The problem of finding an optimal control for a system governed by hyperbolic partial differential equations arises in many applications: two examples are source inversion and optimal turbine placement for wave energy generation. As in any optimal control problem, one must deal with a huge amount of data and computation, and parallelizable numerical algorithms such as domain decomposition is an indispensable tool for solving such problems.

In this talk, I will focus on parallelization in the time direction, which have become an active research area in the past two decades. This class of algorithms has the advantage of exposing more opportunities for parallelization than classical approaches, such as domain decomposition in space. Much progress has been made in this direction for the optimal control of parabolic problems. However, many challenges remain when dealing with hyperbolic problems, such as the need for higher order discretization, the subtle interplay between the discrete and continuous optimization problems, and the effect of dispersion on algorithm performance. I will present a few recent results on this subject, specifically regarding the convergence behaviour of two algorithms (optimized Schwarz method in time and ParaOpt) when applied to hyperbolic problems such as the transport and wave equations.

Refreshments will be served preceding the talk, starting at 2:45.