Anisotropic Radial Basis Function Methods for Continental Size Ice Sheet Simulations
This work addresses the computational challenge of simulating large-scale ice sheet dynamics for glaciologists, offering a method that handles extreme aspect ratios more accurately than existing approaches.
The authors developed anisotropic radial basis function (RBF) methods for ice sheet simulations, demonstrating accurate velocity predictions on continental-scale ice sheets where isotropic RBFs failed due to large aspect ratios. The method outperformed standard finite element methods on benchmark problems.
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.