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The representation of difference operators on adaptive sparse grids and its use for singular perturbation problems
by
Pieter W. Hemker
CWI, P.O. Box 94079, 1090 GB Amsterdam, The Netherlans
Coauthors: Frauke Sprengel (SCAI Institute for Algorithms and Scientific Computing, GMD German National Research Center for Information Technology, Schloss Birlinghoven, D-53754 Sankt Augustin, Germany)
We describe methods to approximate functions and differential operators on adaptive sparse grids. We distinguish between several representations of a function on the sparse grid, and we describe how finite difference (FD) operators can be applied to these representations. For general variable coefficient equations on sparse grids, FD operators allow a more efficient operator evaluation than finite element (FE) operators. However, the structure of the FD operators is more complex. In order to examine the possibility to construct efficient solution methods, we analyze the discrete FD (Laplace) operator and compare its hierarchical representation on sparse and on full grids. The analysis gives a motivation for a MG solution algorithm. This is mainly joint work with F. Sprengel.
Date received: February 11, 2000
Copyright © 2000 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 # caen-23.