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

• Main Authors: De Smedt, Bert, Pattyn, Frank, de Groen, Pieter
• Format: Article in Journal/Newspaper
• Language: English
• Published: 2010
• Subjects: Géologie et minéralogie; Journal of Glaciology
• Online Access: 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

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