Curriculum Vitae of Samir Karaa
Department of Mathematics and Statistics
Sultan Qaboos University
P. O. Box 36, Al-Khod 123
Muscat, Oman
Tel: (968) 24142314 (Office)
Fax: (968) 24141490 (Dept.)
Fax: (968) 24143415 (College)
E-mail: skaraa@squ.edu.om
Research interests
• Scientific computing, computer simulations.
• Preconditionig techniques.
• High-order, optimal numerical schemes.
Education
• 1996, Ph.D., Paul Sabatier University, France.
• 1993, M.Sc., Paul Sabatier University, France.
• 1992, B.Sc, Faculty of Science of Tunis, Tunisia.
Employment
• June 2009 - present: Associate Professor, Dept. of Mathematics and Statistics, Sultan Qaboos University.
• Sept. 2003 - May 2009: Assistant Professor, Dept. of Mathematics and Statistics, Sultan Qaboos Univ.
• April 2002 - Aug. 2003: Postdoctoral Researcher, Dept. of Computer Science, University of Kentucky
(Kentucky, USA).
• March 2001 - Feb. 2002: Postdoctoral Researcher, Dept. of Computer Science, McGill Univ., Montreal.
• 1998 - 99: Research Scientist, ENSEEIHT-France and TDB-Sweden.
• 1996 - 98: Assistant Professor, Paul Sabatier University, France.
Teaching
• Pre-Calculus MATH1106 (SQU)
• Mathematics for Commerce & Economics MATH1061 (SQU)
• Calculus II, III (SQU, Paul Sabatier University)
• Differential Equations with Maple MIA07 (Paul Sabatier University)
• Mathematics for Business MATH1101 (SQU)
• Introduction to Numerical Methods CS321 (University of Kentucky)
• Numerical Analysis (Paul Sabatier University)
• Linear Algebra I (with Matlab) MATH2202 (SQU)
• Linear Algebra II MATH3303 (SQU)
• Linear Algebra and Multivariate Calculus MATH3171 (SQU)
• Differential Equations and Applications for Engineers MATH4174 (SQU)
• Numerical Differential Equations MATH6012 (SQU)
• Finite Element Methods MATH6108 (SQU)
• BSc projects MATH5500 and MSc projects MATH7000 (SQU)
Publications
1. S. Karaa, Error estimates for finite element approximations of a viscous wave equation. Numer. Funct.
Anal. Optim. 32 (2011), no. 7, pp. 750-767.
2. S. Karaa, Finite Element θ-Schemes for the Acoustic Wave Equation. Adv. Appl. Math. Mech., 3
(2011), pp. 181-203.
3. S. Karaa, Approximate factorization for a viscous wave equation. Computing 89 (2010), no. 3-4, pp.
199-215,
4. S. Karaa, A hybrid Pad ADI scheme of higher-order for convection-diffusion problems. International
Journal for Numerical Methods in Fluids 64 (2010), no. 5, pp. 532548..
5. S. Karaa, Unconditionally stable ADI scheme of higher-order for linear hyperbolic equations. International Journal of Computer Mathematics, 87 (2010), pp. 3030-3038.
6. S. Karaa, Improved accuracy for the approximate factorization of parabolic equations, Computing, Vol
86 (2009), no. 1, pp. 23–36.
7. S. Karaa and M. Othman, A two-level compact implicit schemes for three-dimensional parabolic problems,
Comput. Math. Appl. 58 (2009), no. 2, 257–263.
8. S. Karaa, A high-order ADI method for parabolic problems with variable coefficients, Int. J. Comput.
Math. 86 (2009), no. 1, 109–120.
9. H. Bashir and S. Karaa, Assessment of Clustering Tendency for the Design of Cellular Manufacturing
Systems, Journal of Manufacturing Technology Management, Vol. 19 (2008), no.8. pp. 1004-1014.
10. S. Karaa, High-order difference schemes for 2D elliptic and parabolic problems with mixed derivatives,
Numerical Methods Partial Differential Equations, 23 (2007), no. 2, 366–378.
11. R. K. Mohanty, S. Karaa and U. Arora, An O(k 2 + kh2 + h4 ) arithmetic average discretization for
the solution of 1-D nonlinear parabolic equations. Numerical Methods Partial Differential Equations, 23
(2007), no. 3, 640–651.
12. S. Karaa, An accurate finite difference scheme for 2-D parabolic problems with mixed derivative, Far East
J. Appl. Math. 23 (2006), no. 3, 287–297.
13. U. Arora, S. Karaa and R. K. Mohanty, A new stable variable mesh method for 1-D non-linear parabolic
partial differential equations, Applied Mathematics and Computation, 181 (2006), no. 2, 1423–1430.
14. S. Karaa, High-order approximation of 2D convection-diffusion equation on hexagonal grids, Numerical
Methods Partial Differential Equations, 22 (2006), no. 5, 1238–1246.
15. S. Karaa, On the optimal buckling loads of the clamped columns, The Australian Journal of Mathematical
Analysis and Applications, 3 (2006), no. 1, Article 1, 10 pp.
16. M. Fournie and S. Karaa, Iterative methods and high-order difference schemes for 2D elliptic problems
with mixed derivative, Journal of Applied Mathematics & Computing, 22 (2006), no. 3, 349–363.
17. S. Karaa, A high-order compact ADI method for solving three-dimensional unsteady convection-diffusion
problems, Numerical Methods Partial Differential Equations, 22 (2006), no. 4, 983-993.
18. S. Karaa, Upper bounds for the eigenvalues of differential equations, Journal of Inequalities and Applications, Volume 2006, Art. ID 48606, 1–7.
19. R. K. Mohanty, S. Karaa and U. Arora, A fourth-order nine point unequal mesh discretization for the
solution of 2D nonlinear elliptic partial differential equations, Neural, Parallel & Scientific Computations,
13 (2006), no. 3-4, 411–426.
20. S. Karaa, A class of two-level compact implicit schemes for three-dimensional convection-diffusion problems, Far East J. Appl. Math., 21 (2005), no. 2, 141-155.
21. S. Karaa, An accurate LOD scheme for two-dimensional parabolic problems, Applied Mathematics and
Computation, 170 (2005), no. 2, 886–894.
22. X. W. Chang, M. Gander and S. Karaa, Asymptotic properties of the QR factorization of banded
Hessenberg-Toeplitz matrices, Applied Linear Algebra and its Applications, 12 (2005), no. 7, 659–682.
23. S. Karaa, A limit result concerning the QR factorization of banded Toeplitz matrices, Linear Algebra and
its Applications. 405 (2005), 41–44.
24. S. Karaa and J. Zhang, A numerical study of a 3D bioheat transfer problem with different spatial heating,
Mathematics and Computers in Simulation, 68 (2005), no. 4, 375–388.
25. S. Karaa, Rearrangements of the coefficients of ordinary differential equations. Journal of Inequalities in
Pure and Applied Mathematics, 5 (2004), no. 4, Article 90, 12 pp.
26. S. Karaa and J, Zhang, High-order ADI method for solving unsteady convection-diffusion problems,
Journal of Computational Physics, 198 (2004), no. 1, 1–9.
27. S. Karaa, J, Zhang and C. C. Douglas, Preconditioned multigrid solution of an axisymmetric laminar
diffusion flame, Mathematical and Computer Modelling, 38 (2003), no. 3-4, 269–279.
28. S. Karaa, Properties of the first eigenfunctions of the clamped column equation, Theoretical and Applied
Mechanics, 30 (2003), no. 4, 265-276.
29. S. Karaa and J. Zhang, Analysis of stationary iterative methods for discrete convection-diffusion equation
with a high-order compact scheme. Journal of Computational and Applied Mathematics, 154 (2003), no.
2, 447–476.
30. S. Karaa and J. Zhang, Convergence and performance of iterative methods for solving variable coefficient
convection-diffusion equation with a fourth-order compact difference scheme, Computers & Mathematics
with Applications. 44 (2002), no. 3-4, 457–479.
31. S. Karaa and J. Zhang, A note on convergence of line iterative methods for a nine-point matrix, Applied
Mathematics Letters, 15 (2002), no. 4, 495–503.
32. S. Karaa, A block circulant preconditioner for the convection-diffusion equation, Comptes Rendus de
l’Académie des Sciences. Paris. Series I - Mathematics, 330 (2000), no. 9, 851–856.
33. S. Karaa, Inequalities for eigenvalue functionals, Journal of Inequalities and Applications 4 (1999), no.
2, 175–181.
34. S. Karaa, Sharp estimates for the eigenvalues of some differential equations, SIAM Journal on Mathematical Analysis, 29 (1998), no. 5, 1279–1300.
35. S. Karaa, Extremal eigenvalue gaps for the Schrödinger operator with Dirichlet boundary conditions,
Journal of Mathematical Physics, 39 (1998), no. 4, 2325–2332.
36. S. Karaa, Isoperimetric upper bounds for the eigenvalues of the Sturm-Liouville type, Comptes Rendus
de l’Académie des Sciences. Paris. Series I - Mathematics, 325 (1997), no. 8, 835–840.
37. S. Karaa and Y. Egorov, Sur la forme optimale d’une colonne en compression, Comptes Rendus de
l’Académie des Sciences. Paris. Series I - Mathematics, 322 (1996), no. 6, 519–524.
38. S. Karaa, Extremal eigenvalues and their associated nonlinear equations, Boll. Un. Mat. Ital. B (7) 10
(1996), no. 3, 625–649.
39. S. Karaa, Valeurs propres extrémales dans des problèmes de Sturm-Liouville, Comptes Rendus de l’Académie
des Sciences. Paris. Series I - Mathematics, 321 (1995), no. 3, 265–270.
40. S. Karaa, Y. Egorov, Optimisation de la première valeur propre de l’opérateur de Sturm-Liouville,
Comptes Rendus de l’Académie des Sciences. Paris. Series I - Mathematics, 319 (1994), no. 8, 793–
798.