Locally adapted tetrahedral meshes play a crucial role in the efficient computation of the numerical solution for many problems. Bisection of individual tetrahedra can be effectively used to formulate algorithms producing nested sequences of conforming, locally adapted tetrahedral meshes starting with an arbitrary coarse conforming mesh. The talk will explore some of the connections and relations among different "bisection of tetrahedra" algorithms. In particular, I will concentrate on an algorithm that involves very simple data-structures and has the property that the repeated bisection of an arbitrary tetrahedron produces at most thirty-six similarity classes of tetrahedra.

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1996-1997 Mathematics in High Performance Computing