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Using the unstable manifold correction in a Picard iteration to solve the velocity field in higher-order ice-flow models

par De Smedt, Bert;Pattyn, Frank ;de Groen, Pieter
Référence Journal of Glaciology, 56, 196, page (257-261)
Publication Publié, 2010-06

Article révisé par les pairs

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Résumé :

We address the usefulness of the unstable manifold correction (UMC) in a Picard iteration for the solution of the velocity field in higher-order ice-flow models. We explain under-and overshooting and how one can remedy them. We then discuss the rationale behind the UMC, initially developed to remedy overshooting, and how it was previously introduced in a Picard iteration to calculate the velocity field in higher-order models. Using a laminar-flow experiment with two higher-order model implementations, we demonstrate that it is not overshooting, but undershooting, that is the main problem when using a proper implementation for the calculation of the velocity field in higher-order models. We also consider a variant of the original UMC algorithm that often enables a relatively fast solution, but is theoretically less sound. Therefore, neither the variant nor the original algorithm is suited for these problems. We present a more appropriate, stable and simple relaxed Picard algorithm and demonstrate that, compared to the true Picard iteration and the variant of the original UMC algorithm, it results in a faster solution of the velocity field in higher-order models for problems with real data.