EVENT DETAILS AND ABSTRACT

Title: Fast simulation of semilinear time-dependent PDEs
Speaker: Tobin Driscoll
Speaker Info: University of Delaware
Brief Description:
Special Note: More current information may be available at Plan-it Purple
Abstract:

Many PDEs arising from the mathematical modelling of nonlinear phenomena have a special semilinear structure in which the highest spatial derivative appears only linearly. Well-known examples come from optics (cubic Schroedinger), water waves (Korteweg-de Vries, KP), fluid mechanics (Navier-Stokes), chaos (Kuramoto-Sivashinsky), self- organization (Cahn-Hilliard, Gray-Scott) and other fields. Numerical simulation of these models is an indispensable tool for their study. However, "textbook" methods can be unacceptably slow due to the presence of the high-order derivatives. In recent years a number of strategies for circumventing this problem have emerged. Many of the most successful techniques use a time integration method that varies with the local Fourier wavenumber. Although an ideal, general-purpose method has not yet been created, we are getting pretty close.
In this survey I will introduce the major features of the problem, describe the important wavenumber-dependent methods, and show comparisons and experimental results. Beyond a very basic understanding of generic multistep and Runge-Kutta methods for ODEs, no numerical expertise will be assumed.