  Designing the topology of three-dimensional structures is a challenging
problem due to its memory and time consumption. In this paper, we present a
robust and efficient algorithm for solving large-scale 3D topology optimization
problems. The robustness of the algorithm is ensured by adopting a globally
convergent sequential linear programming method with a stopping criterion based
on the first-order optimality conditions of the nonlinear problem. To increase
the algorithm's efficiency, it is combined with a multiresolution scheme that
employs different discretizations to deal with displacement, design, and
density variables. In addition, the time spent solving the linear equilibrium
systems is substantially reduced using multigrid as a preconditioner for the
conjugate gradient method. Since multiresolution can lead to the appearance of
unwanted artefacts in the structure, we propose an adaptive strategy for
increasing the degree of the displacement elements, with a technique for
suppressing unnecessary variables that provides accurate solutions with a
moderate impact on the algorithm's performance. We also propose a new
thresholding strategy, based on gradient information, to obtain structures
composed only by solid or void regions. Computational experiments carried out
in Matlab prove that the new algorithm effectively generates high-resolution
structures at a low computational cost.
