Anisotropic Radial Basis Function Methods for Continental Size Ice Sheet Simulations

In this paper we develop and implement anisotropic radial basis function methods for simulating the dynamics of ice sheets and glaciers. We test our methods on several well established benchmark tests: ISMIP-HOM B and D that correspond to a glacier size ice and modified EISMINT that corresponds to a continental size ice sheet. We illustrate the advantage of the radial basis function methods over a standard finite element method. Also we show how the use of anisotropic radial basis functions allows for accurate simulating the velocity of a large ice sheet, which was not possible with standard isotropic radial basis function methods due to large aspect ratio between ice width and ice thickness. Additionally, we implement the partition of unity method in order to improve the computational efficiency of the radial basis function methods.