MODELING TANGENTIAL VECTOR FIELDS ON REGULAR SURFACES BY MEANS OF MIE POTENTIALS
Willi Freeden, Carsten Mayer · International Journal of Wavelets Multiresolution and Information Processing · 2007
By means of the limit and jump relations of classical potential theory with respect to the vectorial Helmholtz equation, a wavelet approach is established on a regular surface. The multiscale procedure is constructed in such a way that the emerging scalar, vectorial and tensorial potential kernels act as scaling functions. Corresponding wavelets are defined via a canonical refinement equation. A tree algorithm for fast decomposition of a tangential complex-valued vector field given on a regular surface is developed based on numerical integration rules. Some numerical test examples conclude the paper.