Computational optimization in solving the geodetic boundary value problems

Abstract

<p style='text-indent:20px;'>The finite volume method (FVM) as a numerical method can be straightforwardly applied for global as well as local gravity field modelling. However, to obtain precise numerical solutions it requires very refined discretization which leads to large-scale parallel computations. To optimize such computations, we present a special class of numerical techniques that are based on a physical decomposition of the computational domain. The domain decomposition (DD) methods like the Additive Schwarz Method are very efficient methods for solving partial differential equations. We briefly present their mathematical formulations, and we test their efficiency in numerical experiments dealing with gravity field modelling. Since there is no need to solve special interface problems between neighbouring subdomains, in our applications we use the overlapping DD methods. Finally, we present the numerical experiment using the FVM approach with 93 312 000 000 unknowns that would not be possible to perform using available computing facilities without aforementioned methods that can efficiently reduce a numerical complexity of the problem.