”Parareal” Time-Domain Decomposition for Time-dependent PDE-constrained Optimization
نویسنده
چکیده
منابع مشابه
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...
متن کاملDomain decomposition in time for PDE-constrained optimization
PDE-constrained optimization problems have a wide range of applications, but they lead to very large and ill-conditioned linear systems, especially if the problems are time dependent. In this paper we outline an approach for dealing with such problems by decomposing them in time and applying an additive Schwarz preconditioner in time, so that we can take advantage of parallel computers to deal ...
متن کاملDomain 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...
متن کاملA direct solver for time parallelization
Using the time direction in evolution problems for parallelization is an active field of research. Most of these methods are iterative, see for example the parareal algorithm analyzed in [3], a variant that became known under the name PFASST [10], and waveform relaxation methods based on domain decomposition [5, 4], see also [1] for a method called RIDC. Direct time parallel solvers are much mo...
متن کاملOptimization 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...
متن کامل