A 3D derefinement algorithm for tetrahedral grids

Abstract

A novel three-dimensional derefinement algorithm for nested tetrahedral grids based on bisection is presented and discussed. The algorithm is the inverse algorithm of the adaptive refinement scheme presented by Plaza and Carey (1996), and improved in (Plaza and Carey, 1997). Both refinement schemes are fully automatic. The refinement algorithm can be applied to any initial tetrahedral mesh without any preprocessing. Similarly the derefinement scheme can be used to get a coarser mesh from a sequence of nested tetrahedral meshes obtained by successive application of the refinement algorithm. The way in which the edges of each tetrahedron are ordered is compatible with the order in each face, and this makes it possible to write algorithms in such a way that only this order has to be taken into account to perform iteratively the subdivision or coarsening of each tetrahedron. The refinement and derefinement schemes can be easily combined to deal with time dependent problems.