Adaptive triangular element generation and optimization-based smoothing, Part 1: On the plane

Abstract

A systematic approach to adaptive triangular element generation and optimization-based smoothing on the plane is presented in this paper. The approach starts from the input geometry of a rough triangular element that needs to be remeshed in order to meet the desired mesh density. Several density specifying geometries are proposed to specify the desired mesh density distribution in a closed form. To reduce the geometrical error that is inevitable in remeshing, the boundary edges are interpolated by the third-order chord-length spline curves. A virtual grid method is employed in calculating the desired mesh density at an arbitrary point. In order to improve mesh quality, triangular elements are recursively modified through the local transformation processes including face splitting, edge splitting, edge collapsing and edge swapping together with the physically-based smoothing process. Finally, optimization of local mesh quality is carried out by an optimal nodal smoothing scheme. Several application examples are given to show the characteristics of the presented approach.