Abstract
By means of the limit and jump relations of classical potential theory with respect to the Helmholtz equation a wavelet approach is established on a regular surface. The multiscale procedure is constructed in such a way that the emerging potential kernels act as scaling functions, wavelets are defined via a canonical refinement equation. A tree algorithm for fast computation of a function discretely given on a regular surface is developed based on numerical integration rules. By virtue of the tree algorithm, an efficient numerical method for the solution of Fredholm integral equations involving boundary-value problems of the Helmholtz equation corresponding to (general) regular (boundary) surfaces is discussed in more detail.
Acknowledgment
The Geomathematics Group would like to thank the Graduiertenkolleg “Mathematik und Praxis,” University of Kaiserslautern, and the “Stiftung Rheinland-Pfalz für Innovation,” Mainz, for financial support.