On curvature element-size control in metric surface mesh generation

A new procedure is suggested for controlling the element-size distribution of surface meshes during automatic adaptive surface mesh generation. In order to ensure that the geometry of the surface can be accurately cap- tured, the curvature properties of the surface are rst analysed. Based on the principal curvatures and principal directions of the surface, the curvature element-size requirement is de ned in the form of a metric tensor eld. This element-size controlling metric tensor eld, which can either be isotopic or anisotopic depending on the user requirement, is then employed to control the element size distribution during mesh generation. The suggested procedure is local, adaptive and can be easily used with many parametric surface mesh gen- erators. As the proposed scheme de nes the curvature element-size requirement in an implicit manner, it can be combined with any other user de ned element size speci cation using the standard metric intersection procedure. This eventually leads to a simple implementation procedure and a high computational e ciency. Numerical examples indicate that the new procedure can e ectively control the element size of surface meshes in the cost of very little additional computational e ort