Thackeray Hall 427
Abstract or Additional Information
Domain decomposition (DD) methods provide a natural computational framework for multiscale multiphysics problems and a powerful tool for parallel 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 first introduce mathematical concepts of DD methods for evolution problems, then present DD-based time-stepping methods for the rotating shallow water equations discretized on spatial meshes with variable resolutions. Two different approaches will be considered: the first one is a fully explicit local time-stepping algorithm based on the Strong Stability Preserving Runge-Kutta (SSP-RK) schemes, which allows different time step sizes in different regions of the computational domain. The second approach is the so-called Localized Exponential Time Differencing (LETD) method, which makes possible the use of much larger time step sizes compared to explicit schemes and avoids solving nonlinear systems as required in an implicit time discretization. Numerical results on various test cases will be presented to demonstrate the performance of the proposed methods.