Computational Modelling and Optimal Control for Interacting Particle Systems #

Jonna Roden

11:30 Wednesday in 2Q48.

Part of the Optimisation and control for nonlinear dynamics session.

Abstract #

There are many industrial and biological processes, such as beer brewing, nano-separation of colloids and bird flocking, which can be described by integro-PDEs. These PDEs describe the dynamics of a ‘particle’ density within a fluid bath, under the influence of diffusion, external forces, and particle interactions. They often include nonlinear, nonlocal boundary conditions.

A key challenge is to optimize these types of processes, which requires tools from PDE-constrained optimization. In this talk I will introduce a numerical method to solve this class of optimal control problems, which combines spectral elements with a Newton-Krylov algorithm. This provides a tool for the fast and accurate solution of the resulting optimality systems.

In particular, this framework allows for the solution of (integro-)PDE models and optimal control problems on complicated domains, which is a crucial feature in accurately describing various applications. This is joint work with Ben Goddard and John Pearson.