Exploiting symmetries when solving the heat equation on a spherical icosahedral grid

Abstract This thesis considers certain symmetries in partial dierential,equation (PDE) op- erators, and how to exploit these in order to improve computational aspects. Par- ticularly, we study generalized Fourier transforms (GFTs) and how to use them in finite element discretizations of PDEs in geometrically symmetrical domains. GFTs can be used to block-diagonalize operators with certain symmetric properties, and we take advantage of this when solving linear systems of equations. A sparse variant of the GFT, which exploits equivariance and sparsity in the opera-