3D Topology Conformity Of Constrained DT Tetrahedralization Finite Element Mesh Generation

Before the tetrahedra mesh generation, the input data for a Delaunay-based algorithm are often given as a discrete description of the domain boundary which, in the three dimensional space, may represent a surface triangulation of the boundary. Here the three dimensional entity boundary is boundary surface mesh, which owns not only geometric property but also topology property. Boundary surface mesh constrains the mesh generation. Classical Delaunay Tetrahedralization method usually produces a triangulation mesh that forms the convex hull of the point on the boundary. For an arbitrary domain, such a triangulation may not match with the prescribed boundary surface. For the sake of recovering the original of the surface, Delaunay method must be modified. Boundary conformity mesh generation must satisfy not only the boundary geometric constraint but also boundary topology constraint.Need to be specially noticed, existing Delaunay method is effective when applied to three dimensional case, but it is noted that some additional new points are introduced on the edges and triangles, so some original boundary triangles are divided into some other new small size triangles, that is to say, the new boundary is not the original boundary from the critical perspective. So boundary constrained Delaunay triangulation satisfy boundary geometric constraint, but can not strictly satisfy boundary topology constraint. So boundary constrained Delaunay triangulation is not boundary conformity tetrahedra mesh from the critical perspective.Owing to the request of some engineering practice problem, at the same time the theoretic worth, boundary recovery for 3D conformity Delaunay triangulation problem must be completely solved.A topology conformity boundary recovery method for three-dimensional constrained Delaunay Tetrahedralization is proposed. A topology recovery procedure named "Dressing wound" is performed just after the geometry recovery procedure. Firstly, an initial constraint triangles is introduced to cover the injured constraint triangles;secondly, a zero volume non-concave polyhedron is constructed by the initial and injured constraint triangles;thirdly, the non-concave polyhedron is tetrahedralized by introducing a steiner node;at last, a special mesh smoothing procedure is performed to obtain the high quality mesh. The topology recovery procedure recovers and overcomes the boundary topology-injured problem of the classical boundary recovery algorithm and the boundary topology conformity is guaranteed. Anew mesh optimization method combining the physics displacement field and Laplacian smoothing method is proposed in order to improve un-isolated poor quality element yielded by "Dressing wound".According to the above-mentioned algorithm, a program is implemented in C++ language. Computational experiments show that the boundary recovery and mesh smoothing algorithm proposed is robust, efficient and easy to be implemented in practical applications.