Abstracts for the Conference on
Grid Adaptivity in Computational PDEs,
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Radial splines and moving grids

D Djokovic & R van Damme

University of Twente, Department of Applied Mathematics
P.O. Box 217, 7500 AE Enschede, The Netherlands
email: djokovic@math.utwente.nl

Abstract

The choice of using radial splines to solve partial differential equations (PDE) was made because of the simplicity of these functions: They do not require a triangulation, which is a nice feature, especially in higher dimensions. When you solve a PDE (e.g. the wave equation with a localised initial condition) you would like to see that the grid 'moves along' with the solution, or, in the case where shocks are being built up, the grid should concentrate around this shock.

There is another good reason for using radial splines. Radial splines are special solutions of the so-called optimal recovery problem. A generalisation of that problem leads to a very natural way for letting the grid move.

The use of radial splines also have a negative side effect: the linear systems that have to be solved usually are ill-conditioned. So in order to overcome this problem we have to find efficient preconditioners.

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Last modified Fri Jun 21 19:19:12 GB-Eire 1996 (DBD)