An optimized treatment for algorithmic differentiation of an important glaciological fixed-point problem

Abstract : We apply an optimized method to the adjoint generation of a time-evolving land ice model through algorithmic differentiation (AD). The optimization involves a special treatment of the fixed-point iteration required to solve the nonlinear stress balance, which differs from a straightforward application of AD software, and leads to smaller memory requirements and in some cases shorter computation times of the adjoint. The optimization is done via implementation of the algorithm of 5 Christianson [1994] for reverse accumulation of fixed-point problems, with the AD tool OpenAD. For test problems, the optimized adjoint is shown to have far lower memory requirements, potentially enabling larger problem sizes on memory-limited machines. In the case of the land ice model, implementation of the algorithm allows further optimization by having the adjoint model solve a sequence of linear systems with identical (as opposed to varying) matrices, greatly improving per-10 formance. The methods introduced here will be of value to other efforts applying AD tools to ice models, particularly ones which solve a " hybrid " shallow ice / shallow shelf approximation to the Stokes equations.
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Contributor : Laurent Hascoet <>
Submitted on : Friday, December 9, 2016 - 3:54:20 PM
Last modification on : Sunday, March 3, 2019 - 5:38:02 PM

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Daniel Goldberg, Sri Hari Krishna Narayanan, Laurent Hascoet, Jean Utke. An optimized treatment for algorithmic differentiation of an important glaciological fixed-point problem. Geoscientific Model Development, European Geosciences Union, 2016, 9 (5), pp.27. ⟨hal-01413295⟩

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