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Academic Events

Operator Splitting Methods: Ideas, Derivations and Error Estimates

WHEN: Monday, 2019, August 19-15:30

WHERE: Room 526, Xingjian Building

SPONSORSchool of Mathematical Science, Nanjing Normal University

SPEAKER(S): Qin, Sheng

 

DETAILS:Dr. Sheng has been interested in splitting and adaptive numerical methods for solvinglinear and nonlinear partial differential equations. He is also known for the Sheng-Suzuki theorem in numerical analysis. He has published over 110 refereed articles as well as several joint research monographs. He has been an Editor-in-Chief of the SCI journal, International Journal of Computer Mathematics, published by Taylor and Francis Group since 2010. He gives invited presentations, including keynote lectures, in international conferences every year. Dr. Sheng's projects have been supported by several U.S. research agencies.

 

ABSTRACT: Splitting methods have been used for solving a broad spectrum of biomathematical problems. They are for the numerical solution to not only differential equations, but also statistical and optimization approximations. A splitting method separates the original problem into several subproblems, separately computes the solution to each of them, and then combines all sub-solutions to form an approximationof the solution to the original problem. A canonical example is splitting of diffusion and convection terms in a convection-diffusion partial differential equation. The splitting idea generalizes in a natural way to problems with multiple operators. In all cases, the computational advantage is that it is faster to compute the solution of the split components separately, than to compute the solution directly when they are treated together. However, this comes at the cost of an error introduced by the splitting, so strategies must be devised for controlling the error. This talkstudies splitting methods via operator computations. It also surveys recent developments in several areas. An interesting investigation is given in global error analysis of popular exponential splitting formulations. One recent development, adaptive splitting, deserves and receives a special mention in this talk: it is a new splitting method tocollaborate with possible deep machine learning strategies.