Mesh Graph Structure for Longest-Edge Refinement Algorithms.
Ángel Plaza, José Pablo Suárez, Miguel A. Padrón · 1998
. In this paper we introduce and discuss a graph structure associated with longest-edge algorithms (algorithms based on the bisection of triangles by the longest-edge) which can be used to reformulate longest-edge algorithms to develop new algorithms and to design efficient data structures for the refinement/derefinement of 2D and 3D triangulations. Keywords. Longest-edge refinement, bisection, data structures, improvement. 1. Introduction Modern finite element applications make extensive use of adaptive techniques to optimize the number of unknowns with respect to the accuracy of the numerical solutions. For this purpose, the underlying discretization mesh must be locally refined in regions where improved accuracy is needed. Moreover, multigrid or multilevel methods have shown to be of optimal or nearly optimal complexity for the solution of discrete systems arising from a wide range of partial differential equations. Since these methods are based on discretization hierarchies obtain...