Zachary J. Grant of University of Massachusetts, Dartmouth received the 2017 SIAM Student Paper Prize
and presented his winning paper at the SIAM Annual Meeting
, held July 10-14, 2017 in Pittsburgh, Pennsylvania. SIAM recognized Grant for the paper, “Explicit Strong Stability Preserving Multistage Two-Derivative Time-Stepping Schemes,” co-authored with Andrew Christlieb of Michigan State University, Sigal Gottlieb of the University of Massachusetts, Dartmouth, and David C. Seal of the United States Naval Academy. The paper was published in Journal of Scientific Computing
The SIAM Student Paper Prize is awarded annually to the student authors of the most outstanding papers nominated for the prize. The 2017 Student Paper Prize recognized outstanding scholarship by students in applied mathematics and computing as evidenced in a paper submitted for publication in a peer-reviewed journal. The awards are based solely on the merit and content of the student’s contribution to the paper. Up to three awards are given each year.
Zachary J. Grant is a PhD candidate expecting to receive his PhD in May 2018 in engineering and applied science at the University of Massachusetts, Dartmouth, where he earned a BS in 2012 in computational mathematics. His doctoral research, under the supervision of Sigal Gottlieb, is on the topic of strong stability preserving time integrators.
Q: Why are you excited about winning the prize?
A: I am very honored to win this prize. It is particularly meaningful to me that this prize was awarded at the 2017 SIAM Annual Meeting in Pittsburgh because the very first SIAM Annual Meeting I attended and spoke at was the 2010 meeting in Pittsburgh. Coming back to the same meeting in the same city seven years later and winning a prize that was awarded at the Prizes and Awards Luncheon brought back memories of attending the luncheon in 2010 as an undergraduate and watching awards I could then only imagine winning.
Q: Could you tell us a bit about the research that won you the prize and what it means for the public?
A: Strong stability preserving methods are useful for the time evolution of hyperbolic partial differential equations (PDEs), particularly those with solutions that have sharp gradients or shocks. These types of PDEs are used to model many physical phenomena. The class of strong stability preserving methods has been widely studied for Runge-Kutta methods and multistep methods. Recently, multiderivative methods have been used for hyperbolic PDEs, and the question of their SSP properties became relevant. In this work, we described the conditions under which two derivative Runge-Kutta methods are strong stability preserving, and we defined an optimization problem that we proceeded to code and find optimal SSP multi-derivative methods. These methods can now be used for a wide variety of hyperbolic PDEs that require SSP time evolution and benefit from two-derivative methods.
The future impact of the paper is dependent on whether multi-derivative methods will catch on — the two-derivative methods look like efficient alternatives to current one-derivative methods, especially on systems where the Jacobian matrix is already computed. If these methods prove useful to many practitioners in hyperbolic PDEs, their strong stability preserving properties will generate interest, and this paper — which presents a complete theory with closed-form methods of up to order five — may become useful to this field.
Q: What does being a SIAM member mean to you?
A: Being part of SIAM has been very important for my development as a computational mathematician. SIAM has been responsible for some of the best experiences of my career: student chapter funding that allowed us to have seminars and events, SIAM conferences that I attended, and of course the SIAM journals and books.
I have been a SIAM member for seven years! I joined SIAM as an undergraduate when we started a student chapter at University of Massachusetts, Dartmouth in 2010. I served our SIAM chapter as vice-president, president, and treasurer, and am still involved in the chapter's activities, hoping to bring the experiences I benefited from to other students.
I was fortunate to have several opportunities to speak at SIAM conferences about my undergraduate and graduate research, which has helped me improve my public speaking and gain confidence in my presentations. I always come back from a SIAM conference feeling that I learned so much, that there is so much more to learn, and that I have more enthusiasm -- and lots of new ideas -- for my research.