Computational Science Qualifying Exam

Spring 2019

Committee:  Adrian Sandu (Chair), Alexey Onufriev,  Yang Cao.

The Qualifying Exam has both a written and an oral component.

Written: For each of the papers on the reading list write a short (no more than one page) summary and critique of the paper in your own words. Your writeup should identify the main points or contributions of the paper, as well as the significance of the contributions. Highlight any particularly strong or weak aspects of a paper. Submit this written material to Dr. Sandu via email (sandu@cs.vt.edu) by February 8, 2019.

Oral: In February, you will make an oral presentation to the committee on two papers selected by you from the reading list. Prepare roughly 30 minutes of material. Do not provide a tutorial or short course about the details or minutiae in the papers. Your material should:

• synthesize and evaluate the importance of the main ideas and issues from the papers,
• describe how each topic is evolving (make sure you identify the main issues and developments), and
• provide your opinion on potential avenues of research that should be further explored in this sub-area.

The committee will ask questions throughout the oral exam not only regarding the two papers you chose, but on any of the papers in the list (and potential research directions).

In preparing for this exam, you should do the work yourself and should find and read any other references that seem useful. You may discuss papers in the reading list with other students who are preparing for the exam. However, you are not to work with others in preparing submissions to the exam (e.g., summaries and critiques, the talk, etc.). 

Reading List

 

Numerical analysis

 

M. Hochbruck and A. Osterman. Exponential integrators. Acta Numerica, Volume 19, May 2010, pp. 209-286. doi:10.1017/S0962492910000048.

 

C.T. Kelley. Numerical methods for nonlinear equations. Acta Numerica, Volume 27, 01 May 2018, pp. 207-287. doi:10.1017/S0962492917000113.

 

R. Kannan and S. Vempala. Randomized algorithms in numerical linear algebra. Acta Numerica (2017), pp. 95-135, doi:10.1017/S0962492917000058.

 

Inverse problems and uncertainty quantification

 

R.N. Bannister. A review of operational methods of variational and ensemble-variational data assimilation. Quarterly Journal of the Royal Meteorological Society, 143: 607–633, January 2017 B, doi:10.1002/qj.2982.

 

J.T. Oden. Adaptive multiscale predictive modelling. Acta Numerica, Volume 27, 01 May 2018, pp. 353-450. doi:10.1017/S096249291800003X.