3D mesh refinement in compliance with a specified node spacing function

Abstract

A simple and efficient refinement procedure for the three-dimensional tetrahedral element mesh based on successive bisection of edges is proposed. The quality of the elements generated can be guaranteed if the subdivision 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 of the new line segments generated during the subdivision process.

From the examples studied, the CPU time for mesh refinement bears a linear relationship with the number of elements generated, with a refinement rate of more than 50 000 elements per second on a 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.