Dr. Hafiz Abdul Wajid
Assistant Professor, Mathematics
Area of Interest: Computational Wave Propagation
Tel # (Off): 111-001-007  
On Leave

Area of my interest or research is developing schemes for computational wave propagation which are less dispersive and dissipative. Primarily, I study dispersive and dissipative properties of low and high order schemes in detail for acoustics and electromagnetic wave propagations. My interests are two fold providing qualitative description of the nature of the dispersive and dissipative behavior of the schemes along with precise quantitative statements of the accuracy in terms of the mesh size, the order of the scheme and the wave number which serves as an a priori for practical problems. I also work in the development of novel non-standard quadrature rules for the practical implementation numerical schemes for wave propagation problems.


Following are few achievemetns I have earned so far:



  • Won Merit scholarships throughout BSc (Honors) and MSc (Honors) degrees from University of the Punjab, Lahore, Pakistan;
  • Won Merit scholarship for MS leading to PhD in the field of Mathematics at University of Strathclyde, UK from Government of Pakistan through COMSATS Institute of Information Technology, Pakistan under human resource development component;
  • Won the (UKIE SIAM) sponsored best student presentation prize 2009 presented at 24th Biennial Conference 23-26th 2009 held at University of Strathclyde, UK;
  • Higher Education Commission, Pakistan’s approved supervisor for Graduate programs;
  • Member of the Board of Editors for an international journal of Applications and Applied Mathematics (AAM).

MS Research Supervisions

Sobia Ayub, Optimally Blended Spectral-Finite Element Scheme For Maxwell’s Equation, 2011, COMSATS, Completed;

Hifza Iqbal, Optimal finite difference schemes for wave equation, 2012, COMSATS, Completed;

M. Sarmad Arshad, Dispersion free finite difference scheme for Time Harmonic Wave Equation, 2012, COMSATS, Completed;

Mumtaz Ahmed, Corrected finite difference schemes for high frequencies, 2013, COMSATS, Completed;

Arsalan Ali Hamid, Compact finite difference methods for free vibration analysis of Euler-Bernoulli beams, 2013, Completed.



Book Chapters:
1. Ainsworth and H. A. Wajid (2009), "Explicit Discrete Dispersion Relations for the Acoustic Wave Equation in d-Dimensions Using Finite Element, Spectral Element and Optimally Blended Schemes", Computer Methods in Mechanics: Lectures of the CMM 2009 (Advanced Structured Materials)  Abstract  (External URL)
Journal Papers:
2. Muhammad Abid, Hafiz Abdul Wajid, Naeem Dad Khan, Saddam Akhtar, Mirza Ahsan Zahid and Muhammad Usman (2013), "Optimization of Ventilation System For existing Environmentally Controlled poultry Sheds in Pakistan", World Applied Sciences Journal, pp: 1221-1233, Vol: 24, Issue: 9, Standard: 1818-4952   
3. M. Abid, S. Maqsood and H. A. Wajid (2012), "‘Comparative Modal Analysis of Gasketed and Nongasketed Bolted Flanged Pipe Joints: FEA Approach’", Advances in Mechanical Engineering, pp: 1-8, Vol: 2012   
4. H. A. Wajid and Sobia Ayub (2012), "AN OPTIMALLY BLENDED FINITE-SPECTRAL ELEMENT SCHEME WITH MINIMAL DISPERSION FOR MAXWELL EQUATIONS", Journal of Computational Physics, pp: 8176-8187, Vol: 231, Issue: 24, Impact Factor: 2.3   
5. H. A. Wajid, Hifza Iqbal, M. Sarmad Arshad (2012), "Modified finite difference schemes on uniform grids for simulations of the Helmholtz equation at any wave number", Submitted    
6. Muhammad Abid, Adnan Aslam Noon, H. A. Wajid (2011), "Turbulent flow simulations through Tarbela Dam Tunnel 3", IIUM Engineering Journal, Vol: 11, Issue: 02   
7. M. Ainsworth and H. A. Wajid (2010), "Optimally blended spectral-finite element scheme for wave propagation, and non-standard reduced integration", SINUM (SIAM Journal on Numerical Analysis), pp: 346-371, Vol: 48, Issue: 01  Abstract  (External URL)
8. M. Ainsworth and H. A. Wajid (2009), "Dispersive and dissipative behavior of the Spectral Element Method", SINUM (SIAM Journal on Numerical Analysis), pp: 3910-3937, Vol: 47, Issue: 05  Abstract  (External URL)
Conference Papers:
1. H. A. Wajid, Hifza Iqbal, M. Sarmad Arshad (2011) "Dispersion free finite difference schemes for wave propagation", 2nd International Symposium on Frontiers of Computational Sciences (ISFCS)   
2. M. Ainsworth and H. A. Wajid (2009) "Optimally Blended Spectral-Finite Element Scheme for Wave Propagation, and Non-Standard Reduced Integration", CMM-2009, Computer Methods in Mechanics   


PhD in Mathematics
University of Strathclyde, United Kingdom
Dec 2006 to Nov 2009
MSc (Honors) in Mathematics
University of the Punjab, Lahore, Pakistan
2004 to 2006
BSc (Honors) in Mathematics with Computer Applications
University of the Punjab, Pakistan
2000 to 2004


Assistant Professor
COMSATS Institute of Information Technology, Lahore
Dec 2009 to Date
COMSATS Institute of Information Technology, Lahore
Aug 2006 to Dec 2009

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