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https://doi.org/10.5194/egusphere-2023-1569
https://doi.org/10.5194/egusphere-2023-1569
29 Aug 2023
 | 29 Aug 2023

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.

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Journal article(s) based on this preprint

25 Jun 2024
Assessing the benefits of approximately exact step sizes for Picard and Newton solver in simulating ice flow (FEniCS-full-Stokes v.1.3.2)
Niko Schmidt, Angelika Humbert, and Thomas Slawig
Geosci. Model Dev., 17, 4943–4959, https://doi.org/10.5194/gmd-17-4943-2024,https://doi.org/10.5194/gmd-17-4943-2024, 2024
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Future sea-level rise is of big significance for coastal regions. The melting and acceleration...
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