Computational Science Qualifying Exam

Spring 2025

Committee:  Dr. Adrian Sandu (Chair); Dr. Calvin Ribbens; Dr. Young Cao

Timeline. Submit the written material to Dr. Sandu via email (sandu@cs.vt.edu) by February 1, 2025.

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

Written: The reading list can be found below. For each of the papers 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.

Oral: In February, you will make an oral presentation to the committee on the Marz paper, and a second paper 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, 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.). 

Time stepping:

 

März R. Numerical methods for differential algebraic equations. Acta Numerica. 1992;1:141-198. doi:10.1017/S0962492900002269

https://www.cambridge.org/core/journals/acta-numerica/article/abs/numerical-methods-for-differential-algebraic-equations/34D6ABD3DB21AC621FA9EB9E3290DF66

 

Inverse problems:

 

Dan Givoli,

A tutorial on the adjoint method for inverse problems,

Computer Methods in Applied Mechanics and Engineering,

Volume 380, 2021,113810,

Doi:10.1016/j.cma.2021.113810.

https://www.sciencedirect.com/science/article/pii/S0045782521001468

 

Linear Algebra:

 

Y. Saad: Five Key Concepts That Shaped Iterative Solution Methods for Linear Systems. SIAM News, Volume 57, Issue 02, March 2024

https://www.siam.org/publications/siam-news/articles/five-key-concepts-that-shaped-iterative-solution-methods-for-linear-systems/

(This is a rather short note, that motivates committee-student discussions)

 

Optimization:

 

Sebastian Ruder

An overview of gradient descent optimization algorithms

https://arxiv.org/pdf/1609.04747

 

Scientific Machine Learning:

 

Karniadakis, G.E., Kevrekidis, I.G., Lu, L. et al. Physics-informed machine learning. Nat Rev Phys 3, 422–440 (2021).

https://doi.org/10.1038/s42254-021-00314-5