DMS Graduate Student Seminar

Speaker: Dr. Thi-Thao-Phuong Hoang

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 space-time DD methods in mixed formulations with applications related to groundwater flow and contaminant transport in fractured porous media.