Journal of Applied Mathematics
Volume 2003 (2003), Issue 12, Pages 605-645
Multiscale deformation analysis by Cauchy-Navier wavelets
Geomathematics Group, Department of Mathematics, University of Kaiserslautern, P.O. Box 3049, Kaiserslautern 67653, Germany
Received 6 June 2003; Revised 20 August 2003
Copyright © 2003 M. K. Abeyratne et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
A geoscientifically relevant wavelet approach is established for
the classical (inner) displacement problem corresponding to a
regular surface (such as sphere, ellipsoid, and actual earth
surface). Basic tools are the limit and jump relations of
(linear) elastostatics. Scaling functions and wavelets are
formulated within the framework of the vectorial Cauchy-Navier
equation. Based on appropriate numerical integration rules, a
pyramid scheme is developed providing fast wavelet transform
(FWT). Finally, multiscale deformation analysis is investigated
numerically for the case of a spherical boundary.