Faisal Abdulkareem Fairag Department of Mathematical Sciences
King Fahd University of Petroleum & Minerals
Dhahran, 31261
Saudi Arabia
Tel : (9663) 8604463 , (9663) 8602193
Fax: (9663) 8602340
email: ffairag@kfupm.edu.sa
EDUCATION 




1998 
Ph.D. in Mathematics, University of Pittsburgh, Pittsburgh, PA, USA. Title Ph.D. Disertation: A Twolevel Discretization Method for the Streamfunction Form of the NavierStokes Equations. 


1994 
MA in Mathematics, University of Pittsburgh, Pittsburgh, PA, USA. 


1989 
Ms. in Mathematics, King Fahd University of Petroleum and Minerals, Dhahran, Saudi Arabia. 


1987 
B.S. in Mathematics, King Fahd University of Petroleum and Minerals, Dhahran, Saudi Arabia. 

POSITION 




2001Present 
Prepatory Year Mathematics Coordinator, King Fahd University of Petroleum and Minerals, Dhahran, Saudi Arabia. 


1998Present 
Assistant Professor of Mathematics, King Fahd University of Petroleum and Minerals, Dhahran, Saudi Arabia. 


19891998 
Lecturer of Mathematics, King Fahd University of Petroleum and Minerals, Dhahran, Saudi Arabia. 


19871989 
Graduate Assistant of Mathematics, King Fahd University of Petroleum and Minerals, Dhahran, Saudi Arabia. 
SUMMARY OF CURRENT FIELDS OF INTEREST 



Current fields of interest include: multilevel finite element methods and a finite difference discretization methods for a fourth order partial differential equation. Multilevel finite element method of the streamfunction form of the NavierStokes equations, Large Eddy Simulation, global and local adaptive mesh refinement method, parallel iterative solution methods. 

PAPERS PUBLISHED AND IN PREPARATION 



[1] F. Fairag, A Twolevel Finite Element Discretization for the steam function form of the NavierStokes equations., Comput. Math. Appl. 36(2), 117127, (1998). 


[2] F. Fairag, A posteriori error estimator of a TwoLevel Finite Element Method for stream function form of the NavierStokes equations. 


[3] F. Fairag, On the Order of a Conforming and a Nonconforming Finite Element Approximations for the NavierStokes equations. 


[4] F. Fairag, Numerical Results on the TwoLevel Finite Element Method of the NavierStokes equations. 


[5] F. Fairag, Two level finite element technique for pressure recovery from stream function formulation of the NavierStokes equations. Multiscale and multiresolution methods, 297306, Lect. Notes Comput. Sci. Eng., 20, Springer, Berlin, (2002). 


[6] F. Fairag, Numerical Computations of Viscous, Incompressible Flow Problems Using a TwoLevel Finite Element Method, SIAM Journal on Scientific Computing. 24(6), 19191929, (2003) 


[7] ElGebily, M.A., F. Fairag, and R.S. Alassar, Existence and Uniqueness of Solutions for the Stream Function Vorticity Formulation of the NavierStokes Equations with Nonhomogeneous Boundary Conditions. To appear. 

INTERNAL REPORTS 



[1] F. Fairag, A MultiLevel Finite Difference Method for Semilinear Elliptic Problem. Spring 19931994. 

CONFERENCES, SHORTCOURSES AND WORKSHOPS ATTENDED 



§ SIAM Student Conference and Annual Meeting of Southeastern Atlantic Section, Clemson University, South Carolina, USA, March 2830, 1996. 


§ International Workshop on Theoretical and Numerical Fluid Mechanics, The Field Institute and the University of British Columbia Institute for Applied Mathematics, Vancouver, British Columbia, Canada, July 29 – August 2, 1996. 


§ SIAM Annual Meeting, Charlotte, North Carolina, USA, October 2326, 1995. 


§ An Introduction Short Course on the Mathematical Theory of the NavierStokes Equations, The Field Institute and the University of British Columbia Institute for Applied Mathematics, by Professor Galdi, Vancouver, British Columbia, Canada, July 27 – July 28, 1996. 


§ Short Course on Computational Methods for the NavierStokes Equations, The Field Institute and the University of British Columbia Institute for Applied Mathematics, by Professor Rannacher, Vancouver, British Columbia, Canada, July 27 – July 28, 1996. 


§ Engineering Problems: Mathematical Formulation, Analysis, and Computational Treatment, Department of Mathematics, University of Maryland, College Park, March 2124, 1996. 


§ Problems in Applied Mathematics, Carnige Mellon University, Pittsburgh, PA, USA, 1995. 


§ Supercomputing Techniques: Parallel Processing on CRAY C90/T3D SYSTEMS, Pittsburgh Supercomputing Center, Pittsburgh, PA, USA. July 2831, 1995. 


§ Applied Mathematics and its Applications, University of Pittsburgh , Pittsburgh, PA, USA, 1994. 


§ Mathematical Modeling of Fluid Flow in SuperK Reservoirs, Saudi ARAMCO, Dhahran, Saudi Arabia, September 1214, 1998. 


§ Saudi High School Curriculum in Mathematics, Saudi Association for Mathematical Sciences, Ryiadh, Saudi Arabia, March, 1999. 


§ Workshop in Linear Algebra & Applications, King Fahd University of Petroluem and Minearals, Dhahran, Saudi Arabia, November 1999. 


§ The fifth conference of Saudi Association for Mathematical Sciences, King Saud University, Riyadh, Saudi Arabia, April 2000 


§ Advanced Multiscale and Multiresolution Methods, Yoesemite Educational Symposium, Yosemite National Park, October 29 November 1, 2000. 


§ The First Saudi Science Conference, New Trends for the Colleges of Sciences in Saudi Arabia, Creative Educational and Industrial Research, KFUPM, Dhahran, Saudi Arabia, 911 April 2001. 


§ The First Summer Program for Gifted Students, King Fahd University of Petroluem and Minearals, Dhahran, Saudi Arabia, summer 2001. 


§ Lecture series on Symmetry Methods for Differential Equations by Fazal Mahammed, Math Dept. KFUPM, Dhahran, Saudi Arabia, April 2002. 


§ The Sixth Metting of Saudi Associations for Mathematical Sciences, King Saud University, Riyadh, Saudi Arabia, 9 10 April, 2002. 


§ Wokshop on the Role of the Departmental Chairperson in Sustaining and Improving the Quality of Teaching, KFUPM, Dhahran, Saudi Arabia, 16 April, 2002. 


§ Workshop on career Oasis, KFUPM, Dhahran, Saudi Arabia, 17 April, 2002. 


§ Workshop on Striving for Excellence in University Teaching and Learning III, KFUPM, Dahran, Saudi Arabia, April 2002. 


§ Workshop on Introduction to WebCT, KFUPM, Dhahran, Saudi Arabia, May 2002. 


§ Workshop on How to be an Effective University Teacher, KFUPM, Dhahran, Saudi Arabia, Sept 78, 2002. 


§ Workshop on Online Learning and Teaching, UNESCO and American University, Sharja, UAE, March 913, 2003. 


§ The Third Gifted Students Summer Program, King Fahd University of Petroluem and Minearals, Dhahran, Saudi Arabia, summer 2003 


§ Workshop on Teaching Methods for Female Mathematics Teachers in High School, 30 August 4 Sept, 2003 


§ Workshop on Teaching Methods for Male Mathematics Teachers in High School, 6 10 Sept, 2003 

PARTICIPATION IN CONFERENCES, WORKSHOPS, SHORTCOURSES AS AN ORGANIZER 



§ Participated in the Financial & Registration Comm. to organize the First Saudi Science Conference, New Trends for the Colleges of Sciences in Saudi Arabia, Creative Educational and Industrial Research, KFUPM, Dhahran, Saudi Arabia, 911 April 2001. 


§ Participate in Summer Program for Gifted Students as advisor, lecturer, and organizer, King Fahd University of Petroluem and Minearals, Dhahran, Saudi Arabia, summer 2001. 


§ Participated in the committee to organize the Industrial Math Workshop, KFUPM, Dhahran, Saudi Arabia, 2002 


§ President of the Gifted Students Summer Program, King Fahd University of Petroluem and Minearals, Dhahran, Saudi Arabia, summer 2003 

COURSE WORK 



· Numerical Linear Algebra 


· Numerical Solutions of ODE 


· Numerical Solutions of PDE 


· Finite Element Method 


· Computational Fluid Dynamics 


· Functions of Several Variables 


· Complex Analysis 


· Harmonic Analysis 


· Matrices Analysis 


· Computational Approximation Theory 


· Ordinary Differential Equations 


· Matrix Iterative Analysis 

MSC SUPERVISOR 



2001 Student Name: N. AlMulla, Deg: Msc.Thesis Title:FEM for Linearized NSE Using Argyres Elememts. 

SERVICES DEPARTMENTAND UNIVERSITY 



§ Member in Computer Utilization Committee(University) (1998current) 

§ Member in Computer Aided Learning Committee )(1998) 

§ Member in Contact with Industries comm (1998) 

§ Member in Evaluating the Proposed BS Program (1998) 

§ Member in Chair the Computer Utilization Committee (Department) (1999) 

§ Member in The Planning and Advisory Committee, Math Dept (1999current). 

§ Member in Increas Number of Students Comm (19992000) 

§ Member in Math Learning Center Comm (19992000) 

§ Member in Math ComputerAided Learning Lab at the Prep. Year (19992000) 

§ Member in Financial & Registration Comm for the First Saudi Science Conference (19992000) 

§ Member in Math Exam In RAM II Comm (1999current) 

§ Member in Planning Comm. (Math Department) (19992000) 

§ Member in Prepare Department Booklet & Brochure for the BS Prog. Comm (20002001). 

§ Member in Evaluate Graduate Assistanship Application Forms (20002001) 

§ Member in Faculty Affairs Comm (2000 20001) 

§ Member in Faculty Affairs subcomm. To review faculty evaluation (20002001). 

§ Member in Computer Alowance for Saudi Faculty Comm (2000current) 

§ Member in Study the Math ChairmanPrep Year Coordinator relationship (administrative and academic ) comm (20002001). 

§ Member in Current Staff Affairs Comm (2001current) 

§ Member in Plan Comm. For Math PYP Prog (2001current). 

§ Member in Curriculum development Comm (2001current) 

§ Memebr in Adhoc Comm. on selection of MATH 260 textbook (2001) 

§ Member in Adhoc Comm. to design a graduate course in Numerical Linear Algebra (2002). 

§ Memebr in Comm. to review the Prep Year Prog (2002) 

§ Member in College Council Meetings Comm (2002current) 

§ Member in Adhoc Comm at the selective of MATH 321 textbook (2002). 

§ Member in Adhoc Comm. on Smart Classrooms in the College of Sciences (2002) 

§ Member in The subcomm. on TOEFL Scores for Waiver of English 001 & 002 (2002) 

PRESENTATIONS 



§ Numerical Solutions of Nonlinear Equations, Fall 1991. 


§ TwoLevel Method for A Finite Difference Scheme, Spring 9394. 


§ Streamfunction Formulation of the NavierStokes Equations, Spring 9495. 


§ TwoLevel Method for the VelocityPressure Formulation of the NavierStokes Equations, Spring 9596. 


§ A numerical solver for the NavierStokes equatios using a twolevel method, Spring 98. 


§ Pressure recovery from stram function form of the incompressible fluids, Fall 2000 


§ Challenged problems in mathematics, Summer 2001. 


§ Shortcourse in MATHEMATICA, Summer 2001. 


§ Useful mathematics websites on the Internet. Fall 2002, Fall 2003. 


§ How to enjoy mathematics, Summer 2003 

PROFESSIONAL ASSOCIATION 



n AMS: American Mathematical Society 


n SIAM: Society for Industrial and Applied Mathematics 


n SAMS: Saudi Association for Mathematical Sciences. 

INTERNET NEWSGROUP AND LISTSERVE 



· sci.physics.computational.fluid.dynamics 


· sci.math.numanalysis 


· sci.math.research 


· sci.math.symbolic 


· sci.math 


· MGNET.Digest 


· NA Digest 


· MATLAB Digest 

THESIS/DISSERTATION ABSTRACTS 



§ Title Ph.D. Dissertation A TwoLevel Discretization Method for the Streamfunction Form of the NavierStokes Equations. Abstract: We analyze a twolevel finite element method for the streamfunction formulation of the NavierStokes equations. This report presents the twolevel algorithm and a priori error analysis for the case of conforming elements. The streamfunction formulation in two dimensions has the great advantages that one solves for only a single scalar variable rather than a coupled system. Further, the incompressible constraint is automatically satisfied so there are no compatibility conditions between velocity and pressure spaces. The disadvantage is that the linear system, though small, arises from a fourth order problem so it can be very ill conditioned. The nonlinear system is also, at higher Reynolds numbers, very sensitive to small perturbations. The twolevel algorithm consists of solving a small nonlinear system on the coarse mesh, then solving a large linear system on the fine mesh. The basic results states that the error between the coarse and fine meshes is related superlinearly.
FORTRAN programs for this algorithm and a complete discussion of these programs are included. These programs are used to solve the NavierStokes equations with a known solution in a rectangular domain for a range of Reynolds numbers to compare one level vs. two level methods in terms of computer time. Also, we solve the driven flow in a square cavity. These flows have been widely used as test cases for validating incompressible fluid dynamics algorithms. Streamfunction contours are displayed showing the main features of the flow.
A posteriori error estimator for the twolevel algorithm is derived which can be used as an indicator for an assessment of the reliability of the results. 


§ Title M.Sc. Thesis: Spectral Characterization of Trees. Abstract: We study the spectral characterizations of trees. The largest and second largest eigenvalues of trees with three ends are obtained. Upper and lower bound estimates of the eigenvalues for these types of trees also obtained. 

WORK EXPERINCES 



§ May 1987 May 1989: Graduate Assistant, Department of Mathematics and Statistics, King Fahd University of Petroleum and Minerals, Duties involved teaching, designing, and grading an undergraduate class in precalculus course. 


§ May 1989 May 1993: Lecturer, Department of Mathematics and Statistics, King Fahd University of Petroleum and Minerals, Duties involved teaching, designing, and grading an undergraduate class in precalculus course. 


§ May 1993 May 1998: Lecturer, Department of Mathematics and Statistics, King Fahd University of Petroleum and Minerals, Duties involved studying Ph.D. program in University of Pittsburgh, Pittsburgh, PA, USA,. 


§ May 1998 present: Assistant Professor, Department of Mathematics and Statistics, King Fahd University of Petroleum and Minerals, Duties involved teaching, designing, and grading an undergraduate class in Numerical Analysis, Linear Algebra, Differential Equations and precalculus course. § September 2001 – January 2001:PrepYear Mathematics Program Associate Coordinator, King Fahd University of Petroulem and Minerals, Saudi Arabia. 


§ January 2001 – September 2003:PrepYear Mathematics Program Coordinator, King Fahd University of Petroulem and Minerals, Saudi Arabia. 

COMPUTER SKILLS 




§ OS 
UNIX(Sun workstation), VAX/VMS, Windows3.11, windows98, WindowsNT, Mac OS, Linux. 


§ LANGUAGES 
FORTRAN 77, FORTRAN 90, C, MATLAB Programming, QBASIC. 


§ PACKAGES 
MS Office, LaTeX, TeX. 


§ MATH PACKAGES 
Mathematica, MATLAB, PDE Toolbox, Maple, MathCad, IMSL, Linpak, Numerical Recipe. 
