Faisal Abdulkareem Fairag               Department of Mathematical  Sciences

                                                                                                King Fahd University of Petroleum & Minerals

                                                                                                Dhahran, 31261

                                                                                                Saudi Arabia

                                                                                                Tel : (9663) 860-4463  ,  (9663) 860-2193

                                                                                                Fax: (9663) 860-2340

                                                                                                e-mail: ffairag@kfupm.edu.sa

                                                                                                www: http://www.kfupm.eud.sa/~ffairag

 

 

EDUCATION

 

 

 

1998

Ph.D. in Mathematics, University of Pittsburgh, Pittsburgh, PA, USA. Title Ph.D. Disertation: A Two-level Discretization Method for the Streamfunction Form of the Navier-Stokes 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

 

 

 

2001-Present

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

 

1998-Present

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

 

1989-1998

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

 

1987-1989

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: multi-level finite element methods and a finite difference discretization methods for a fourth order partial differential equation. Multi-level finite element method of the streamfunction form of the Navier-Stokes equations, Large Eddy Simulation, global and local adaptive mesh refinement method, parallel iterative solution methods.

 

 

PAPERS PUBLISHED AND IN PREPARATION

 

 

[1] F. Fairag,  A Two-level Finite Element Discretization  for the steam function form of the Navier-Stokes equations., Comput. Math. Appl. 36(2), 117-127, (1998).

 

[2] F. Fairag, A posteriori error estimator of a Two-Level Finite Element Method for stream function form of the Navier-Stokes equations.

 

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

 

[4] F. Fairag,  Numerical Results on the Two-Level Finite Element Method of  the Navier-Stokes equations.

 

[5] F. Fairag, Two level finite element technique for pressure recovery from stream function formulation of the Navier-Stokes equations. Multiscale and multiresolution methods, 297--306, Lect. Notes Comput. Sci. Eng., 20, Springer, Berlin, (2002).

 

[6] F. Fairag,  Numerical Computations of Viscous, Incompressible Flow Problems Using a Two-Level Finite Element Method, SIAM Journal on Scientific Computing. 24(6), 1919-1929, (2003)

 

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

 

 

INTERNAL REPORTS

 

 

[1] F. Fairag, A Multi-Level Finite Difference Method for Semilinear Elliptic Problem. Spring 1993-1994.

 

 

CONFERENCES, SHORTCOURSES AND WORKSHOPS ATTENDED

 

 

§  SIAM Student Conference and Annual Meeting of Southeastern Atlantic Section, Clemson University, South Carolina, USA, March 28-30, 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 23-26, 1995.

 

§  An Introduction Short Course on the Mathematical Theory of the Navier-Stokes 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  Navier-Stokes 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 21-24, 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 28-31, 1995.

 

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

 

§  Mathematical Modeling of Fluid Flow in Super-K Reservoirs, Saudi ARAMCO, Dhahran, Saudi Arabia, September 12-14, 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, 9-11 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 7-8, 2002.

 

§  Workshop on Online Learning and Teaching, UNESCO and American University, Sharja, UAE, March 9-13, 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, 9-11 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. Al-Mulla, Deg: Msc.Thesis Title:FEM for Linearized NSE Using Argyres Elememts.

 

 

SERVICES DEPARTMENT

AND UNIVERSITY

 

 

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

§     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 (1999-current).

§     Member in Increas Number of Students Comm (1999-2000)

§     Member in Math Learning Center Comm (1999-2000)

§     Member in Math Computer-Aided Learning Lab at the Prep. Year (1999-2000)

§     Member in Financial & Registration Comm for the First Saudi Science Conference (1999-2000)

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

§     Member in Planning Comm. (Math Department) (1999-2000)

§     Member in Prepare Department Booklet & Brochure for the BS Prog. Comm (2000-2001).

§     Member in Evaluate Graduate Assistanship Application Forms (2000-2001)

§     Member in Faculty Affairs Comm (2000- 20001)

§     Member in Faculty Affairs sub-comm. To review faculty evaluation (2000-2001).

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

§     Member in Study the Math Chairman-Prep Year Coordinator relationship (administrative and academic ) comm (2000-2001).

§     Member in Current Staff Affairs Comm (2001-current)

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

§     Member in Curriculum development Comm (2001-current)

§     Memebr in Ad-hoc Comm. on selection of MATH 260 textbook (2001)

§     Member in Ad-hoc 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 (2002-current)

§     Member in Ad-hoc Comm at the selective of MATH 321 textbook (2002).

§     Member in Ad-hoc Comm. on Smart Classrooms in the College of Sciences (2002)

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

 

 

 

 

 

PRESENTATIONS

 

 

§  Numerical Solutions of Nonlinear Equations, Fall 1991.

 

§  Two-Level Method for A Finite Difference Scheme, Spring 93-94.

 

§  Streamfunction Formulation of the Navier-Stokes Equations, Spring 94-95.

 

§  Two-Level Method for the Velocity-Pressure Formulation of the Navier-Stokes Equations, Spring 95-96.

 

§  A numerical solver for the Navier-Stokes equatios using a two-level 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.num-analysis

 

·    sci.math.research

 

·    sci.math.symbolic

 

·    sci.math

 

·    MGNET.Digest

 

·    NA Digest

 

·    MATLAB Digest

 

 

THESIS/DISSERTATION ABSTRACTS

 

 

§   Title Ph.D. Dissertation A Two-Level Discretization Method for the Streamfunction Form of the Navier-Stokes Equations. Abstract: We analyze a two-level finite element method for the streamfunction formulation of the Navier-Stokes equations. This report presents the two-level 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 two-level 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 Navier-Stokes 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 two-level 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:Prep-Year Mathematics Program Associate Coordinator, King Fahd University of Petroulem and Minerals, Saudi Arabia.

 

§  January 2001 – September 2003:Prep-Year 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.