3D anisotropic mesh refinement in compliance with a general metric specification

Abstract

A simple and efficient anisotropic refinement procedure for the three-dimensional tetrahedral element mesh based on successive bisection of edges is proposed. Refinement is done by dividing lines of the mesh based on the lengths calculated on three points as specified by the metric tensor along the direction of the line. To obtain the best mesh quality, the subdivision of line segments is performed in the sequence according to the length of the line segments to be divided. Such an order of priority can be determined by a simple sorting process on all the line segments for which refinement is needed. This list of ordered line segments has to be updated from time to time to take into account the new line segments generated during the subdivision process. From the examples studied, the CPU time for mesh refinement seems to bear a linear relationship with the number of elements generated, with a refinement rate of up to 30000 elements/s on an IBM Power Station 3BT. Shape optimization procedures can be applied to the refined mesh to further improve the quality of the elements. The refinement scheme is useful as part of a general three-dimensional mesh generation package, or as the mesh refinement module in an adaptive finite element analysis. © 2001 Elsevier Science B.V. All rights reserved.