Using the unstable manifold correction in a Picard iteration to solve the velocity field in higher-order ice-flow models
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...
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ftunivbruxelles:oai:dipot.ulb.ac.be:2013/184743 2023-05-15T16:57:28+02:00 Using the unstable manifold correction in a Picard iteration to solve the velocity field in higher-order ice-flow models De Smedt, Bert Pattyn, Frank de Groen, Pieter 2010-06 1 full-text file(s): application/pdf http://hdl.handle.net/2013/ULB-DIPOT:oai:dipot.ulb.ac.be:2013/184743 https://dipot.ulb.ac.be/dspace/bitstream/2013/184743/3/doi_168370.pdf en eng uri/info:doi/10.3189/002214310791968395 uri/info:scp/77956974119 https://dipot.ulb.ac.be/dspace/bitstream/2013/184743/3/doi_168370.pdf http://hdl.handle.net/2013/ULB-DIPOT:oai:dipot.ulb.ac.be:2013/184743 1 full-text file(s): info:eu-repo/semantics/restrictedAccess Journal of Glaciology, 56 (196 Géologie et minéralogie info:eu-repo/semantics/article info:ulb-repo/semantics/articlePeerReview info:ulb-repo/semantics/openurl/article 2010 ftunivbruxelles 2022-06-12T22:09:17Z 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. SCOPUS: ar.j info:eu-repo/semantics/published Article in Journal/Newspaper Journal of Glaciology DI-fusion : dépôt institutionnel de l'Université libre de Bruxelles (ULB) |
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Open Polar |
collection |
DI-fusion : dépôt institutionnel de l'Université libre de Bruxelles (ULB) |
op_collection_id |
ftunivbruxelles |
language |
English |
topic |
Géologie et minéralogie |
spellingShingle |
Géologie et minéralogie De Smedt, Bert Pattyn, Frank de Groen, Pieter Using the unstable manifold correction in a Picard iteration to solve the velocity field in higher-order ice-flow models |
topic_facet |
Géologie et minéralogie |
description |
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. SCOPUS: ar.j info:eu-repo/semantics/published |
format |
Article in Journal/Newspaper |
author |
De Smedt, Bert Pattyn, Frank de Groen, Pieter |
author_facet |
De Smedt, Bert Pattyn, Frank de Groen, Pieter |
author_sort |
De Smedt, Bert |
title |
Using the unstable manifold correction in a Picard iteration to solve the velocity field in higher-order ice-flow models |
title_short |
Using the unstable manifold correction in a Picard iteration to solve the velocity field in higher-order ice-flow models |
title_full |
Using the unstable manifold correction in a Picard iteration to solve the velocity field in higher-order ice-flow models |
title_fullStr |
Using the unstable manifold correction in a Picard iteration to solve the velocity field in higher-order ice-flow models |
title_full_unstemmed |
Using the unstable manifold correction in a Picard iteration to solve the velocity field in higher-order ice-flow models |
title_sort |
using the unstable manifold correction in a picard iteration to solve the velocity field in higher-order ice-flow models |
publishDate |
2010 |
url |
http://hdl.handle.net/2013/ULB-DIPOT:oai:dipot.ulb.ac.be:2013/184743 https://dipot.ulb.ac.be/dspace/bitstream/2013/184743/3/doi_168370.pdf |
genre |
Journal of Glaciology |
genre_facet |
Journal of Glaciology |
op_source |
Journal of Glaciology, 56 (196 |
op_relation |
uri/info:doi/10.3189/002214310791968395 uri/info:scp/77956974119 https://dipot.ulb.ac.be/dspace/bitstream/2013/184743/3/doi_168370.pdf http://hdl.handle.net/2013/ULB-DIPOT:oai:dipot.ulb.ac.be:2013/184743 |
op_rights |
1 full-text file(s): info:eu-repo/semantics/restrictedAccess |
_version_ |
1766049031948075008 |