Speaker: Prof. Yulong Xing（邢雨龙教授）

Time: 10:00-11:00, 16 May 2024 (Thursday) (Beijing time)

Venue: 华信书院，CC126

Tencent meeting ID: 219-135-089

Abstract

In the common practice of the method-of-lines (MOL) approach for discretizing a time-dependent partial differential equation (PDE), one first applies spatial discretization to convert the PDE into an ordinary differential equation system. Subsequently, a time integrator is used to discretize the time variable. When a multi- stage Runge-Kutta (RK) method is used for time integration, by default, the same spatial operator is used at all RK stages. However, recent studies on perturbed RK methods indicate that not all RK stages are born equal – breaking the MOL structure and applying rough approximations at specific RK stages may not affect the overall accuracy of the numerical scheme. In this talk, we present two of our recent explorations on blending rough stage operators in RK discontinuous Galerkin (DG) methods for solving hyperbolic conservation laws. In our first work, we mix the DG operator with the local derivative operator, yielding an RKDG method featuring compact stencils and simple boundary treatment. In our second work, we mix the DG operators with polynomials of degrees k and k-1, and the resulting method may allow larger time step sizes and fewer floating- point operations per time step.

About Prof. Xing

Dr. Yulong Xing is a professor in the Department of Mathematics at the Ohio State University. He received his bachelor degree from University of Science and Technology of China in 2002, and Ph.D. in Mathematics from Brown University in 2006 under the supervision of Prof. Chi-Wang Shu. Prior to joining OSU, he worked as a Postdoctoral Researcher at Courant Institute, New York University, a staff scientist at Oak Ridge National Laboratory, a joint assistant professor at University of Tennessee Knoxville, and an assistant professor at University of California Riverside. He works in the area of numerical analysis and scientific computing, wave propagation, computational fluid dynamics. His research focuses on the design, analysis and applications of accurate and efficient numerical methods for partial differential equations. He has received a CAREER Award from the National Science Foundation.