Smoothing by optimisation for a quadrilateral mesh with invalid elements

Finite Elements in Analysis and Design, Elsevier, Vol 34, pp.37-60, 2000

MESHING
RESEARCH
CORNER

T.S. Li, S.M. Wong
Open University of Hong Kong, 30 Good Shepherd Street, Homantin, Hong Kong, China
Y.C. Hon
City University of Hong Kong, 83 Tat Chee Avenue, Hong Kong, China
C.G. Armstrong, R.M. McKeag
The Queen's University of Belfast, Belfast BT9 5AR; N. Ireland, UK

Abstract
In this paper, a smoothing algorithm is introduced which can be applied to a mesh with invalid elements. The first step of the method is to allow those invalid elements to be disconnected from the remaining mesh. This means that the nodes on the invalid elements are all split into two, one on the invalid element, the other on the remaining mesh. The invalid element can then be shaped to become valid. The distance between the two copies of the same node is called offset. In later iterative steps, the nodes will be moved into order to reduce the offset back to zero and at the same time improve the quality of the mesh.