EAS Doctoral Dissertation Defense by Benjamin Burnett
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): Dr. Sigal Gottlieb, 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.
Zoom
https://umassd.zoom.us/j/96334992315?pwd=KyrUYjs5KUduhldDk4cMxvJrIX5dAv.1