Stability of time discretizations for semi-discrete high order schemes for time-dependent PDEs
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：舒其望
：2020-04-16 10:00
：行政楼313(offline) ZOOM APP(online)
Speaker：Prof. Chi-Wang Shu
Division of Applied Mathematics, Brown University
Title: Stability of time discretizations for semi-discrete high order schemes for time-dependent PDEs
Time：16 April. 2020,10:00
Location： 行政楼313(offline)
ZOOM APP(online)
ZOOM Info: https://zoom.com.cn/j/4530715653?pwd=WGp2ZWUrZlZIYjhCV1lRSFhEem5SUT09
会议 ID: 453 071 5653
密码: 2580115
附件：PPT（Stability of time discretizations for semi-discrete high order schemes for time-dependent PDEs）
Abstract:
In scientific engineering computing, we encounter time-dependent partial differential equations (PDEs) frequently. When designing high order schemes for solving these time-dependent PDEs, we often first develop semi-discrete schemes paying attention only to spatial
discretizations leaving time $t$ continuous. It is then important to have a high order time discretization to main the stability properties of the semi-discrete schemes. In this talk we discuss several classes of high order time discretization, including the strong stability preserving (SSP) time discretization, which preserves strong stability from a stable spatial discretization with Euler forward, the implicit-explicit (IMEX) Runge-Kutta or multi-step time marching, which treats the more stiff term (e.g. diffusion term in a convection-diffusion equation) implicitly the less stiff term (e.g. the convection term in such an equation) explicitly, for which strong stability can be proved under the condition that the time step is upper-bounded by a constant under suitable conditions, the explicit Runge-Kutta methods, for which strong stability can be proved in many cases for semi-negative linear semi-discrete schemes. Numerical examples will be given to demonstrate the performance of these schemes.
Speaker Introduction：
舒其望，美国布朗大学教授。1982年毕业于中国科学技术大学数学系并获学士学位，1986年在美国加州大学洛杉矶分校获博士学位。1987年起任职于布朗大学。其中在1999年至2005年间担任布朗大学应用数学系系主任。现为美国布朗大学Theodore B. Stowell应用数学讲座教授。
舒其望教授的研究领域包括用于求解双曲方程和对流占优偏微分方程的高精度WENO有限差分及有限体积方法、间断有限元方法和谱方法等。这些方法被广泛应用于计算流体力学、半导体元件模拟及计算宇宙学等领域。
他的研究工作有着深远的影响，其发表的学术论文及著作在Google学术的引用率高达五万余次。舒其望教授现任计算数学国际期刊Journal of Scientific Computing主编，同时还担任多个国际学术期刊的编委，其中包括Journal of Computational Physics和Mathematics of Computation。
他曾获第一届冯康科学计算奖（1995年）和SIAM/ACM计算科学与工程奖（2007年）。现任美国工业与应用数学学会会士（2009年首届当选）及美国数学学会会士（2012年首届当选）。
联系人：邱建贤教授
