Non-overlapping domain decomposition methods for time parallel solution of PDE-constrained optimization problems

Abstract

In this talk, we will explore non-overlapping domain decomposition methods and their application to parabolic PDE-constrained optimization problems. We will compare the difference between decomposing in space with decomposing in time. Then, we will discuss some properties of time domain decomposition methods, such as Dirichlet–Neumann method, Neumann–Neumann method, based on the forward-backward structure of the optimality system. We will also comment on the classical Schwarz method, which fails to converge when applied to non-overlapping spatial subdomains. For each method, several variants can be identified, some of these are only good smoothers, while others could lead to efficient solvers.

卢 柳 䃅

Postdoctoral Fellow in Applied Mathematics

My research interests include numerical analysis, scientific computing, mathematical modelling, optimization and control.