# A Non-Intrusive Parallel-in-Time Adjoint Solver with the XBraid Library

## TL;DR

This paper introduces a non-intrusive parallel-in-time adjoint solver integrated with the XBraid library, enabling efficient sensitivity analysis for unsteady simulations on multiple processors.

## Contribution

It develops a novel discrete adjoint solver for XBraid that is highly non-intrusive and compatible with existing time propagators, improving parallel efficiency for sensitivity computations.

## Key findings

- Provides similar strong scaling as primal XBraid solver
- Validates the adjoint solver on advection-dominated flow
- Offers potential for faster sensitivity analysis using multiple processors

## 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. 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.