MC 5501 and Zoom
Chi-Wang Shu | Theodore B. Stowell University Professor of Applied Mathematics, Brown University
High order numerical methods for hyperbolic equations
Hyperbolic equations are used extensively in applications including fluid dynamics, astrophysics, electro-magnetism, semi-conductor devices, and biological sciences. High order accurate numerical methods are efficient for solving such partial differential equations, however they are difficult
to design because solutions may contain discontinuities. In this talk we will survey several types of high order numerical methods for such problems, including weighted essentially non-oscillatory (WENO) finite difference and finite volume methods, discontinuous Galerkin finite element methods, and spectral methods. We will discuss essential ingredients, properties and relative advantages of each method, and provide comparisons among these methods. Recent development and applications of these methods will also be discussed.
Professor Chi-Wang Shu obtained his BS degree from the University of Science and Technology of China in 1982 and his PhD degree from UCLA in 1986. He has been at Brown University since 1987, where he was the Chair of the Division of Applied Mathematics between 1999 and 2005, and is now the Theodore B. Stowell University Professor of Applied Mathematics. His research interest includes high order numerical methods for solving hyperbolic and other convection dominated PDEs, with applications in CFD and other areas. He is the Chief Editor of Journal of Scientific Computing and of Communications on Applied Mathematics and Computation, and serves in the editorial boards of several other journals including Journal of Computational Physics and Mathematics of Computation. He is a SIAM Fellow, an AMS Fellow and an AWM Fellow, and an invited 45-minute speaker in the International Congress of Mathematicians (ICM) in 2014. He received the First Feng Kang Prize of Scientific Computing in 1995, the SIAM/ACM Prize in Computational Science and Engineering in 2007, and the SIAM John von Neumann Prize in 2021.