Parallel-in-Time Optimization with Unsteady PDEs
A simultaneous optimization framework for unsteady PDEs using the parallel-in-time software library XBraid is presented. XBraid provides a non-intrusive approach for parallelization in the time domain by applying an iterative multigrid reduction in time algorithm to existing sequential time-stepping codes. We develop a non-intrusive adjoint solver for XBraid that enhances these primal iterations by an iteration for computing adjoint sensitivities parallel in time. The adjoint sensitivities are then used in a simultaneous optimization method, namely the One-shot method which solves the optimization problem in the full space. We validate the time-parallel simultaneous optimization approach by applying it to an inverse design problem with unsteady PDEs that mimics the behavior of separated flows past bluff bodies.