602 RWTH Publication No: 853277        2022       
TITLE Multilevel Representations of Isotropic Gaussian Random Fields on the Sphere
AUTHORS Markus Bachmayr, Ana Djurdjevac
ABSTRACT Series expansions of isotropic Gaussian random fields on S2 with independent Gaussian coefficients and localized basis functions are constructed. Such representations with multilevel localised structure provide an alternative to the standard Karhunen-Loève expansions of isotropic random fields in terms of spherical harmonics. The basis functions are obtained by applying the square root of the covariance operator to spherical needlets. Localization of the resulting covariance-dependent multilevel basis is shown under decay conditions on the angular power spectrum of the random field. In addition, numerical illustrations are given and an application to random elliptic PDEs on the sphere is analyzed.
DOI 10.1093/imanum/drac034
PUBLICATION IMA Journal of Numerical Analysis, Volume 43, Issue 4, July 2023, Pages 1970–2000