Ice flow forced by gravity is governed by the full Stokes (FS) equations, which are computationally expensive to solve due to the nonlinearity introduced by the rheology. Therefore, approximations to the FS equations are commonly used, especially when modeling a marine ice sheet (ice sheet, ice shelf, and/or ice stream) for 103 years or longer. The shallow ice approximation (SIA) and shallow shelf approximation (SSA) are commonly used but are accurate only for certain parts of an ice sheet. Here, we report a novel way of iteratively coupling FS and SSA that has been implemented in Elmer/Ice and applied to conceptual marine ice sheets. The FS-SSA coupling appears to be very accurate; the relative error in velocity compared to FS is below 0.5 % for diagnostic runs and below 5 % for prognostic runs. Results for grounding line dynamics obtained with the FS-SSA coupling are similar to those obtained from an FS model in an experiment with a periodical temperature forcing over 3000 years that induces grounding line advance and retreat. The rapid convergence of the FS-SSA coupling shows a large potential for reducing computation time, such that modeling a marine ice sheet for thousands of years should become feasible in the near future. Despite inefficient matrix assembly in the current implementation, computation time is reduced by 32 %, when the coupling is applied to a 3-D ice shelf..@en

We describe our recent attempts to produce effective parallel block preconditioners by employing the open source finite element package Elmer. Two example problems corresponding to the computational simulation of land ice flow and the high-fidelity modelling of small acoustical devises are considered. We present features which make these problems challenging from the viewpoint of the preconditioner design and also demonstrate how the requirement of achieving scalability can even lead to rethinking the overall formulation of the problem. The utility of the preconditioners implemented has been explored experimentally.@en

The Fourth IPCC Assessment Report concluded that ice sheet flow models, in their current state, were unable to provide accurate forecast for the increase of polar ice sheet discharge and the associated contribution to sea level rise. Since then, the glaciological community has undertaken a huge effort to develop and improve a new generation of ice flow models, and as a result a significant number of new ice sheet models have emerged. Among them is the parallel finite-element model Elmer/Ice, based on the open-source multi-physics code Elmer. It was one of the first full-Stokes models used to make projections for the evolution of the whole Greenland ice sheet for the coming two centuries. Originally developed to solve local ice flow problems of high mechanical and physical complexity, Elmer/Ice has today reached the maturity to solve larger-scale problems, earning the status of an ice sheet model. Here, we summarise almost 10 yr of development performed by different groups. Elmer/Ice solves the full-Stokes equations, for isotropic but also anisotropic ice rheology, resolves the grounding line dynamics as a contact problem, and contains various basal friction laws. Derived fields, like the age of the ice, the strain rate or stress, can also be computed. Elmer/Ice includes two recently proposed inverse methods to infer badly known parameters. Elmer is a highly parallelised code thanks to recent developments and the implementation of a block preconditioned solver for the Stokes system. In this paper, all these components are presented in detail, as well as the numerical performance of the Stokes solver and developments planned for the future.

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