|
Organizers |
Wavelet Methods for Elliptic Boundary Value Problems and Control Problems
by
Angela Kunoth
University of Bonn, Institute for Applied Mathematics
While wavelets are primarily employed in signal analysis and image compression, in the past years it has been recognized that this multiscale approach can also be favorably used in the numerical analysis of partial differential and integral equations. There the aim is to investigate the following: Given a prescribed accuracy, how can a problem be efficiently discretized and numerically solved with a minimal number of unknowns ? To use wavelets as a conceptual tool for analysis purposes and the resulting potential has proven to be a successful strategy for obtaining theoretical results, e.g. for preconditioning issues or an adaptive approximation of the solution.
For an example from control theory, I would like to demonstrate how wavelets can be employed for the different issues appearing for this class of problems: from the treatment of 'broken' Sobolev norms over preconditioning questions to the full iterative solution of the resulting weakly coupled systems of differential equations. Particular emphasis is placed on the treatment of boundary conditions.
Date received: February 24, 2001
Copyright © 2001 by the author(s). The author(s) of this document and the organizers of the conference have granted their consent to include this abstract in Atlas Conferences Inc. Document # cafv-40.