Events
DMS Colloquium: Thi-Thao-Phuong Hoang |
| Time: Jan 19, 2018 (04:00 PM) |
| Location: Parker Hall 249 |
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Details: Speaker: Thi-Thao-Phuong Hoang, Interdisciplinary Mathematics Institute, University of South Carolina Title: Domain Decomposition and Local Time-Stepping Methods for Numerical Solution of Evolution Equations and Their Applications Abstract: 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: i) DD methods in mixed formulations with applications related to ground water flow and contaminant transport in fractured porous media, ii) DD-based exponential integrator methods for stiff systems, and iii) conservative, explicit, local time-stepping algorithms for shallow water equations. Both mathematical analysis and numerical performance of these methods will be studied, in particular, numerical simulation of contaminant transport around a nuclear waste repository with nonconforming time grids will be presented.
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