Application of time decomposition to PDE-constrained optimization problems

Abstract

PDE-constrained optimization problems arise in various areas, often containing multiphysics or multiscale phenomena on different time scales. This requires very fine spatial and temporal discretizations, resulting in very large problems, for which efficient parallel solvers are needed. Using the Lagrange multiplier technique, optimal solutions can be characterized by the first-order optimality system. When the governing PDEs are time-dependent, this system has typically a forward-backward structure. In this talk, we will explore some non-overlapping domain decomposition methods to solve this forward-backward optimality system. We will first introduce the idea of time domain decomposition and compare with the space decomposition, the so-called waveform relaxation methods. Based on the forward-backward structure of the optimality system, we will then discuss some properties of Dirichlet-Neumann methods and Neumann-Neumann methods in the time decomposition framework. Some tests will be shown to reveal numerical properties of these methods.

卢 柳 䃅

Postdoctoral Fellow in Applied Mathematics

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