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On simplicial grid refinement in N dimensions
and the optimal number of congruence classes
J Bey
Math. Inst. Univ. Tuebingen,
Auf der Morgenstelle 10,
72076 Tuebingen,
Germany
Abstract
We present a refinement algorithm for unstructured simplicial grids in
$N$ dimensions. The triangulations generated are stable and consistent,
in the sense that the flatness of all elements is uniformly bounded and
any two adjacent elements of the same refinement level
meet at a common lower-dimensional subsimplex. For any initial simplex $T$,
the elements generated by successive refinement of $T$ can be divided into
at most $N!/2$ congruence classes, independent of the refinement depth.
We prove that this number is optimal, i.e. any
refinement algorithm of the same kind produces at least the same number
of congruence classes for almost all initial simplices $T$.
Thus, in comparison with other methods, the proposed algorithm may
be advantageous in adaptive finite element or finite volume computations,
where the efficiency of several time-consuming tasks can be improved by
calculating and storing just once element related data that depend
on the congruence class only.
Last modified Fri Jun 21 19:19:10 GB-Eire 1996
(DBD)