A Generalized Graph-Theoretic Mesh Optimization Model

This paper presents a generic approach to mesh global optimization via node movement, based on a discrete graph-theoretic model. Mesh is considered as an electric system with lumped parameters, governed by the Kirchhoff’s voltage and circuit laws. Each mesh element is treated as a multi-pole electric component, relating input electric potentials to the output via a transfer function. We automatically derive an element transfer function and finally a mesh optimization model using a formal analysis of the coefficients couplings in the finite element stiffness matrix, similar to the method, used in Algebraic Multigrid. Our mesh model is a transient dynamic system and proposed optimization can be also used for mesh deformation problems. We will show that new method works well for realistic 3D meshes and provide a number of mesh optimization examples and details of our implementation.