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Mr. Toni SAYAH

Faculty of Science

Professor

(+961) 1 421 000 ext 3373 toni.sayah@usj.edu.lb

Toni Sayah, born in 1969, is a researcher and professor of mathematics at the Faculty of Sciences of Saint-Joseph University of Beirut (USJ), Lebanon. He was appointed as a assistant professor at USJ in 2000, promoted to associate professor in 2008, and then to full professor in 2013. He earned his engineering degree from the Lebanese University in 1993, followed by a DEA in numerical analysis from École Polytechnique in 1994. In 1998, he completed his Ph.D. at the Jacques-Louis Lions Laboratory (LJLL) of Pierre and Marie Curie University (Paris VI). His doctoral research focused on retarded potential methods for heterogeneous media and the approximation of thin layers using generalized impedance conditions in electromagnetism. In 2011, he obtained his habilitation to supervise research (HDR) in mathematics, also from Pierre and Marie Curie University, with a focus on the study of wave problems and fluid mechanics. At the Faculty of Sciences at USJ, Toni Sayah has held several administrative positions. He was the coordinator of the master's program Mathematics and Computer Science for Finance from 2002 to 2005, and later of the master's programs Actuarial and Financial Sciences and Numerical Analysis: Partial Differential Equations Option during 2005–2006. From 2006 to 2012, he served as the head of the Mathematics Department. Since 2014, he has been the director of the research unit Mathematics and Modeling. His research focuses on partial differential equations and numerical analysis. He has worked on integral equation methods for studying electromagnetic wave diffraction problems and on modeling, analyzing, and simulating various types of fluid problems (Stokes, Navier-Stokes, second-grade fluids, convection-diffusion-reaction problems, etc.), both stationary and non-stationary. Toni Sayah has supervised 16 doctoral theses and published 59 articles in peer-reviewed international journals.

Highest degree : HDR in Mathematics - Université Pierre et Marie Curie, Paris VI (Sorbonne Université) - France

DegreesUniversityCountryYear
HDR in mathematicsUniversité Pierre et Marie Curie (Paris VI)France2011
PhD in mathematicsUniversité Pierre et Marie Curie (Paris VI)France1998
Analyse numériqueEcole polytechniqueFrance1994
Electrical and Electronics EngineerUniversité Libanaise (UL)Lebanon1993

  1. Finite elements: theoretical and numerical aspects, course in the second year of the master: Analysis and Probability for Partial Differential Equations.
  2. Partial differential equations and numerical applications, course in the first year of the master: Analysis and Probability for Partial Differential Equations.
  3. Differential equations and approximation schemes, course in the third year of the Bachelor's Degree in Mathematics.
  4. Matrix Analysis, course in the third year of the Bachelor's Degree in Mathematics.
  5. Calculus III, course in the second year of the Bachelor's Degree in Mathematics.
  6. Calculus II, course in the first year of the Bachelor's Degree in Mathematics.
  7. Calculus I, course in the first year of the Bachelor's Degree in Mathematics.

Professional ExperienceOrganizationStart dateEnd date
ProfessorSaint-Joseph University of Beirut01/09/201210/05/2024
Associate professorSaint-Joseph University of Beirut01/09/200831/08/2012
Assistant professorSaint-Joseph University of Beirut01/09/200031/08/2008

Engineering and Technology, Sciences

Partial differential equations with applications in:

1-Electromagnetic Waves:

  • Integral equations methods for studying diffraction problems of electromagnetic waves by different types of obstacles (perfectly conducting obstacle, obstacle with impedance conditions, dielectric obstacle, ...)
  • Propagation of electromagnetic waves in waveguides and study of junctions.

2-Fluid Mechanics:

  • Discretization and study of systems of equations associated with fluid problems (Finite Element Method, convergence, numerical simulations, ...)
  • Study of the a priori and a posteriori error estimates for different types of stationary and time dependent fluid problems (Darcy, Stokes, Navier-Stokes, Second order grade fluid, Convection-diffusion-reaction type problem, coupling problems, ...).

  1. R. Aldbaissy, N. Chalhoub, J. K Djoko and T. Sayah, Full discretization of the time dependent Navier-Stokes equations with anisotropic slip boundary condition coupled with the convection-diffusion-reaction equation, SeMA Journal, https ://doi.org/10.1007/s40324-024-00355-7, (2024).
  2. Nancy Chalhoub, Pascal Omnes, Toni Sayah and Rebecca El Zahlaniyeh, A posteriori error estimate for the non-stationary concentration equation coupled with the Darcy system discretized by the Raviart-Thomas finite element, "Computational and Applied mathematics", 43(170), https ://doi.org/10.1007/s40314-024-02682-x,(2024).
  3. J.K. Djoko, H.H Gidey, J. Koko, and T. Sayah, Discontinuous Galerkin methods for Stokes equations under power law slip boundary condition : a priori analysis, CALCOLO, 61, 13, https ://doi.org/10.1007/s10092-023-00563-z, (2024).
  4. T. Sayah, G. Semaan and F. Triki, A Posteriori error estimates for Darcy-Forchheimer's problem coupled with the convection-diffusion-reaction equation, international journal of numerical analysis and modeling, 21(1), pp. 65-103, doi :10.4208/ijnam2024-1003, (2024).
  5. J. Djoko Kamdem, V.S. Konlack and T. Sayah, Power law slip boundary condition for Navier-Stokes equations : Discontinuous Galerkin schemes, Computational Geosciences, 28, 107-127, https ://doi.org/10.1007/s10596-023-10265-8, (2023)
  6. Toni Sayah, Georges Semaan. Faouzi Triki, A posteriori error estimates for Darcy-Forchheimer's problem, Computational Methods in Applied Mathematics, 23(2), 517-544, https ://doi.org/10.1515/cmam-2022-0047, (2023). 
  7. Ghina Nassreddine, Pascal Omnes, Toni Sayah, A posteriori error estimates for the Large Eddy Simulation applied to incompressible fluids, ESAIM Mathematical Modelling and Numerical Analysis, 57(4), (2023).
  8. Jad Dacroub, Joanna Faddoul, Pascal Omnes, Toni Sayah, A posteriori error estimates for the time dependent Navier-Stokes system coupled with the convection-diffusion-reaction equation, "Advances in Computational Mathematics", 49(67), (2023). 
  9. N. Chalhoub, Rim Al Dbaissy, J. Djoko, and T. Sayah, Full discretisation of the time dependent Navier-Stokes equation with anisotropic slip boundary condition, International Journal of Numerical Analysis and Modeling, 20(4), 497-517, (2023).
  10. J.K. Djoko, J. Koko, M. Mbehou, and T. Sayah, Stokes and Navier Stokes equations under power law slip boundary condition: Numerical Analysis, Computers and Mathematics with Applications, 126, 198-213, https ://doi.org/10.1016/j.camwa.2022.10.016, (2022). 
  11. Bruno Dépres, Maria El Ghaoui and Toni Sayah, A Treftz method with reconstruction of the normal derivative applied to elliptic equations, "Computation of mathematics", 91, 2645-2679, (2022).
  12. Ghina Nassreddine, Pascal Omnes, Toni Sayah, A posteriori error estimates for the Large Eddy Simulation applied to stationary Navier-Stokes equations, "Numerical Methods for Partial Differential Equations", 38, 1468-1498, (2022). (https ://doi.org/10.1002/num.22850).
  13. 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", 89, pp. 1247-1286, (2022).
  14. Rim Aldbaissy, Fréedéric 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, 99(3), pp. 591-606, (2022).
  15. Toni Sayah, Georges Semaan. Fauzi Triki, Finite element methods for the Darcy-Forchheimer problem coupled with the convection-diffusion-reaction problem, 55 (6), pp: 2643-2678, M2AN (2021).
  16. Toni Sayah, A posteriori error estimates for the Brinkman-Darcy-Forchheimer problem, Computational and Applied Mathematics, 40, 256, (2021).
  17. 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).
  18. 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).
  19. 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).
  20. 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).
  21. 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).
  22. 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).
  23. 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).
  24. 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).
  25. 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 flow by the method of characteristics, Numerical Algorithm, 80(2), pp. 447-467, https ://doi.org/10.1007/s11075-018-0492-4, (2018).
  26. 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).
  27. 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).
  28. 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).
  29. 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 Scientific Computing, 71 (1), DOI : 10.1007/s10915-016-0301-y, (2017).
  30. Mireille El Haddad, Frédéric Hecht and Toni Sayah, Interface transport scheme of a two-phase flow by the method of characteristics, International Journal for Numerical Methods in Fluids, DOI :10.1002/d.4280, 28, 6, (2017), pp 513-543.
  31. Christine Bernardi, Jad Dakroub, Gihane Mansour and Toni Sayah, A posteriori analysis of iterative algorithms for Navier-Stokes Problem, ESIAM : Mathematical Modelling and Numerical Analysis, 50 (4), doi :10.1051/m2an/2015062, (2016), pp. 1035-1055.
  32. Toufic El Arwadi and Toni Sayah, An Lp estimate for Dirichlet-to-Neumann operator and application., Electronic Journal of Differential Equations, Vol. 2015, No.258, pp. 1-8, (2015).
  33. 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.
  34. 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.
  35. 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
  36. 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.
  37. 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.
  38. 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.
  39. 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.
  40. 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.
  41. 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.
  42. Hyam Abboud et Toni Sayah, Upwind discretization of a time-dependent two dimensional grade-two fluid model, Computers & Mathematics with applications, 57 (2009), pp. 1249-1264.
  43. 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.
  44. 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.
  45. Toni Sayah et Badih Azar, Effect of Junction on Electromagnetic Waveguide transmission, Mathematica Balkanica, vol. 18, No 3-4 (2004), pp 443-452.
  46. 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.
  47. 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.
  48. Toni Sayah, Boundary conditions for the electromagnetic scattering by thin layers, International journal of applied mathematics, vol. 11, No 2 (2002), pp 121-136.
  49. 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.
  50. Toufic 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 Scientific, Singapore, 2000, pp. 198-205.
  51. 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.