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Flexible Time Integration Methods for Multiphysics PDE Systems with Dan Reynolds

Abstract: In recent years computational simulations have rapidly evolved in complexity (high order discretizations, spatial adaptivity, wide arrays of physical processes), placing ever larger strains on the time integration methods on which they rely. High spatial order necessitates comparably high order time integration. Spatial adaptivity and multiphysics processes give rise to subsets of the solution that evolve at differing time scales, or to simulations that combine nonstiff/nonlinear processes with others that may be highly stiff but that are frequently linear. 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 techniques for flexible time integration have existed for some time, including additive Runge--Kutta 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 the newly developed IMEX-MRI-GARK (Chinomona and R., 2022) and IMEX-MRI-SR (Fish, R. and Roberts, 2023) families of methods, along with novel techniques for time adaptivity in multirate infinitesimal time integration methods (Fish and R., 2023). In addition to discussing these methods themselves, I'll also present our work implementing and releasing these as part of the open-source SUNDIALS library. Bio: Daniel Reynolds is Professor and Chair of the Department of Mathematics at Southern Methodist University. His research focuses on the development and application of robust time integrators and iterative nonlinear and linear solvers for large-scale multiphysics systems -- simulations comprised of multiple interacting physical processes. Reynolds is the lead developer of the ARKODE library, a collection of solvers for adaptive implicit-explicit and multirate time integration methods for large-scale systems of differential equations, and is a senior developer for the larger SUNDIALS suite of time integration and nonlinear solver libraries (which includes ARKODE). Prior to joining SMU in 2008, Reynolds held postdoctoral research positions in the Department of Mathematics and the Center for Astrophysics and Space Sciences at the University of California, San Diego (2005-2008), and in the Center for Applied Scientific Computing at Lawrence Livermore National Laboratory (2003-2005). He received a PhD in Computational and Applied Mathematics from Rice University in 2003, and a BA in Mathematics from Southwestern University in 1998. ----- Watch more videos from University of Colorado Boulder Engineering & Applied Science and subscribe: https://bit.ly/37UmM5X Founded in 1893, the College of Engineering and Applied Science at the University of Colorado Boulder is the second largest of seven schools and colleges at one of the nation's top public research institutions. Join Our Community:   / cuengineering     / cuengineering     / cuengineering   Contact University of Colorado Boulder Engineering & Applied Science: https://www.colorado.edu/engineering/... #Engineering #CUBoulder #EngineeringBuff