VisualPDE: Using WebGL to Rapidly Explore PDE Dynamics for Fun and Profit #

Andrew Krause, Benjamin Walker, Adam Townsend

11:10 Monday in 2Q49.

Part of the Dynamics of reaction-transport systems session.

Abstract #

Computing has revolutionized the study of complex nonlinear systems, in part by allowing us to solve previously-intractable models, but also through the accessibility of visualizing solutions in different ways. In this talk, I hope to convince you that we can go one step further in using computers to really understand such nonlinear models through instantaneous and interactive exploration. Abstract dynamical systems concepts such as symmetry-breaking instabilities, subcritical bifurcations, and the role of initial data in multistable nonlinear models become much more intuitive when you can play with these models yourself, and immediately answer questions about how the system responds to changes in parameters, initial conditions, boundary conditions, or even spatiotemporal forcing. This talk will focus on a recent tool we have developed for this purpose for partial differential equations, though many other tools exist and are being developed for different classes of dynamical systems and mathematical models. Importantly, the tool I will present is freely-available, and endlessly customizable for use in teaching and research.