Contributed Talk
Mixed precision Runge⧿Kutta methods
UMass Dartmouth, United States
Abstract
In this talk we present a mixed precision approach to accelerate the implemetation of multi-stage methods. We show that Runge-Kutta methods can be designed so that certain costly intermediate computations can be performed as a lower-precision computation without adversely impacting the accuracy of the overall solution. In particular, a properly designed Runge⧿Kutta method will damp out the errors committed in the initial stages. This is of particular interest when we consider implicit Runge⧿Kutta methods. In such cases, the implicit computation of the stage values can be considerably faster if the solution can be of lower precision (or, equivalently, have a lower tolerance). We provide a general theoretical additive framework for designing mixed precision Runge-Kutta methods, and use this framework to derive order conditions for such methods. We also demonstrate the performance and analyze stability of these methods.
Joint work with Sigal Gottlieb and Ben Burnett.