Boundary Conforming Delaunay Mesh Generation

Many physical phenomena can be modeled by partial differential equations which may be solved by numerical methods such as finite element and finite volume methods. In this context, a given domain must first be subdivided into many simple cells. Both the shape and size of the cells will affect the accuracy and convergence of the method. A boundary conforming Delaunay mesh is a partition of a polyhedral domain into simplices that satisfy the Delaunay and additional criteria. It has many optimal properties and is particularly needed in Voronoi-box-based finite volume schemes [1] which are well-suited for diffusion and transportation problems, such as, porous media flow, semiconduct device simulation, etc. In this paper, we discuss the problem of generating three-dimensional boundary conforming Delaunay meshes with well-shaped tetrahedra and appropriate mesh size.