Numerical Tests for the Recovery of the Gravity Field by Fast Boundary Element Methods

The purpose of this paper is to test the applicability of a fast boundary element method in the context of geoid computations of the gravity. The fast multipole method is the method of choice due to the its advantageous property of a fast evaluation in the post-processing. Several sets of trianglar meshes for the approximation of the unit sphere and several modifications of the prediscribed data have been tested. Also, adapted settings of the fast multipole method have been applied. Finally, the potential of fast boundary element method for this kind of applcations is shown. 1 The single layer potential ansatz and the fast multipole method First numerical tests have been executed to evaluate the potential use of fast approximation techniques like the fast multipole method [3], adaptive cross approximation [1] and hierarchical matrix arithmetics [4]. As test problem for geoid computations of the gravity, a single layer potential ansatz 1 4π ∫ Γ 1 |xl − y| t(y)dsy = f(xl) was chosen to recover the predescribed data f(xl) for l = 1, . . . ,M by an unknown density function t. The surface Γ of the unit sphere is approximated by several sets of plane triangles. The unknown density function t(x) is approximated by a linear combination of piecewise constant trial functions,