Advancing Front Mesh Generation Techniques with Application to the Finite Element Method

The present study deals with automatic mesh generation with application to finite element methods. We focus our interest on unstructured mesh generation, and in particular on advancing front methods for which algorithms for meshing of two and three dimensional domains as well as of free-form surfaces are devised.<p /> To get an understanding of the mesh generation problem, and the approaches taken by different researchers for solving the problem, to begin with we give a brief survey of geometric modeling tech niques as used in computer aided design (CAD). With the underlying incentive to get some guidance for algorithm development, we review and discuss automatic mesh generation methods as proposed in the literature. We concentrate on spatial decomposition (octree) methods, Delaunay triangulation methods, and advancing front methods. In addition, we review and discuss results regarding the topology and geometry of general space decompositions as well as of triangulations and finite element meshes. Moreover, the computer representations of space decompositions, triangulations, and finite element meshes are briefly discussed.<p /> We discuss and propose data structures which makes an efficient implementation possible of the to pological and geometric operations necessary in advancing front mesh generation. We concentrate on hierarchical data structures based on the concept of recursive spatial decomposition and discuss implementation issues as well as devising some new ideas.<p /> An issue of automatic mesh generation that we pay particular attention to is the development of methods for specifying mesh size distributions on general domains. This is a key issue which deter mines the robustness of any automatic mesh generation method. Furthermore, we note that automatic mesh generation methods may in a way be distinguished by the technique utilized for implement ing the mesh size distribution.<p /> Regarding the implementation of the proposed advancing front methods, we emphasize the importance for obtaining a robust method that the development of the advancing front is controlled so as to prevent algorithm failure. Hence, algorithms for controlling the front development are devised. This includes a strategy for deciding where on the front a new element should be constructed as well as methods for the actual construction of the elements