An improved derefinement algorithm of nested meshes

Abstract

In this paper we present a new version of the derefinement algorithm developed by Plaza et al. (in Numerical Methods in Engineering, Elsevier Science, Amsterdam, 1992, pp. 225–232; in Algorithms, Software, Architecture, Elsevier Science, Amsterdam, 1992, pp. 409–415; A. Plaza, PhD thesis, University of Las Palmas de Gran Canaria, 1993; Commun. Numer. Meth. Engng., 1994, 10, 403–412).1–4 The purpose is to achieve a better derefinement algorithm with a lesser degree of complexity. We present the theoretical study of this improved derefinement algorithm and of the inverse one for refinement. Firstly, our initial version of the derefinement algorithm is summarized. Then we present the refinement algorithm associated with the improved derefinement one. Finally, automatic control of the sequences of irregular nested triangulations is shown by means of the resolution of an unsteady problem. In this problem the initial mesh has only nine nodes and a combination of refinements and derefinements have been applied to approach both the circular domain and the initial solution.