Anisotropic metric-based mesh adaptation for ice flow modelling in Firedrake

Abstract. Glaciological modelling is a computationally challenging task due to its high cost and complexity associated with large spatial- and long time-scale simulations. In this paper, we provide a comprehensive overview of state-of-the-art feature-based anisotropic mesh adaptation methods and demonstrate their effectiveness for time-dependent glaciological modelling using the Python-based Firedrake finite element library. We introduce a novel hybrid time-dependent fixed-point mesh adaptation algorithm that generates a more optimal initial mesh sequence. The algorithm requires approximately 50 % fewer iterations in order to reach mesh convergence, while still controlling spatial error and its temporal distribution. We demonstrate the effectiveness of anisotropic mesh adaptation and the novel fixed-point algorithm on a Marine Ice Sheet Model Intercomparison Project (MISMIP+) experiment. We show that we are able to achieve solution accuracy comparable to a uniform 0.5 km resolution mesh simulations by using a sequence of adapted meshes with, on average, 10–30 times fewer vertices, depending on the sensor field used to drive mesh adaptation. Due primarily to the iterative nature of the mesh adaptation process employed, this translates in practice into a 3–6 times lower overall computational cost.