Anisotropic Radial Basis Function Methods for Continental Size Ice Sheet Simulations

TL;DR

This paper introduces anisotropic radial basis function methods for simulating large-scale ice sheet dynamics, demonstrating improved accuracy and efficiency over traditional methods, especially for continental-sized ice sheets.

Contribution

The paper develops and applies anisotropic radial basis function methods with partition of unity for efficient, accurate large-scale ice sheet simulations, surpassing standard isotropic approaches.

Findings

Enhanced velocity simulation accuracy on large ice sheets.

Anisotropic RBF methods outperform isotropic RBF in high aspect ratio scenarios.

Partition of unity improves computational efficiency.

Abstract

In this paper we develop and implement anisotropic radial basis function methods for simulating the dynamics of ice sheets and glaciers. We test the methods on two problems: the well-known benchmark ISMIP-HOM B that corresponds to a glacier size ice and a synthetic ice sheet whose geometry is inspired by the EISMINT benchmark that corresponds to a continental size ice sheet. We illustrate the advantages of the radial basis function methods over a standard finite element method. We also show how the use of anisotropic radial basis functions allows for accurate simulation of the velocities on a large ice sheet, which was not possible with standard isotropic radial basis function methods due to a large aspect ratio between the ice length and the ice thickness. Additionally, we implement a partition of unity method in order to improve the computational efficiency of the radial basis function methods.