Efficient use of iterative solvers in nested topology optimization

In the nested approach to structural optimization, most of the computational effort is invested in the solution of the finite element analysis equations. In this study, it is suggested to reduce this computational cost by using an approximation to the solution of the nested problem, generated by a Krylov subspace iterative solver. By choosing convergence criteria for the iterative solver that are strongly related to the optimization objective and to the design sensitivities, it is possible to terminate the iterative solution of the nested equations earlier compared to traditional convergence measures. The approximation is shown to be sufficiently accurate for the practical purpose of optimization even though the nested equation system is not solved accurately. The approach is tested on several medium-scale topology optimization problems, including three dimensional minimum compliance problems and two dimensional compliant force inverter problems. Accurate optimal designs are obtained while the time spent on the nested problem is reduced significantly.