Mesh quality improvement: radial basis functions approach

Abstract

In this paper, we present a novel simple method, based on an implementation of space mapping technique, for improvement of the quality of tetrahedral and hexahedral meshes. The same approach is used for surface meshes where geometry of the initial surface mesh is preserved by a local mesh improvement such that new positions of the interior nodes of the mesh remain on the original discrete surface. The proposed method can be used in the pre-processing stage for subsequent studies (finite element analysis, computer graphics, etc.) by providing better input parameters for these processes. Experimental results are included to demonstrate the functionality of our method.

Keywords:

• space mapping
• radial basis function
• mesh improvement
• surface mesh
• volume mesh

2000 AMS Subject Classification :

• 65D18
• 68U05
• 68U07
• 65D10
• 65D05

Acknowledgements

The authors would like to thank Julien Dompierre for providing the tetrahedral benchmark meshes. They would also like to acknowledge the anonymous reviewers for their generous comments and suggestions. Thanks are also due to Andrey Sherstuk for improvement of the manuscript.