For Zoom Link please contact ddelreyfernandez@uwaterloo.ca
Speaker
Professor David I. Ketcheson, Professor, Applied Mathematics and Computational Science, King Abdullah University of Science and Technology
Title
Efficient PDE time discretizations that enforce conservation or dissipation properties
Abstract
The most fundamental properties of a physical model are often related to the conservation or dissipation energy or similar functionals. Numerical methods that fail to preserve the correct behavior with respect to such functionals often give solutions with poor accuracy or unrealistic behavior. However, traditional approaches to preserving dissipation or conservation at the discrete level require expensive fully-implicit time stepping. I will describe a simple modification that can be applied to any time stepping method in order to enforce energy conservation or dissipation in an essentially-explicit manner, while at the same time maintaining conservation of relevant linear functionals like mass or momentum. After reviewing work in this area, I will highlight some recent advances in enforcing multiple conservation laws for the Korteweg-de Vries and nonlinear Schrodinger equations. I will also describe empirical results showing that conservative methods lead to drastically improved long-time error propagation for a wide variety of dispersive wave models.