# Computational Challenges in Ice Sheet Simulations

**Josefin Ahlkrona
**

Division of Scientific Computing

Department of Information Technology

Uppsala University

Uppsala

### Abstract:

This talk is meant to spark a following discussion between visiting experts in ice sheet modeling and the experts in numerical methods at TDB. Three fundamental, open, problems of computational ice sheet dynamics are presented: large non-linear systems, free surface problems stability, and moving interfaces.

Problem 1: The velocity of ice is given by the solution to the p-Stokes equations, which is a non-linear version of the Stokes equations. The standard approach in ice sheet models is to apply a Newton or Picard iteration, in which a linear Stokes system is solved in each iteration. For finite elements, 80 - 90 % of the simulation time may be spent in the repeated assembly.

Problem 2: Ice dynamics is a free surface problem. The shape of the ice body evolves according to an equation on convection form, in which the velocity of the ice enters as coefficients. Due to non-linear feedbacks, this equation behaves as a parabolic equation. Unfortunately, implicit time-stepping is not possible as it is costly to compute the velocity.

Problem 3: The ice/atmosphere interface, the grounding line, the calving front, and ice margins are all examples of moving interfaces in ice sheet dynamics which are important to track accurately. The standard approach in ice sheet modeling today is frequent re-meshing or keeping interfaces fixed.