报告人：Sheng Qin 教授

 

报告题目：The Legacy of ADI and LOD Methods and an Application for Highly Oscillatory Wave Problems

报告地点：理A110

报告时间：5月13日，上午10:00-11:00

摘要：Splitting, or decomposition, methods have been widely used for achieving higher computational efficiency in solving wave equations. ADI and LOD are two typical splitting methods which have led a legacy of fast computations. A recent concern is, however, if the wave number involved is exceptionally large. In the case, merits of a conventional splitting method may diminish due to the fact that tiny discretization steps need to be employed to compensate high oscillations. Our exploration studies an alternative way for solving highly oscillatory paraxial wave problems via a modified splitting strategy. In the process, an exponential transformation is first introduced to convert the underlying differential equation to coupled nonlinear equations. Then the equations are approximated by an oscillation-free  semidiscretized system which can be treated by a LOD procedure for desired accuracy, efficiency and computability. The splitting method acquired is stable asymptotically and easy to use. Some computational experiments will be presented to illustrate our results and simulations.

个人简介：Dr. Sheng received his BS and MS in Mathematics from Nanjing University in 1982, 1985, respectively. Then he obtained his Ph.D. from University of Cambridge under the supervision of Professor Arieh Iserles. After his postdoctoral research with Professor Frank Smith, FRS, in University College London, he joined National University of Singapore in 1990. Since then, Dr. Sheng was on faculty of several major universities till his joining Baylor University, which is one of known research institutions and the second largest private university in the United States.

Dr. Sheng has been interested in splitting and adaptive numerical methods for solving linear and nonlinear partial differential equations. He is also an active member of the CASPER Research Center. He is also known for the Sheng-Suzuki theorem in numerical analysis. He has published over 105 refereed journal articles as well as 6 joint research monographs. He has been an Editor-in-Chief of the SCI journal, International Journal of Computer Mathematics, published by Taylor and Francis since 2010. He gives invited presentations, including keynote lectures, in international conferences every year. Dr. Sheng currently has 3 doctoral students and 1 postdoctoral research fellow.