Many physical models are characterized by the property that some measure of energy is conserved or is non-increasing in time. This property may be challenging to guarantee in numerical discretizations; often it requires the use of costly implicit methods. I will review some approaches to energy stability and describe a new approach that guarantees energy stability with a general class of explicit schemes that are a simple modification of standard Runge-Kutta methods.
David Ketcheson is an Associate Professor of Applied Mathematics and Computational Science (AMCS) and Principal Investigator of the Numerical Mathematics Group. He is also a member of the Extreme Computing Research Center. He obtained his Ph.D. in 2009 from the University of Washington, USA. His research interests are in Nonlinear waves in heterogeneous media, Numerical analysis of ODE and PDE discretizations, Numerical methods for hyperbolic PDEs, High-performance computing and scalable algorithms, Scientific software development and Scientific computing in Python...