Towards Unstructured Mesh Generation Using the Inverse Poisson Problem

A novel approach to unstructured quadrilateral mesh generation for planar domains is presented. Away from irregular vertices, the resulting meshes have the properties of nearly conformal grids. The technique is based on a theoretical relation between the present problem, and the inverse Poisson (IP) problem with point sources. An IP algorithm is described, which constructs a point-source distribution, whose sources correspond to the irregular vertices of the mesh. Both the background theory and the IP algorithm address the global nature of the mesh generation problem. The IP algorithm is incorporated in a complete mesh generation scheme, which also includes an algorithm for creating the final mesh. Example results are presented and discussed.