29 Aug 2023
 | 29 Aug 2023
Status: this preprint is open for discussion.

The Newton solver with step size control is faster than the Picard iteration in simulating ice flow (FEniCS-full-Stokes v1.1.0)

Niko Schmidt, Angelika Humbert, and Thomas Slawig

Abstract. Solving the momentum balance is the computationally expensive part of simulating the evolution of ice sheets. The momentum balance is described by the nonlinear full-Stokes equations. As a nonlinear problem, they are solved iteratively. We solve these equations with Newton's method. We obtain global superlinear convergence by using a step size control. For the step size control, we need a minimization problem. Solving the full-Stokes equations is equivalent to minimizing a specific convex function. We use the Armijo and the exact step sizes for Newton's method. Additionally, we use the exact step sizes for the Picard iteration. Finally, we compare the Picard iteration and the variants of Newton's method in two benchmark experiments, called ISMIP-HOM experiments A and B. These experiments consist of a more realistic domain and are designed to test the quality of ice models. We obtain that Newton's method and the Picard iteration with exact step sizes greatly reduce the necessary number of iterations.

Niko Schmidt et al.

Status: open (until 02 Nov 2023)

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  • RC1: 'Comment on egusphere-2023-1569', Anonymous Referee #1, 27 Sep 2023 reply

Niko Schmidt et al.

Niko Schmidt et al.


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Short summary
Future sea-level rise is of big significance for coastal regions. The melting and acceleration of glaciers plays a major role in sea-level change. Computer simulation of glaciers costs a lot of computational resources. In this publication, we test a new way of simulating glaciers. This approach produces the same results but has the advantage that it needs much less computation time. As simulations can be obtained with fewer computation resources, higher resolution and physics becomes affordable.