Discrete adjoints on many cores Algorithmic differentiation of accelerated fluid simulations
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Simulations are used in science and industry to predict the performance of technical systems. Adjoint derivatives of these simulations can reveal the sensitivity of the system performance to changes in design or operating conditions, and are increasingly used in shape optimisation and uncertainty quantification. Algorithmic differentiation (AD) by source-transformation is an efficient method to compute such derivatives. AD requires an analysis of the computation and its data flow to produce efficient adjoint code. One important step is the activity analysis that detects operations that need to be differentiated. An improved activity analysis is investigated in this thesis that simplifies build procedures for certain adjoint programs, and is demonstrated to improve the speed of an adjoint fluid dynamics solver. The method works by allowing a context-dependent analysis of routines. The ongoing trend towards multi- and many-core architectures such as the Intel XeonPhi is creating challenges for AD. Two novel approaches are presented that replicate the parallelisation of a program in its corresponding adjoint program. The first approach detects loops that naturally result in a parallelisable adjoint loop, while the second approach uses loop transformation and the aforementioned context-dependent analysis to enforce parallelisable data access in the adjoint loop. A case study shows that both approaches yield adjoints that are as scalable as their underlying primal programs. Adjoint computations are limited by their memory footprint, particularly in unsteady simulations, for which this work presents incomplete checkpointing as a method to reduce memory usage at the cost of a slight reduction in accuracy. Finally, convergence of iterative linear solvers is discussed, which is especially relevant on accelerator cards, where single precision floating point numbers are frequently used and the choice of solvers is limited by the small memory size. Some problems that are particular to adjoint computations are discussed.
AuthorsHückelheim, Jan Christian
- Theses