METHOD OF FUNDAMENTAL SOLUTIONS FOR GRAVITY FIELD MODELLING OF THE EARTH
Presented by Dr. Robert CUNDERLIK
Type: Oral presentation
Track: Numerical Methods for Partial Differential Equations
The method of fundamental solutions (MFS) is used to derive the geopotential and its first derivatives from the second derivatives observed by the GOCE satellite mission. The MFS is based on the fundamental solution of a partial differential equation that represents its basis functions. In contrast to the boundary element method, the MFS is an inherent mesh-free method and avoids the numerical integration of singular fundamental solution introducing a fictitious boundary outside the domain, i.e. below the Earth’s surface, where the source points are located. In this study we present how a depth of the fictitious boundary influences accuracy of the obtained numerical solution on or above the Earth’s surface. In case that the source points are located directly on the Earth’s surface we apply ideas of the singular boundary method that isolate singularities of the fundamental solution and its derivatives. As input data we use the Tzz components of the gravity disturbing tensor observed by GOCE satellite mission. They are filtered by the nonlinear diffusion filtering and then unknown coefficients in the source points are obtained by solving linear system of equations. Finally the disturbing potential and gravity disturbances on or above the Earth’s surface are evaluated. The large-scale parallel computations are performed on the cluster with 1TB of the distributed memory. The obtained numerical solutions are compared with the GOCO03S satellite-only geopotential model, i.e. with the solution based on the spherical harmonics approach.