Sparse spectral BEM for elliptic problems with random input data on a spheroid

Abstract: 

We introduce and analyse a sparse spectral discretization scheme based on spherical harmonics for elliptic problems with random input data on a spheroid. Problems of this type appear in geophysical applications, in particular in data acquisition by satellites. We establish convergence theorems showing that the sparse discretization scheme is superior to the full tensor product discretization scheme in the case of mixed regularity. We prove that analytic regularity of the data implies analytic regularity of the solution to the kth moment equation and illustrate performance of the sparse and full tensor product discretization schemes on several numerical experiments.