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

Günther, Stefanie; Gauger, Nicolas R.; Schroder, Jacob B.

doi:10.1007/s00791-018-0300-7

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

Journal Article · Wed Jun 27 00:00:00 EDT 2018 · Computing and Visualization in Science

DOI:https://doi.org/10.1007/s00791-018-0300-7· OSTI ID:1773254

Günther, Stefanie ^[1]; Gauger, Nicolas R. ^[1]; Schroder, Jacob B. ^[2]

Technische Universität Kaiserslautern (Germany)
Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States)

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 (XBraid: Parallel multigrid in time, http://llnl.gov/casc/xbraid). 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. We report 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.

View Accepted Manuscript (DOE)

Research Organization:: Lawrence Livermore National Laboratory (LLNL), Livermore, CA (United States)

Sponsoring Organization:: USDOE National Nuclear Security Administration (NNSA)

Grant/Contract Number:: AC52-07NA27344

OSTI ID:: 1773254

Report Number(s):: LLNL-JRNL--730159; 881043

Journal Information:: Computing and Visualization in Science, Journal Name: Computing and Visualization in Science Journal Issue: 3-4 Vol. 19; ISSN 1432-9360

Publisher:: SpringerCopyright Statement

Country of Publication:: United States

Language:: English

References (37)

A note on MGR methods Ries, Manfred; Trottenberg, Ulrich; Winter, Gerd Linear Algebra and its Applications, Vol. 49 https://doi.org/10.1016/0024-3795(83)90091-5	journal	February 1983
Practical and theoretical aspects of adjoint parameter estimation and identifiability in meteorology and oceanography Navon, I. M. Dynamics of Atmospheres and Oceans, Vol. 27, Issue 1-4 https://doi.org/10.1016/s0377-0265(97)00032-8	journal	January 1998
On optimum design in fluid mechanics Pironneau, O. Journal of Fluid Mechanics, Vol. 64, Issue 1 https://doi.org/10.1017/s0022112074002023	journal	June 1974
Evaluating Derivatives Griewank, Andreas; Walther, Andrea https://doi.org/10.1137/1.9780898717761	book	January 2008
Parallel methods for integrating ordinary differential equations Nievergelt, J. Communications of the ACM, Vol. 7, Issue 12 https://doi.org/10.1145/355588.365137	journal	December 1964
A General Framework for the Optimal Control of Unsteady Flows with Applications Rumpfkeil, Markus; Zingg, David 45th AIAA Aerospace Sciences Meeting and Exhibit https://doi.org/10.2514/6.2007-1128	conference	June 2012
Solution of the Unsteady Discrete Adjoint for Three-Dimensional Problems on Dynamically Deforming Unstructured Meshes Mavriplis, Dimitri 46th AIAA Aerospace Sciences Meeting and Exhibit https://doi.org/10.2514/6.2008-727	conference	June 2012
Time-decomposed parallel time-integrators: theory and feasibility studies for fluid, structure, and fluid-structure applications Farhat, Charbel; Chandesris, Marion International Journal for Numerical Methods in Engineering, Vol. 58, Issue 9 https://doi.org/10.1002/nme.860	journal	January 2003
Grid Adaptation for Functional Outputs: Application to Two-Dimensional Inviscid Flows Venditti, David A.; Darmofal, David L. Journal of Computational Physics, Vol. 176, Issue 1 https://doi.org/10.1006/jcph.2001.6967	journal	February 2002
50 Years of Time Parallel Time Integration Gander, Martin J. Contributions in Mathematical and Computational Sciences https://doi.org/10.1007/978-3-319-23321-5_3	book	January 2015
Aerodynamic design via control theory Jameson, Antony Journal of Scientific Computing, Vol. 3, Issue 3 https://doi.org/10.1007/BF01061285	journal	September 1988
Practical and theoretical aspects of adjoint parameter estimation and identifiability in meteorology and oceanography Navon, I. M. Dynamics of Atmospheres and Oceans, Vol. 27, Issue 1-4 https://doi.org/10.1016/S0377-0265(97)00032-8	journal	January 1998
Résolution d'EDP par un schéma en temps «pararéel » Lions, Jacques-Louis; Maday, Yvon; Turinici, Gabriel Comptes Rendus de l'Académie des Sciences - Series I - Mathematics, Vol. 332, Issue 7 https://doi.org/10.1016/S0764-4442(00)01793-6	journal	April 2001
A time-domain decomposition iterative method for the solution of distributed linear quadratic optimal control problems Heinkenschloss, Matthias Journal of Computational and Applied Mathematics, Vol. 173, Issue 1 https://doi.org/10.1016/j.cam.2004.03.005	journal	January 2005
Simultaneous single-step one-shot optimization with unsteady PDEs Günther, Stefanie; Gauger, Nicolas R.; Wang, Qiqi Journal of Computational and Applied Mathematics, Vol. 294 https://doi.org/10.1016/j.cam.2015.07.033	journal	March 2016
Robust optimization – A comprehensive survey Beyer, Hans-Georg; Sendhoff, Bernhard Computer Methods in Applied Mechanics and Engineering, Vol. 196, Issue 33-34 https://doi.org/10.1016/j.cma.2007.03.003	journal	July 2007
Explicit parallel-in-time integration of a linear acoustic-advection system Ruprecht, D.; Krause, R. Computers & Fluids, Vol. 59 https://doi.org/10.1016/j.compfluid.2012.02.015	journal	April 2012
Domain decomposition in time for PDE-constrained optimization Barker, Andrew T.; Stoll, Martin Computer Physics Communications, Vol. 197 https://doi.org/10.1016/j.cpc.2015.08.025	journal	December 2015
On optimum design in fluid mechanics Pironneau, O. Journal of Fluid Mechanics, Vol. 64, Issue 1 https://doi.org/10.1017/S0022112074002023	journal	June 1974
Adjoint methods for PDEs: a posteriori error analysis and postprocessing by duality Giles, Michael B.; Süli, Endre Acta Numerica, Vol. 11 https://doi.org/10.1017/S096249290200003X	journal	January 2002
An Introduction to the Adjoint Approach to Design Giles, Michael B.; Pierce, Niles A. Flow, Turbulence and Combustion, Vol. 65, Issue 3/4, p. 393-415 https://doi.org/10.1023/A:1011430410075	journal	December 2000
Multi-level adaptive solutions to boundary-value problems Brandt, Achi Mathematics of Computation, Vol. 31, Issue 138 https://doi.org/10.1090/S0025-5718-1977-0431719-X	journal	May 1977
Analysis of the Parareal Time‐Parallel Time‐Integration Method Gander, Martin J.; Vandewalle, Stefan SIAM Journal on Scientific Computing, Vol. 29, Issue 2 https://doi.org/10.1137/05064607X	journal	January 2007
Stabilization of Unstable Procedures: The Recursive Projection Method Shroff, Gautam M.; Keller, Herbert B. SIAM Journal on Numerical Analysis, Vol. 30, Issue 4 https://doi.org/10.1137/0730057	journal	August 1993
Analysis of Block Parareal Preconditioners for Parabolic Optimal Control Problems Mathew, Tarek P.; Sarkis, Marcus; Schaerer, Christian E. SIAM Journal on Scientific Computing, Vol. 32, Issue 3 https://doi.org/10.1137/080717481	journal	January 2010
Parallel Time Integration with Multigrid Falgout, R. D.; Friedhoff, S.; Kolev, Tz. V. SIAM Journal on Scientific Computing, Vol. 36, Issue 6 https://doi.org/10.1137/130944230	journal	January 2014
Two-Level Convergence Theory for Multigrid Reduction in Time (MGRIT) Dobrev, V. A.; Kolev, Tz.; Petersson, N. A. SIAM Journal on Scientific Computing, Vol. 39, Issue 5 https://doi.org/10.1137/16M1074096	journal	January 2017
Multigrid Reduction in Time for Nonlinear Parabolic Problems: A Case Study Falgout, R. D.; Manteuffel, T. A.; O'Neill, B. SIAM Journal on Scientific Computing, Vol. 39, Issue 5 https://doi.org/10.1137/16M1082330	journal	January 2017
Adjoint Recovery of Superconvergent Functionals from PDE Approximations Pierce, Niles A.; Giles, Michael B. SIAM Review, Vol. 42, Issue 2 https://doi.org/10.1137/S0036144598349423	journal	January 2000
Toward an efficient parallel in time method for partial differential equations Emmett, Matthew; Minion, Michael Communications in Applied Mathematics and Computational Science, Vol. 7, Issue 1 https://doi.org/10.2140/camcos.2012.7.105	journal	January 2012
Optimum Shape Design for Unsteady Flows with Time-Accurate Continuous and Discrete Adjoint Method Nadarajah, Siva K.; Jameson, Antony AIAA Journal, Vol. 45, Issue 7 https://doi.org/10.2514/1.24332	journal	July 2007
Discrete Adjoint-Based Design Optimization of Unsteady Turbulent Flows on Dynamic Unstructured Grids Nielsen, Eric J.; Diskin, Boris; Yamaleev, Nail K. AIAA Journal, Vol. 48, Issue 6 https://doi.org/10.2514/1.J050035	journal	June 2010
Time dependent calculations using multigrid, with applications to unsteady flows past airfoils and wings Jameson, Antony 10th Computational Fluid Dynamics Conference https://doi.org/10.2514/6.1991-1596	conference	August 1991
Adjoint equations in CFD - Duality, boundary conditions and solution behaviour Giles, M.; Pierce, N.; Giles, M. 13th Computational Fluid Dynamics Conference https://doi.org/10.2514/6.1997-1850	conference	August 1997
Unsteady Aerodynamic Design on Unstructured Meshes with Sliding Interfaces Economon, Thomas; Palacios, Francisco; Alonso, Juan 51st AIAA Aerospace Sciences Meeting including the New Horizons Forum and Aerospace Exposition https://doi.org/10.2514/6.2013-632	conference	January 2013
Assessment of the Recursive Projection Method for the Stabilization of Discrete Adjoint Solvers Albring, Tim A.; Dick, Thomas; Gauger, Nicolas R. 18th AIAA/ISSMO Multidisciplinary Analysis and Optimization Conference https://doi.org/10.2514/6.2017-3664	conference	June 2017
Van der Pol oscillator Kanamaru, Takashi Scholarpedia, Vol. 2, Issue 1 https://doi.org/10.4249/scholarpedia.2202	journal	January 2007

Similar Records

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

Journal Article · Mon Aug 06 00:00:00 EDT 2018 · Optimization Methods and Software · OSTI ID:1773244

Two-Level Convergence Theory for Multigrid Reduction in Time (MGRIT)

Journal Article · Thu Oct 26 00:00:00 EDT 2017 · SIAM Journal on Scientific Computing · OSTI ID:1764758

Non-Intrusive Parallel-in-Time Solvers for Partial Differential Equations (Final Report)

Technical Report · Fri Oct 04 00:00:00 EDT 2024 · OSTI ID:2459413

Related Subjects

97 MATHEMATICS AND COMPUTING
Adjoint sensitivity
High performance computing
Multigrid-in-time
Optimization
Parallel-in-time
Parareal
Unsteady adjoint

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

Citation Formats

References (37)

Similar Records

Related Subjects