A fully adaptive topology optimization algorithm with goal-oriented error control

We present a fully adaptive finite element scheme, named ATOPT algorithm, to address topology optimization for minimum compliance. The algorithm performs a set of optimization loops on an underlying grid that is iteratively adapted to improve: (a) the description quality of the structural topology; (b) the accuracy of the finite element compliance approximation. Two suitable error estimators are defined to address both issues. Numerical simulations show that ATOPT algorithm achieves layouts that are in full agreement with standard results obtained on uniform fine grids, while remarkably reducing the number of design variables and the computational cost of the optimization procedure.