Accounting for curved domains in mesh adaptation

This paper presents a procedure to project vertices created by re ning straight sided tetrahedra to appropriate locations on curved model boundaries. Although many of the vertices introduced by re nement of mesh edges and faces on the boundary of the model can easily be projected to the model geometry, there are situations where this projection creates invalid elements. To ensure the ability to place those vertices on the model boundary an e cient two-step procedure has been developed. The rst step applies local mesh modi cation operations such as collapse and swap to incrementally project vertices. It is shown that the e ective application of mesh modi cations that will yield a mesh in which the vertex in question can be projected to the boundary must focus on ensuring the vertex in question moves at least as far as the plane on which the mesh would have element shapes degrade to zero volume. The second step applies a generalized local cavity triangulation algorithm to ensure the success of the process when the set of local mesh modi cations considered is unable to project the vertex to the boundary