International Student & Scholar Center

EAS Doctoral Dissertation Defense by Benjamin Burnett

Date: Monday, March 24, 2025
Time: 3pm–4:30pm

Topic: Accelerating Implicit Runge-Kutta Methods with Mixed-Precision and Linearization Techniques

Zoom Link:
https://umassd.zoom.us/j/96334992315?pwd=KyrUYjs5KUduhldDk4cMxvJrIX5dAv.1
Meeting ID: 963 3499 2315
Passcode: 155913

Abstract:

Implicit Runge-Kutta (IRK) methods are notoriously expensive to compute, especially in the context of solving nonlinear partial differential equations (PDEs). In this dissertation we explore two main techniques that aim to accelerate solutions to these nonlinear PDEs when using IRK based methods. The first of these is the use of mixed-precision, wherein we use mixed-precision additive Runge-Kutta (MPARK) methods to solve implicit stages in low precision, then correct any errors introduced in high precision. In this portion of the dissertation, we explore implementation strategies for mixed precision computing by solving the Van der Pol equation and Viscous Burgers' Equation using the MPARK methods. The second portion of this dissertation focuses on the use of linearization as an acceleration technique, wherein we linearize the implicit stages using different strategies, including a novel linearization strategy based on a two-point Taylor series expansion. In this portion of the dissertation we focus on exploring the stability and performance of the two-point linearization strategy by solving several problems including the Viscous Burgers' Equation, Heat Equation, and Cahn-Hilliard Equation.

Advisor(s): , Dept of Mathematics

Committee members:
Dr. Zheng Chen, Department of Mathematics
Dr. Alfa Heryudono, Department of Mathematics
Dr. Gaurav Khanna, Department of Physics, University of Rhode Island

Note: All EAS Students are ENCOURAGED to attend.

Join us for the Meet & Mentor Mixer, a networking event that builds connections between successful UMass Dartmouth alumni and hard-working students striving to achieve the extraordinary. Learn from each other’s experiences as Corsairs, past and present, while establishing your professional network.

On Sunday, March 30, 2025, the Claire T. Carney Library Association will welcome former Boston Globe television critic Matthew Gilbert for a talk, followed by a question-and-answer conversation with Gilbert on his insights into the world of television. 

Since 1987, Boston Globe readers enjoyed Gilbert’s features on books, television, movies, and pop culture. When his weekly column focused on television in 1997, he reviewed such popular shows as “Deadwood,” “NYPD: Blue,” “The Sopranos,” “Six Feet Under,” and countless others. As television shifted to cable and streaming services, Gilbert explored outstanding shows that were now able to create deeper, more complex characters, calling “Breaking Bad” the second-best TV series ever. His column curated a viewing list for readers and thoughtfully analyzed the plot lines, characters, and cliffhangers that become discussion topics for many fans. 

Gilbert holds an MA in English literature from the University of New Hampshire where he was the managing editor of the bimonthly arts magazine, Boston Review, from 1981-1986.  He also served as managing editor of a national magazine, The New Age Journal, from 1986-1987 and has contributed articles for Slate, Esquire.com, San Francisco Chronicle, Parade and Bark. His book, Off the Leash:  A Year at the Dog Park, was published by St. Martin's Press in 2014. Gilbert has also interviewed actors, writers, authors, and celebrities including Shirley MacLaine, Meryl Streep, John Travolta, David Foster Wallace, Richard Ford, and Barbara Kingsolver. Gilbert’s column ran in the Boston Globe until 2024. He continues to write, working as a freelancer and developing a second book.
                                                                                                                 
A Q&A and light refreshments will follow his talk. Free parking is available on campus in lot 13.

Register for the event!