Matthias Heinkenschloss, Rice University
Optimization of systems governed by partial differential equations (PDEs) plays a crucial role in many science and engineering applications where one needs to identify model parameters or determine inputs to improve the performance of systems. The solution of these optimization problems poses many mathematical and computational challenges, which arise, e.g., from the structure of the underlying PDEs, the large number of optimization variables, or possible uncertainties in PDE model parameters.
In this talk I will discuss several applications of PDE constrained optimization ranging from shape optimization of shell structure acoustics motivated by the design of musical instruments to well-rate optimization arising in subsurface reservoir management. I will describe mathematical formulations of these optimization problems, hint at some of the challenges that arise in their numerical solution, and sketch some of the current solution approaches.
Flyer PDF: matthais_heinkenschloss_math_flyer.pdf