Automatic mesh generation using the symmetric axis transformation of polygonal domains

An automatic method for generating finite element meshes for multiply connected planar domains with polygonal boundaries (i.e. planar polygons with polygonal holes) is described. The symmetric axis transform is used to obtain a planar graph that partitions the given domain. This transformation may introduce edges in the graph that are too long or too short for generating good meshes. A silver processing algorithm, which transforms the graph into another graph devoid of such edges, is presented. Finally, additional modes are placed on the edges of the graph to obtain a triangulation, and this process is applied iteratively, yielding the final mesh. The method automatically increases the mesh density in regions of rapid change in shape and allows both global and local control of the mesh density. The method also admits the imposition of node compatibility constraints along domain boundaries, thus making the method suitable for meshing planar cell complexes (i.e multiple polygonal domains with shared boundaries in two-dimensional space) and for generating boundary elements for polyhedra in three-dimensional space