Abstract
In this talk, we will present the Dirichlet-Neumann (DN) and Neumann-Neumann (NN) methods applied to optimal control problems arising from parabolic partial differential equations (PDE) under an $L^2$ regularization form. This problem reads as for a given state $y$ governed by a parabolic PDE on the time interval $[0,T]$, we wish to drive the solution of this parabolic PDE to a desired state $\hat y$ through a control $u$. The goal into non-overlapping subdomains is to find the optimal control $u^*$ which minimizes the discrepancy between these states (i.e. original state $y$ and desired state $\hat y$). After a semi-discretization in space, we use the Lagrange multiplier approach to derive a coupled forward-backward system. This system can then be solved by using DN and NN methods by separating the time domain into two non-overlapping subdomains. Finally, we provide the convergence analysis for these two methods along with some numerical results.
卢 柳 䃅
Postdoctoral Fellow in Applied Mathematics
My research interests include Numerical Analysis, Mathematical Biology, Scientific Computing, Optimization and Control.