Title  An Optimized Treatment for Algorithmic Differentiation of an Important Glaciological FixedPoint Problem 
Publication Type  Journal Article 
Year of Publication  2016 
Authors  Goldberg, D, Narayanan, SHK, Hascoet, L, Utke, J 
Journal  Geoscientific Model Development 
Volume  9 
Pagination  18911904 
Date Published  05/2016 
Abstract  We apply an optimized method to the adjoint generation of a timeevolving land ice model through algorithmic differentiation (AD). The optimization involves a special treatment of the fixedpoint 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 Christianson [1994] for reverse accumulation of fixedpoint 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 memorylimited 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 performance. 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.

DOI  10.5194/gmd918912016, 2016. 
PDF  http://www.mcs.anl.gov/papers/P55160116.pdf 