Generation of Gaussian random fields on the sphere
Typ
Examensarbete för masterexamen
Program
Publicerad
2019
Författare
Jansson, Erik
Modellbyggare
Tidskriftstitel
ISSN
Volymtitel
Utgivare
Sammanfattning
In order to approximate solutions to a fractional elliptic SPDE used to generate
random fields on the sphere with Matérn covariance, a sinc quadrature approach
combined with a surface finite element method is used. The right hand side of
the equation is replaced with trace class noise on the sphere. Error bounds in
L2(
; L2(S2))-norm are proved using energy estimates and an Aubin–Nitsche duality
type argument. P-almost surely asymptotic error estimates are shown. Some
properties of the exact solution to both trace class right hand side and white noise
right hand side are discussed and the relation between the mean square differentiability
and the parameters of the equation are established. Some properties of white noise
on the sphere are considered. The method is implemented in FEniCS and parts of
the algorithm is verified which agree with the theoretical results.