A parallel-in-time approach for accelerating direct-adjoint studies

Parallel-in-time methods are developed to accelerate the direct-adjoint looping procedure. Particularly, we utilize the Paraexp algorithm, previously developed to integrate equations forward in time, to accelerate the direct-adjoint looping that arises from gradient-based optimization. We consider both linear and non-linear governing equations and exploit the linear, time-varying nature of the adjoint equations. Gains in efficiency are seen across all cases, showing that a Paraexp based parallel-in-time approach is feasible for the acceleration of direct-adjoint studies. This signifies a possible approach to further increase the run-time performance for optimization studies that either cannot be parallelized in space or are at their limit of efficiency gains for a parallel-in-space approach. Code demonstrating the algorithms considered in this paper is available. (C) 2020 Elsevier Inc. All rights reserved.

Automated summary

Parallel-in-time methods using the Paraexp algorithm are developed to accelerate the direct-adjoint looping process for both linear and non-linear governing equations. Efficiency gains are observed in all cases, indicating the feasibility of using a Paraexp-based approach for direct-adjoint studies.