Physically based node distributions for mesh generation

A new physically based approach to mesh generation is proposed, which uses the variants of Monte-Carlo (MC) technique. The mesh nodes are treated as interacting particles and their positions are determined using energy minimization. When the approach is extended with the grand-canonical MC scheme the optimization is performed for both the number of particles and their positions. It is shown how a molecular dynamics technique can be applied to accelerate the convergence of the simulations. Local mesh refinement can be achieved with appropriate node spacing functions. The final mesh is created by connecting the generated node distributions with constrained Delaunay triangulation. Well-shaped triangular or tetrahedral mesh elements are usually obtained. The proposed method is simple, flexible, and works in an identical way in spaces of any number of dimensions.