3D refinement/derefinement algorithm for solving evolution problems

Abstract

In the present study, a novel three-dimensional refinement/derefinement algorithm for nested tetrahedral grids based on bisection is presented. The algorithm is based on an adaptive refinement scheme and on an inverse algorithm introduced by the authors. These algorithms work first on the skeleton of the 3D triangulation, the set of the triangular faces. Both schemes are fully automatic. The refinement algorithm can be applied to any initial tetrahedral mesh without any preprocessing. The non-degeneracy of the meshes obtained by this algorithm has been experimentally shown. 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. In this case, the algorithm presents a self-improvement quality property: the minimum solid angle after derefining is not less than the minimum solid angle of the refined input mesh. The refinement and derefinement schemes can be easily combined to deal with time dependent problems. These combinations depend only on a few parameters that are fixed into the input data by the user. Here we present a simulation test case for these kind of problems. The main features of these algorithms are summarized at the end.