Generalized multiresolution analysis on unstructured grids |
| |
| Authors: | Friederike Schr?der-Pander Thomas Sonar and Oliver Friedrich |
| |
| Institution: | (1) Institut für Angewandte Mathematik, Universit?t Hamburg, Bundesstrasse 55, 20146 Hamburg, Germany , DE;(2) Faculteit Toegepaste Wetenschappen, Universiteit Gent, Jozef Plateaustraat 22, 9000 Gent, Belgium , BE;(3) Institut für Analysis, TU Braunschweig, Pockelsstrasse 14, 38106 Braunschweig, Germany , DE |
| |
| Abstract: | Summary. Efficiency of high-order essentially non-oscillatory (ENO) approximations of conservation laws can be drastically improved
if ideas of multiresolution analysis are taken into account. These methods of data compression not only reduce the necessary
amount of discrete data but can also serve as tools in detecting local low-dimensional features in the numerical solution.
We describe the mathematical background of the generalized multiresolution analysis as developed by Abgrall and Harten in
14], 15] and 3]. We were able to ultimately reduce the functional analytic background to matrix-vector operations of linear
algebra. We consider the example of interpolation on the line as well as the important case of multiresolution analysis of
cell average data which is used in finite volume approximations. In contrast to Abgrall and Harten, we develop a robust agglomeration
procedure and recovery algorithms based on least-squeare polynomials. The efficiency of our algorithms is documented by means
of several examples.
Received April 4, 1998 / Revised version August 2, 1999 / Published online June 8, 2000 |
| |
| Keywords: | Mathematics Subject Classification (1991): 65M55 |
| 本文献已被 SpringerLink 等数据库收录！ |
|
