Finite element grid optimization with geometric approach

This paper presents a geometric approach which is used to optimize the grid distribution of a two dimensional finite element model composed of quadrilateral elements. The method is based on the comparison between the Jacobian matrices of a square element and real elements, followed by the reduction of their differences. The physical interpretation involved in the comparison is discussed. An unconstrained mesh optimization scheme, constructed using a least squares formulation, is used to minimize the difference between the square and real elements. By assigning weighing factors to the differences, the convergence rate can be improved. Several examples are presented to demonstrate the validity of this approach.