Daniel Reynolds: Adaptive multirate time integration for multiphysics PDE systems

Multiphysics models couple two or more physical processes together in a single simulation. These combinations may include systems of differential equations with different type (parabolic, hyperbolic, etc.), with different degrees of nonlinearity, and that evolve on disparate time scales. As a result, such simulations prove challenging for "monolithic" time integration methods that treat all processes using a single approach.

In this talk, I will discuss recent work on time integration methods that allow the flexibility to apply different techniques to distinct physical processes. While such techniques have existed for some time, including additive Runge-Kutta implicit-explicit (ImEx), multirate (a.k.a., multiple time stepping), and operator-splitting methods, there have been comparably few that combine these types of flexibility into a single family, while also supporting high orders of accuracy and temporal adaptivity. In this talk, I focus on newly developed implicit-explicit families of methods for multirate problems, along with novel techniques for time adaptivity in multirate infinitesimal time integration methods.