“Stability and convergence analysis of multirate decoupling schemes for time dependent multi-physics problems”

In this talk, I will introduce multirate numerical schemes solving coupled free flow with porous media flow problems. Multirate methods are computationally efficient because they decouple the flow problem and utilize subdomain-specific time step sizes that are based on the rate of flow in each domain. Specifically, a large time step is used to integrate a slow changing porous media flow problem and a much smaller time step for the fast changing free flow problem. While computationally efficient, fully decoupled multirate schemes are only conditionally stable, i.e., the schemes require small time steps for problems with small parameter values in order to maintain stability. I will discuss the source of numerical instabilities for multirate methods, provide numerical remedies, and compare existing schemes to recent work in terms of stability and convergence to smooth solutions.