joint work with Michael L. Minion
Time-parallel methods have received increasing interest in recent years as they allow to obtain speedup when spatial parallelization saturates. In this talk, we exploit the state-of-the art "Parallel Full Approximation Scheme in Space and Time" (PFASST) for the time-parallel solution of optimization problems with parabolic PDEs. As PFASST is based on spectral deferred correction methods their iterative nature provides additional flexibility, e.g., by re-using previously computed solutions. We focus especially on adapting the accuracy of state and adjoint solves to the optimization progress.
We consider optimization problems governed by time-dependent parabolic PDEs and discuss the construction of parallel solvers based on time-domain decomposition. We propose an ADMM-based approach to decompose the problem in independent subproblems and combine it with a multigrid strategy. Moreover, we discuss a preconditioner for the solution of the subproblems that decouples into a forward and backward PDE solve on the time-subdomains. Numerical results are presented.
joint work with Eric Cyr
To address the serial bottleneck of forward and adjoint time integration in solving dynamic optimization problems, we propose a parallel multigrid-in-time technique for the solution of optimality systems in a matrix-free trust-region sequential quadratic programming method for equality-constrained optimization. Additionally, to handle general inequality constraints, we develop and analyze an augmented-Lagrangian extension, which only augments simple bound constraints. We present scaling studies for large-scale fluid dynamics control problems and inverse problems involving Maxwell's equations.