Adaptive tetrahedral mesh generation by constrained Delaunay refinement

This paper presents a tetrahedral mesh generation method for numerically solving partial differential equations using finite element or finite volume methods in three-dimensional space. The main issues are the mesh quality and mesh size, Which directly affect the accuracy of the numerical solution and the computational cost. Two basic problems need to be resolved. namely boundary conformity and field points distribution. The proposed method Utilizes a special three-dimensional triangulation so-called constrained Delaunay tetrahedralization to conform the domain boundary and create field points simultaneously. Good quality tetrahedra and graded mesh size call be theoretically guaranteed for a large class of mesh domains. In addition, all isotropic size field associated with the numerical solution call be supplied the field points will then be distributed according to it. Good mesh size conformity call be achieved for smooth sizing in format ions. The proposed method has been implemented. Various examples are provided to illustrate its theoretical aspects its well as practical performance. Copyright (c) 2008 John Wiley & Sons, Ltd.