Contributed Talk
Implicit-Explicit Generalized Additive Runge–Kutta Methods
Lawrence Livermore National Laboratory, USA
Abstract
Historically, implicit-explicit (IMEX) Runge–Kutta methods have been represented and analyzed almost exclusively within the confines of two frameworks:
Additive Runge–Kutta (ARK) and Additive Semi-Implicit Runge–Kutta (ASIRK). While numerous high-quality integrators have been developed with these frameworks,
their structures have several limitations. For example, the underlying implicit and explicit methods must have the same number of stages. Order conditions and
simplifying assumptions are very restrictive and tightly couple the methods together. In this presentation, we explore Generalized Additive Runge–Kutta (GARK)
as a platform for constructing IMEX schemes. GARK naturally reveals hidden coupling coefficients that control the interactions between an implicit and explicit method.
It encompasses ARK and ASIRK as special cases but offers roughly twice the coefficients. Using this additional flexibility, we address the aforementioned limitations
and devise novel structures for IMEX methods. New methods up to order 4 suitable for ODEs and index-1 DAEs are presented and compared to existing IMEX methods.
LLNL-ABS-831917