Optimization of finite element grids by direct energy search

One of the possible approaches to the reduction of computational costs in finite element analysis is the selection of ‘optimal grids’, which produce the ‘best’ answers, in the sense of minimizing a discretization error measure, for a fixed level of computational effort. The grid optimization problem is studied in the case of grids of similar topology having a fixed number of degrees of freedom per node. A general formulation based on weighted-residual error measures is specialized to field problems associated with a positive-definite energy functional, the minimization of which, with respect to variable node locations, is adopted as a grid optimality criterion. The problem is then embedded in the framework of the general nonlinear programming problem, and desirable computational features of candidate search algorithms are described.