Quality mesh generation is primary concern for methods where simplices are used as input for analysis. Requirements for good meshes can be found in computer graphics for radiosity method[1, 9] where surface elements are used for form-factor determination. Triangular mesh is the first choice when generating surface meshes. Triangulation via Vornoi diagrams[5] can be used to achieve well-shaped elements for given set of nodes. Delaunay triangulation which is geometric dual of Vornoi diagrams has the property of maximizing minimum angle in the mesh.
Finite element method[10] relies on elements in one, two or three dimensions. Triangular or tetrahedral elements are not preferred for FE analysis[4]. Triangular elements can be converted to quadrilateral[8] to achieve better accuracy with FEA. Shape of the elements is an important issue for accuracy of numerical solution. Most CAD models are based on mesh representation. Ill shaped elements are prone to have inaccurate surface normals, collinear vertices and similar singularities when manipulating mesh.
In general elements should be as equiangular as possible. Highly distorted simplices e.g. long thin triangles or tetrahedra can lead to accuracy and convergence problems. In practice only triangle and tetrahedra mesh generation are fully automatic. Other methods requires domain decomposition and manual interventions at boundaries. FE method preferres block elements which are difficult to pack in arbitrary boundaries. Some tetrahedra are necessary in corners for smooth mesh. Unstructured mesh with arbitrary connectivity is a common practice in FEA. Such meshes can be ill shaped, thus some sort of mesh smoothing and other improvements in the preprocess stage is desirable.
This paper presents a new mesh smoothing procedure based on physical relaxation for an arbitrary input geometries including, wire-frame, surface and solid.