A Non-Intrusive Parallel-in-Time Approach for Simultaneous Optimization with Unsteady PDEs

TL;DR

This paper introduces a non-intrusive, parallel-in-time optimization framework that integrates existing unsteady PDE solvers with XBraid, enabling faster simultaneous optimization of unsteady PDEs through time-parallelization.

Contribution

It extends XBraid for adjoint sensitivity computation and embeds it into a One-shot optimization framework for efficient, parallel-in-time PDE-based design optimization.

Findings

Significant speedup over classical serial optimization methods.

Successful validation on an advection-dominated flow control problem.

Demonstrates effective integration of existing solvers into a parallel optimization scheme.

Abstract

This paper presents a non-intrusive framework for integrating existing unsteady partial differential equation (PDE) solvers into a parallel-in-time simultaneous optimization algorithm. The time-parallelization is provided by the non-intrusive software library XBraid, which applies an iterative multigrid reduction technique to the time domain of existing time-marching schemes for solving unsteady PDEs. Its general user-interface has been extended for computing adjoint sensitivities such that gradients of output quantities with respect to design changes can be computed parallel-in-time alongside with the primal PDE solution. In this paper, the primal and adjoint XBraid iterations are embedded into a simultaneous optimization framework, namely the One-shot method. In this method, design updates towards optimality are employed after each state and adjoint update such that optimality and feasibility of the design and the PDE solution are reached simultaneously. The time-parallel optimization method is validated on an advection-dominated flow control problem which shows significant speedup over a classical time-serial optimization algorithm.