Using the unstable manifold correction in a Picard iteration to solve the velocity field in higher-order ice-flow models
| Autor: | Brigitte De Smedt, Frank Pattyn, Pieter P. N. de Groen |
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| Rok vydání: | 2010 |
| Předmět: | |
| Zdroj: | Journal of Glaciology. 56:257-261 |
| ISSN: | 1727-5652 0022-1430 |
| DOI: | 10.3189/002214310791968395 |
| Popis: | 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. |
| Databáze: | OpenAIRE |
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