Algorithm 799: revolve. An implementation of checkpointing for the reverse or adjoint mode of computational differentiation. This is an excellent paper, describing a variant (“revolve”) of the basic form for reverse differentiation for computing the gradient of a scalar valued function, which enables computing this gradient of a function using no more than five times the number of operations needed for evaluating the function. This basic algorithm usually requires a large memory for storage of intermediate computations. The variant presented here circumvents this large memory requirement. A detailed description of the variant is given, along with motivation and proofs. The authors then illustrate the application of their algorithm to the solution of Burgers equation (Source:

This software is also peer reviewed by journal TOMS.

References in zbMATH (referenced in 38 articles , 1 standard article )

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  1. Aupy, Guillaume; Herrmann, Julien; Hovland, Paul; Robert, Yves: Optimal multistage algorithm for adjoint computation (2016)
  2. Bauman, Paul T.; Stogner, Roy H.: GRINS: a multiphysics framework based on the libMesh finite element library (2016)
  3. Papoutsis-Kiachagias, E.M.; Giannakoglou, K.C.: Continuous adjoint methods for turbulent flows, applied to shape and topology optimization: industrial applications (2016)
  4. Bakhos, Tania; Saibaba, Arvind K.; Kitanidis, Peter K.: A fast algorithm for parabolic PDE-based inverse problems based on Laplace transforms and flexible Krylov solvers (2015)
  5. Götschel, Sebastian; von Tycowicz, Christoph; Polthier, Konrad; Weiser, Martin: Reducing memory requirements in scientific computing and optimal control (2015)
  6. Götschel, Sebastian; Weiser, Martin: Lossy compression for PDE-constrained optimization: adaptive error control (2015)
  7. Naumann, Uwe; Lotz, Johannes; Leppkes, Klaus; Towara, Markus: Algorithmic differentiation of numerical methods: tangent and adjoint solvers for parameterized systems of nonlinear equations (2015)
  8. Wilcox, Lucas C.; Stadler, Georg; Bui-Thanh, Tan; Ghattas, Omar: Discretely exact derivatives for hyperbolic PDE-constrained optimization problems discretized by the discontinuous Galerkin method (2015)
  9. Carnarius, Angelo; Thiele, Frank; Özkaya, Emre; Nemili, Anil; Gauger, Nicolas R.: Optimal control of unsteady flows using a discrete and a continuous adjoint approach (2013)
  10. Degroote, Joris; Hojjat, Majid; Stavropoulou, Electra; Wüchner, Roland; Bletzinger, Kai-Uwe: Partitioned solution of an unsteady adjoint for strongly coupled fluid-structure interactions and application to parameter identification of a one-dimensional problem (2013)
  11. Farrell, P.E.; Ham, D.A.; Funke, S.W.; Rognes, M.E.: Automated derivation of the adjoint of high-level transient finite element programs (2013)
  12. Kast, Steven M.; Fidkowski, Krzysztof J.: Output-based mesh adaptation for high order Navier-Stokes simulations on deformable domains (2013)
  13. Kunoth, Angela; Schwab, Christoph: Analytic regularity and GPC approximation for control problems constrained by linear parametric elliptic and parabolic PDEs (2013)
  14. Cole-Mullen, Heather; Lyons, Andrew; Utke, Jean: Storing versus recomputation on multiple DAGs (2012)
  15. Krakos, Joshua A.; Wang, Qiqi; Hall, Steven R.; Darmofal, David L.: Sensitivity analysis of limit cycle oscillations (2012)
  16. Özkaya, Emre; Nemili, Anil; Gauger, Nicolas R.: Application of automatic differentiation to an incompressible URANS solver (2012)
  17. Pearson, John W.; Stoll, Martin; Wathen, Andrew J.: Regularization-robust preconditioners for time-dependent PDE-constrained optimization problems (2012)
  18. Bücker, H.Martin; Willkomm, Johannes; Groß, Sven; Fortmeier, Oliver: Discrete and continuous adjoint approaches to estimate boundary heat fluxes in falling films (2011)
  19. Probst, M.; Lülfesmann, M.; Nicolai, M.; Bücker, H.M.; Behr, M.; Bischof, C.H.: Sensitivity of optimal shapes of artificial grafts with respect to flow parameters (2010)
  20. Stumm, Philipp; Walther, Andrea: New algorithms for optimal online checkpointing (2010)

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