Solving ordinary differential equations I (2nd revised. ed.): nonstiff problems
Solving ordinary differential equations I (2nd revised. ed.): nonstiff problems
ACM Transactions on Mathematical Software (TOMS)
Second Order Methods for Optimal Control of Time-Dependent Fluid Flow
SIAM Journal on Control and Optimization
Perspectives in Flow Control and Optimization
Perspectives in Flow Control and Optimization
A differentiation-enabled Fortran 95 compiler
ACM Transactions on Mathematical Software (TOMS)
Efficient numerical solution of parabolic optimization problems by finite element methods
Optimization Methods & Software
Evaluating Derivatives: Principles and Techniques of Algorithmic Differentiation
Evaluating Derivatives: Principles and Techniques of Algorithmic Differentiation
MultiStage Approaches for Optimal Offline Checkpointing
SIAM Journal on Scientific Computing
Minimal Repetition Dynamic Checkpointing Algorithm for Unsteady Adjoint Calculation
SIAM Journal on Scientific Computing
Euro-Par'06 Proceedings of the 12th international conference on Parallel Processing
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Frequently, the computation of derivatives for optimizing time-dependent problems is based on the integration of the adjoint differential equation. For this purpose, the knowledge of the complete forward solution may be required. Similar information is needed in the context of a posteriori error estimation with respect to a given functional. In the area of flow control, especially for three dimensional problems, it is usually impossible to keep track of the full forward solution due to the lack of storage capacities. Further, for many problems, adaptive time-stepping procedures are needed toward efficient integration schemes in time. Therefore, standard optimal offline checkpointing strategies are usually not well suited in that framework. In this paper we present two algorithms for an online checkpointing procedure that determines the checkpoint distribution on the fly. We prove that these approaches yield checkpointing distributions that are either optimal or almost optimal with only a small gap to optimality. Numerical results underline the theoretical results.