Multiscale Solution of Oblique Boundary-Value Problems by Layer Potentials
With the aid of classical results of potential theory, the limit- and jump-relations, a multiscale framework on geodetically relevant regular surfaces is established corresponding to oblique derivative data. By the oblique distance to the regular surface a scale factor in the kernel functions of the limit- and jump-operators is introduced, which connects these intergral kernels with the theory of scaling functions and wavelets.
As applications of the wavelet approach some numerical examples are presented on an ellipsoid of revolution. At the end we discuss a fast multiscale representation of the solution of the (exterior) oblique derivative (boundary—value) problem corresponding to geoscientifically relevant surfaces. A local as well as global reconstruction of the gravitational potential model EGM96 on the reference ellipsoid will illustrate the power of this appoach.
KeywordsScaling functions and wavelets on regular surfaces potential operators jump relations multiscale analysis (exterior) oblique derivative problem of potential theory
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