Mesh generation using unstructured computational meshes and elliptic partial differential equation smoothing

A novel approach for generating unstructured meshes using elliptic smoothing is presented. Like structured mesh generation methods, the approach begins with the construction of a computational mesh. The computational mesh is used to solve elliptic partial differential equations that control grid point distributions and improve mesh quality. Two types of elliptic partial differential equations are employed; modified linear-elastic theory and Winslow equations, with or without forcing functions. Results are included to illustrate the use of these methods for unstructured mesh generation, mesh boundary shape modification, mesh untangling and mesh movement.