Adaptive finite element methods for parabolic problems. I.: a linear model problem
SIAM Journal on Numerical Analysis
Stability of higher-order Hood-Taylor methods
SIAM Journal on Numerical Analysis
Adaptive finite element methods for parabolic problems II: optimal error estimates in L∞L2 and L∞L∞
SIAM Journal on Numerical Analysis
ACM Transactions on Mathematical Software (TOMS)
Perspectives in Flow Control and Optimization
Perspectives in Flow Control and Optimization
Iterative Methods for Sparse Linear Systems
Iterative Methods for Sparse Linear Systems
New Algorithms for Optimal Online Checkpointing
SIAM Journal on Scientific Computing
Online checkpointing with improved worst-case guarantees
ICALP'13 Proceedings of the 40th international conference on Automata, Languages, and Programming - Volume Part I
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The computation of derivatives for the optimization of time-dependent flow problems is based on the integration of the adjoint differential equation. For this purpose, the knowledge of the complete forward solution is required. Similar information is needed for 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 store the full forward solution due to the lack of memory capacities. Additionally, adaptive time-stepping procedures are needed for efficient integration schemes in time. Therefore, standard optimal offline checkpointing strategies are usually not well-suited in that framework. We present a new online procedure for determining the checkpoint distribution on the fly. Complexity estimates and consequences for storing and retrieving the checkpoints using parallel I/O are discussed. The resulting checkpointing approach is integrated in HiFlow, a multipurpose parallel finite-element package with a strong emphasis in computational fluid dynamic, reactive flows and related subjects. Using an adjoint-based error control for prototypical three dimensional flow problems, numerical experiments demonstrate the effectiveness of the proposed approach.