Advances in Implicit / Explicit (IMEX) Time integration of Multiphysics Systems

John Shadid, Sandia National Laboratories
Eric Cyr, Sandia National Laboratories


Implicit / Explicit (IMEX) methods are an important and widely used class of time integration techniques for complex scalar and systems of partial differential equations (PDEs). While there are many forms of IMEX methods, these techniques share the basic structure of decomposing the differential operator into two components in which one component is treated implicitly, and the other component explicitly.  This flexibility of mixing explicit and implicit discretization is intended to allow the application of specialized numerical solution methods for systems composed of operators with differing time-scales. This mini-symposium will explore the analysis, evaluation, and application of these methods to multiphysics systems. Topics of interest include (but are not limited to) the analysis of IMEX methods for complex systems, error estimation for IMEX integrators, and application to: transport-reaction systems, incompressible and compressible Navier-Stokes, MHD and multi-physics shock-hydro type systems.