Parallel-in-Time for Parabolic Optimal Control Problems Using PFASST

accepted for publication on 2018-02-15
  • In gradient-based methods for parabolic optimal control problems, it is necessary to solve both the state equation and a backward-in-time adjoint equation in each iteration of the optimization method. In order to facilitate fully parallel gradient-type and nonlinear conjugate gradient methods for the solution of such optimal control problems, we discuss the application of the parallel-in-time method PFASST to adjoint gradient computation. In addition to enabling time parallelism, PFASST provides high flexibility for handling nonlinear equations, as well as potential extra computational savings from reusing previous solutions in the optimization loop. The approach is demonstrated here for a model reaction-diffusion optimal control problem.
Author:Sebastian Götschel, Michael Minion
Document Type:In Collection
Parent Title (English):Domain Decomposition Methods in Science and Engineering XXIV
Year of first publication:2018