High Performance Computing Qualifying Exam Process

The high performance track qualifying exam will cover five subareas:

• Parallel algorithms and computing.
• Numerical linear algebra.
• Differential equations.
• Optimization and nonlinear equations.
• Approximation.

Then, sometime during the period February 11-20, you will need to take an oral exam in front of the committee. In the oral exam, basic knowledge on all five subareas will be tested. Here basic knowledge is limited by the topics covered in the CS3414, CS4234, and CS5465 courses. For your reference, please check the corresponding course webpage and the following textbooks:

• Kahaner, Moler, and Nash, Numerical Methods and Software, Prentice-Hall, 1989.
• Ananth Grama, George Karypis, Vipin Kumar, and Anshul Gupta: "Introduction to Parallel Computing". Addison-Wesley, 2003
• E.W. Cheney and D. Kincaid, Numerical Mathematics and Computing, 6th Ed., Brooks/Cole, 2008.

For more advanced knowledge, you will choose two of the five sub-areas and carefully read the corresponding papers (and related references) listed. You are not expected to teach a short-course on the details of a particular topic. Instead, we want to see how you would begin to explore a particular topic: synthesize a few key papers, pull out the main points, relate them to each other, perhaps follow leads to a few related papers, etc. This exam is supposed to test your ability to do some of the main things you need to do to really get going in a particular research area. That means finding papers not in our library. That means reading papers carefully. That means identifying the main issues and developments in a particular area. That means learning how to pursue other references, if there are a few key ones that fill in some gaps. That means learning to present, in your own words, a particular sub-topic.

Prepare 40-50 minutes of material. Assume we will ask questions. Assume also that we will ask questions to explore limits of your knowledge and skills. We do not expect you to have memorized those papers, of course. We do expect you to have read them carefully and have a good idea of what's in them. It is fine to bring copies of the papers to your presentation — it's a good idea, in fact, since we may want to look at a section of one of them together.

In preparing for this exam, you should do the work yourself. That means not talking to other students. You are certainly welcome to look at any other references that seem useful. And you are welcome to ask any of us questions about the papers too. However, we will only answer specific, narrowly focused questions (e.g., "What does this notation mean?" or "I've stared at this for two hours and I'm pretty sure this is a typo!") We cannot spend a lot of time helping you figure out the paper — that's your job!

Reading List in Subareas

1. Parallel Computing
   • Buttari, A., Langou, J., Kurzak, J., Dongarra, J. A Class of Parallel Tiled Linear Algebra Algorithms for Multicore Architectures, Parallel Computing, 35, pp. 38-53, 2009.
   • Gustafson, J.L., Montry, G.R., and Benner, R.E., Development of parallel methods for a 1024-processor hypercube, SIAM J. Sci. Stat. Comput., 9(4), pp. 609-638, 1988.

2. Numerical Linear Algebra
   • Bowdler, H., Martin, R.S., Reinsch, C., and Wilkinson, J.H., The QR and QL algorithms for symmetric matrices, Numer. Math., 11, pp. 293-306, 1968.
   • aYoucef Saad and Martin Schultz, GMRES: A generalized minimal residual algorithm for solving nunsymmetric linear systems, Siam J. Sci. Stat. Comput. 7(3), 1986.

3. Optimization and Nonlinear Equations
   • Dennis., J.E., and More, J.J., Quasi-Newton methods, motivation and theory, SIAM Review, 19(1), pp. 46-89, 1977.
   • Lewis, R.M., Torczon, V., and Trosset, M.W., Direct search methods: then and now, Journal of Computational and Applied Mathematics, 124, pp. 191-207, 1985.

4. Differential Equations
   • Gupta, G. K., Sacks-Davis, R., and Tischer, P. E., A review of recent developments in solving ODES, ACM Computing Surveys, 17(1), pp. 5-47, 1985.
   • J.C. Butcher, A history of Runge-Kutta methods, Applied Numerical Mathematics 20, pp. 247-260, 1996.

5. Approximation
   • Rene Pinnau, Model Reduction via Proper Orthogonal Decomposition, Model order reduction: Theory, research aspects and applications, Mathematics in Industry, 13(II), pp. 95-109, 2008.
   • Sobieszczanski-Sobieski, J., and Haftka, R.T., Multidisciplinary aerospace design optimization: survey of recent developments, Structural Optimization, 14, pp. 1-23, 1996.

   Examining Committee

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   Yang Cao (Chair), Calvin J. Ribbens. Layne Watson, Adrian Sandu