Abstract
The oblique derivative boundary value problem of potential theory plays an important role in physical geodesy, in particular in modeling the gravitational field. Thereby, the boundary is the known surface of the Earth itself and the measurements can be considered as discrete scattered directional derivatives of the potential on the surface or on parts of that surface. The Runge–Walsh approximation allows the construction of the solution in terms of harmonic splines. These localizing trial functions lead to a system of linear equations whose solution provides directly the—possibly local—solution of the boundary value problem. To obtain a fast matrix-vector multiplication, fast multipole methods are developed for the occurring kernels. In combination with a domain decomposition method that helps to precondition the system of linear equations, an iterative solver can quickly determine the desired approximation. Parameter studies of the numerical realization of the developed algorithms are included as well as global and local examples for the method.
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Gutting, M. Fast multipole accelerated solution of the oblique derivative boundary value problem. Int J Geomath 3, 223–252 (2012). https://doi.org/10.1007/s13137-012-0038-1
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DOI: https://doi.org/10.1007/s13137-012-0038-1