problem coupled with the heat equation, Computational and applied mathematics, 39 (1), pp :1-16, DOI : 10.1080/17476933.2020.1747056, (2020).
6- Nancy Chalhoub, Pascal Omnes, Toni Sayah and Rebecca Zahlaniyeh, Full discretization of time dependent convection-diffusion-reaction equation coupled with the Darcy system, CALCOLO, 57(4), pp. 3-28, DOI : 10.1007/s10092-019-0352-1, (2020).
7- Séréna Dib, Vivette Girault, Frédéric Hecht and Toni Sayah, A posteriori error estimate for Darcy's problem coupled with the heat equation, ESIAM : Mathematical Modelling and Numerical Analysis, 53 (6), pp. 2121-2159, (2019).
8- Toufic El Arwadi and Toni Sayah, A Regularization Scheme for 2D Conductivity Imaging by the D-bar Method, Numerical Functional Analysis and Optimization, 40 (12), pp. 1410-1425, DOI :10.1080/01630563.2019.1606011, (2019).
9- Toni Sayah, Adaptive stratified Monte Carlo algorithm for numerical computation of integrals, Mathematics and Computers in Simulation, 157, pp. 143-158, doi.org/10.1016/j.matcom.2018.10.004, (2019).
10- Noura Morcos and Toni Sayah, reduced basis method for the adapted mesh and Monte Carlo methods applied to an elliptic stochastic problem, Computational and Applied Mathematics, 38(93), DOI : 10.1007/s40314-019-0859-8, (2019).
11- Mireille Haddad, Frédéric Hecht, Toni Sayah and Pierre Henri Tournier, Parallel computing investigations for the projection method applied to the interface transport scheme of a two-phase ow by the method of characteristics, Numerical Algorithm, 80(2), pp. 447-467, https ://doi.org/10.1007/s11075-018-0492-4, (2018).
12- Rim Dbaissy, Frédéric Hecht, Gihane Mansour and Toni Sayah, A full discretization of the time-dependent Boussinesq (buoyancy) model with nonlinear viscosity, CLACOLO, 55(44), DOI :10.1007/s10092-018-0285-0 (2018).
13- Séréna Dib, Toni Sayah, Vivette Girault, François Murat, Christine Bernardi and Frédéric Hecht, Finite element method for Darcy's problem coupled with the heat equation, Numerische Mathematik, 139(2), pp. 315-348, DOI10.1007/s00211-017- 0938-y, (2018).
14- Ghina Nassreddine, Toni Sayah, New Results for the A Posteriori Estimates of the Two Dimensional Time Dependent Navier-Stokes Equation, International Journal of Mechanics, 11, pp. 155-165, (2017).
15- Christine Bernardi, Jad Dakroub, Gihane Mansour, Farah Rafei and Toni Sayah, Convergence analysis of two numerical schemes applied to a nonlinear elliptic problem, Journal of Scientic Computing, 71 (1), DOI : 10.1007/s10915-016-0301-y, (2017).
16- Mireille El Haddad, Frédéric Hecht and Toni Sayah, Interface transport scheme of a two-phase ow by the method of characteristics, International Journal for Numerical Methods in Fluids, DOI :10.1002/d.4280, 28, 6, (2017), pp 513-543.
17- Christine Bernardi, Jad Dakroub, Gihane Mansour and Toni Sayah, A posteriori analysis of iterative algoriths for Navier-Stokes Problem, ESIAM : Mathematical Modelling and Numerical Analysis, 50 (4), doi :10.1051/m2an/2015062, (2016), pp. 1035-1055.
18- Toufic El Arwadi and Toni Sayah, An Lp estimate for Dirichlet-to-Neumann operator and application., Electronic Journal of Dierential Equations, Vol. 2015, No.258, pp. 1-8, (2015).
19- Toufic El Arwadi, Serena Dib and Toni Sayah, A piori and a posteriori estimations of a linear elliptic problem with dynamical boudary condition, 9, 6, doi :10.12785/amis/100121, Journal of Applied Mathematics & Information Sciences, (2015), pp 2205-3317.
20- Christine Bernardi and Toni Sayah, A posteriori error analysis of the time dependent Navier-Stokes equations with mixed boundary conditions, 69, 1, DOI 10.1007/s40324-015-0033-1, SeMA Journal (SEMJ), (2015), pp 1-23.
21- Christine Bernardi, Jad Dakroub, Gihane Mansour and Toni Sayah, A posteriori analysis of iterative algorithms for a nonlineair problem, Journal of Scientic Computing, 65, 2, DOI 10.1007/s10915-014-9980-4, (2015), pp 672-697.2
22- Christine Bernardi and Toni Sayah, A posteriori error analysis of the time dependent Stokes equations with mixed boundary conditions, IMA J Numer Anal, 35, 1, 2015, doi : 10.1093/imanum/drt067(2012), pp 179-198.
23- Fida El Chami, Gihane Mansour et Toni Sayah, Error studies of the Coupling Darcy-Stokes systems with velocity-pressure formulation, CALCOLO, 49, Issue 2 (2012), Page 73-93.
24- Hyam Abboud, Fida El Chami et Toni Sayah, A priori and a posteriori estimates for three-dimensional Stokes equations with non standard of boundary conditions, Numerical Methods for Partial Differential Equations, Volume 28, (2012), pp 1178-1193.
25- Hyam Abboud, Fida El Chami et Toni Sayah, Error estimates for three-dimensional Stokes problem with non-standard boundary conditions, C. R. Acad. Sci. Paris, Ser. I 349, (2011), pp. 523-528.
26- Touc Abboud et Toni Sayah, Retarded Potential Method for Computational Electromagnetics, Proceedings of AP2000 Millennium Conference on Antennas & Propagation, Davos-Switzerland, April 9-14, 2000. ESA Publication, CD-ROM SP-444.
27- Fida El Chami et Toni Sayah, A posteriori error estimators for the fully discrete time dependent Stokes problem with some different boundary conditions , CALCOLO, 47 (2010), pp 169-192.
28- Hyam Abboud, Vivette Girault et Toni Sayah, A second order accuracy in time for a full discretized time-dependent Navier-Stokes equations by a two-grid scheme, Numerische Mathematik, 14, 2 (2009) pp. 189-231.
29- Hyam Abboud et Toni Sayah, Upwind discretisation of a time-dependent two dimensional grade-two uid model, Computers & Mathematics with applications, 57 (2009), pp. 1249-1264.
30- Hyam Abboud et Toni Sayah, A full discretization of the time-dependent Navier-Stokes by two-grid scheme, ESIAM : Mathematical Modelling and Numerical Analysis, vol. 42, No. 1 (2008), pp 141-174.
31- Hyam Abboud, Vivette Girault et Toni Sayah, Two-grid scheme for the fully discrete time-dependent Navier-Stokes problem, C. R. Acad. Sci. Paris , ser.I 341 (2005), pp 451-456.
32- Toni Sayah et Badih Azar, Eect of Junction on Electromagnetic Waveguide transmission, Mathematica Balkanica, vol. 18, No 3-4 (2004), pp 443-452.
33- Toni Sayah et Badih Azar, Coupling finite element method-modal expansion method for the junction of electromagnetic waveguides, International journal of applied mathematics, vol. 12, No 3 (2003), pp 221-234.
34- Toufic Abboud et Toni Sayah, Discretisation of the Engquist-Nedelec approximation of thin layer, International journal of computational and numerical analysis and applications, vol. 3, No 3, (2003), pp 249-261.
35-Toni Sayah, Boundary conditions for the electromagnetic scattering by thin layers, International journal of applied mathematics, vol. 11, No 2 (2002), pp 121-136.
36- Toufic Abboud et Toni Sayah, Retarded Potential Method for Computational Electromagnetics, Proceedings of AP2000 Millennium Conference on Antennas & Propagation, Davos-Switzerland, April 9-14, 2000. ESA Publication, CD-ROM SP-444.
37- Touic Abboud et Toni Sayah, The retarded potential method for computational electromagnetics, Proceedings of the 3rd European Conference on Numerical Mathematics and Advanced Applications, Jyvskyl, Finland, July 26-30, 1999, ed. by P. Neittaanmki, T. Tiihonen and P. Tarvainen, World Scientic, Singapore, 2000, pp. 198-205.
38- Toufic Abboud, Joseph El Gharib, Jean Claude Nédélec et Toni Sayah, An accelerated retarded potential method for the time dependent wave scattering , ASME 15th Biennal Conference on Mechanical Vibration and Noise, Boston, septembre 1995, pp. 3-8.