EAPSI: A New Class of Parallel High-Order Time Integrators

Buvoli Tommaso, Seattle WA

Investigators

Abstract

Partial differential equations are ideal for developing accurate mathematical descriptions for many physical phenomena. In the last century, the study of partial differential equations has grown into an interdisciplinary venture spanning across the fields of mathematics, computation, physics, biology, economics and more. This project seeks to develop new computational methods for solving time-dependent partial differential equations. This research will be conducted at the University of Auckland under the mentorship of Dr. John Butcher, a noted expert on time-integration schemes. These new methods will advance the state of computational science, allowing for more accurate physical models that use fewer resources. General linear methods are powerful extensions of classical time-integration techniques as they allow for multistep, multistage methods. When implemented with adaptive step and order changing strategies, general linear methods consistently outperform competing Runge-Kutta and linear multistep schemes. This grant will fund research to develop an adaptive time-stepping code for a new class of high-order time-integrators which can expressed as general linear methods. These new schemes are designed to leverage existing parallel computer architectures, and will incorporate novel adaptive step and order changing strategies. This award under the East Asia and Pacific Summer Institutes program supports summer research by a U.S. graduate student and is jointly funded by NSF and the Royal Society of New Zealand.