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Locally Adapted Tetrahedral Meshes Using Bisection

2000; Society for Industrial and Applied Mathematics; Volume: 22; Issue: 2 Linguagem: Inglês

10.1137/s1064827597323373

1095-7197

Douglas N. Arnold, Arup Mukherjee, Luc Pouly,

Computer Graphics and Visualization Techniques

We present an algorithm for the construction of locally adapted conformal tetrahedral meshes. The algorithm is based on bisection of tetrahedra. A new data structure is introduced, which simplifies both the selection of the refinement edge of a tetrahedron and the recursive refinement to conformity of a mesh once some tetrahedra have been bisected. We prove that repeated application of the algorithm leads to only finitely many tetrahedral shapes up to similarity, and we bound the amount of additional refinement that is needed to achieve conformity. Numerical examples of the effectiveness of the algorithm are presented.