Domain decomposition in time for PDE-constrained optimization

”Parareal” Time-Domain Decomposition for Time-dependent PDE-constrained Optimization

Domain decomposition and model reduction for the numerical solution of PDE constrained optimization problems with localized optimization variables

We introduce a technique for the dimension reduction of a class of PDE constrained optimization problems governed by linear time dependent advection diffusion equations for which the optimization variables are related to spatially localized quantities. Our approach uses domain decomposition applied to the optimality system to isolate the subsystem that explicitly depends on the optimization var...

Schedule of Talks

9:15 9:30 Opening 9:30 10:30 John A. Burns Sensitivity Analysis, Transition to Turbulence and Control 10:30 11:00 Coffee Break 11:00 12:00 Rainer Tichatschke Bregman-function-based regularization of variational inequalities with monotone operators 12:00 13:00 Lunch Break 13:00 14:00 Stefan Ulbrich Parallel All-at-Once methods with ”Parareal” time-domain decomposition for time-dependent PDE-cons...

Multi-preconditioned Gmres

Standard Krylov subspace methods only allow the user to choose a single preconditioner, although in many situations there may be a number of possibilities. Here we describe an extension of GMRES, multi-preconditioned GMRES, which allows the use of more than one preconditioner. We give some theoretical results, propose a practical algorithm, and present numerical results from problems in domain ...

Optimization with the time-dependent Navier-Stokes equations as constraints

In this paper, optimal distributed control of the time-dependent Navier-Stokes equations is considered. The control problem involves the minimization of a measure of the distance between the velocity field and a given target velocity field. A mixed numerical method involving a quasi-Newton algorithm, a novel calculation of the gradients and an inhomogeneous Navier-Stokes solver, to find the opt...