IMI Interdisciplinary Mathematics InstituteCollege of Arts and Sciences

Ninth Annual Graduate Student Mini-conference in Computational Mathematics

Thi Thao Phuong Hoang
University of South Carolina
https://sites.google.com/site/thithaophuonghoang/
Abstract

Domain decomposition and local time-stepping methods for numerical solution of evolution equations and their applications

  • Feb. 18, 2018
  • 9 a.m.
  • LeConte 412

Due to the development of multiprocessor supercomputers and parallel computing, domain decomposition (DD) methods have become a powerful tool for numerical simulation of large-scale problems. As many physical and engineering processes are described by evolution partial differential equations, extensions of DD methods to dynamic systems (i.e. those changing with time) have been a subject of great interest. Moreover, for applications in which the time scales vary considerably across the whole domain due to changes in the physical properties or in the spatial grid sizes, it is critical and computationally efficient to design DD methods which allow the use of different time step sizes in different subdomains. In this talk, we will introduce mathematical concepts of DD methods for evolution equations and present our recent work in this direction, including DD-based exponential integrator methods for stiff systems and conservative, explicit, local time-stepping algorithms for shallow water equations. This is joint work with Lili Ju, Zhu Wang (University of South Carolina) and Wei Leng (Chinese Academy of Sciences).

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