DMS Colloquium: Thi-Thao-Phuong Hoang

Speaker: Thi-Thao-Phuong Hoang

Title: Efficient time-stepping methods for nonlinear evolution problems

Abstract: Numerical modeling of geophysical flows is challenging due to the presence of various coupled processes that occur at different spatial and temporal scales. It is critical for the numerical schemes to efficiently capture such a wide range of scales in both space and time to produce accurate and robust simulations over long time horizons. In this talk, I will present advanced time-stepping methods for the rotating shallow water equations discretized on spatial meshes with variable resolutions. Two different approaches will be considered, and both allow spatially dependent time step sizes to be used for time integration in different regions of the computational domain. The first approach is a fully explicit local time-stepping algorithm based on strong stability preserving Runge-Kutta schemes. The second approach, namely the localized exponential time differencing method, is based on spatial domain decomposition and exponential time integrators, which makes possible the use of much larger time step sizes compared to explicit schemes and avoids solving nonlinear systems. Numerical results on various test cases are presented to demonstrate the performance of the proposed methods.