Adaptive Multigrid Methods for coupled ice sheet and ice shelf models
Final Report Abstract
To better evaluate sea level rise in a climate change regime, it is crucial to develop modern ice flow models that are mechanically complete while being computationally tractable. To meet this demand, two paths of research were followed in this project. The first path focuses on the numerical modelling while the second one focuses on the mechanical modelling. The first path of research was to develop a fast adaptive multigrid Newton solver for the linearly combined SIA+SSA model, which describes the ice flows of marine ice sheets. For that, the truncated nonsmooth Newton multigrid method (TNNMG) proved to be efficient because i) it treats the non-smoothness by convexity rather than by regularization which is known to usually deteriorate the convergence speed of the solver, ii) its convergence was found to be insensitive to local refinements. Combined to an heuristic mesh adaptive refinement, the overall method proved its worth when running the model for the experiments of the marine ice sheet model inter-comparison project MISMIP (2D and 3D). The second path of research consisted of developing a new hybrid model that can recover the non-linear coupling between the SIA and SSA flow components (in opposition to the linearly combined SIA+SSA). For that, a multilayer generalisation of the SSA was derived. Advantageously, this new model keeps intact the mathematical structure of the SSA equation such that the TNNMG solver could be easily generalized column-wise. When running the model for the ISMIP-HOM inter-comparison benchmark experiments, the multilayer solutions have shown good agreement with solutions of the common nonsimplied 3D models, while being computationally cheaper.
Publications
- A Newton multigrid method for a hybrid shallow ice model based on an energy minimization approach. Proceeding to SCA 2012, Las-Vegas, USA
G. Jouvet, E. Bueler, C. Gräser, R. Kornhuber
- Steady, shallow ice sheets as obstacle problems: well-posedness and nite element approximation. SIAM Journal on Applied Mathematics, 72(4), 1292-1314, 2012
G. Jouvet, E. Bueler
(See online at https://doi.org/10.1137/110856654) - An adaptive Newton multigrid method for a model of marine ice sheets. Journal of Computational Physics, Vol. 252, 2013
G. Jouvet, C. Gräser
(See online at https://doi.org/10.1016/j.jcp.2013.06.032) - Grounding-line migration in plan-view marine ice-sheet models: results of the ice2sea MISMIP3d intercomparison. Journal of Glaciology, 59(215), 2013
F. Pattyn, L. Perichon, G. Durand, L. Favier, O. Gagliardini, R. Hindmarsh, T. Zwinger, T. Albrecht, S. Cornford, D. Docquier, J. Fuerst, D. Goldberg, G. H. Gudmundsson, A. Humbert, M. Huetten, P. Huybrechts, G. Jouvet, T. Kleiner, E. Larour, D. Martin, M. Morlighem, T. Payne, D. Pollard, M. Rueckamp, O. Rybak, H. Seroussi, M. Thoma, N. Wilkens
(See online at https://doi.org/10.3189/2013JoG12J129) - Modelling the trajectory of the corpses of mountaineers who disappeared in 1926 on Aletschgletscher. Journal of Glaciology, 60(220), 2014
G. Jouvet, M. Funk
(See online at https://doi.org/10.3189/2014JoG13J156) - A multilayer ice-flow model generalising the Shallow Shelf Approximation. Journal of Fluid Mechanics, Vol 764, 10 February 2015, pp. 26-51
G. Jouvet
(See online at https://doi.org/10.1017/jfm.2014.689)
