A non-intrusive parallel-in-time adjoint solver with the XBraid library

Abstract

In this paper, an adjoint solver for the multigrid-in-time software library XBraid is presented. XBraid provides a non-intrusive approach for simulating unsteady dynamics on multiple processors while parallelizing not only in space but also in the time domain [60]. It applies an iterative multigrid reduction in time algorithm to existing spatially parallel classical time propagators and computes the unsteady solution parallel in time. Techniques from Automatic Differentiation are used to develop a consistent discrete adjoint solver which provides sensitivity information of output quantities with respect to design parameter changes. The adjoint code runs backwards through the primal XBraid actions and accumulates gradient information parallel in time. It is highly non-intrusive as existing adjoint time propagators can easily be integrated through the adjoint interface. The adjoint code is validated on advection-dominated flow with periodic upstream boundary condition. It provides similar strong scaling results as the primal XBraid solver and offers great potential for speeding up the overall computational costs for sensitivity analysis using multiple processors.

Schwarz Waveform Relaxation with Adaptive Pipelining

“…Then the maximum possible speedup for the adaptive WR method with P = M is k tot M + \k max . (19) This speedup can be estimated by realizing that k tot = M k avg , and the ratio…”

An Efficient Parallel-in-Time Method for Optimization with Parabolic PDEs

“…While they report excellent speedups and linear scaling up to 50 processors and show convergence if sufficiently small step sizes for updating the control are used, it is unclear how to automatically select such a step size. Alternatively, space-time parallel multigrid methods are applied to adjoint gradient computation and simultaneous optimization [24,25] within the XBraid software library [4]. XBraid provides a non-intrusive framework adding time-parallelism to existing serial time stepping codes, and using simultaneous instead of reduced space optimization, a speedup of 19 using 256 time processors has been reported.…”

A non-intrusive parallel-in-time approach for simultaneous optimization with unsteady PDEs

“…It then converges to the same solution as the existing serial simulation code, but can achieve a speedup due to new concurrency in the time domain. In [19], XBraid's multigrid iterations have been enhanced with the ability to compute discrete adjoint sensitivities. Utilizing techniques from Automatic Differentiation (AD), the adjoint code runs backwards through the primal XBraid computations and accumulates sensitivity information parallel-in-time alongside the primal computations.…”

“…While [19] parallelized the state and adjoint solvers in time with XBraid, this paper novelly integrates that work into the context of an optimization process. We choose the non-intrusive simultaneous One-shot optimization method, because it reduces the optimization overhead of common reduced-space optimization techniques, allowing for greater speedups.…”

“…The time-parallelization is provided by the non-intrusive software library XBraid [41], which applies an iterative multigrid reduction technique to the time domain of existing timemarching schemes for solving unsteady PDEs. Its general user-interface has been extended in [19] 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.…”