  We propose a new algorithm for the design of topologically optimized
lightweight structures, under a minimum compliance requirement. The new process
enhances a standard level set formulation in terms of computational efficiency,
thanks to the employment of a strategic computational mesh. We pursue a twofold
goal, i.e., to deliver a final layout characterized by a smooth contour and
reliable mechanical properties. The smoothness of the optimized structure is
ensured by the employment of an anisotropic adapted mesh, which sharply
captures the material/void interface. A robust mechanical performance is
guaranteed by a uniform tessellation of the internal part of the optimized
configuration. A thorough numerical investigation corroborates the
effectiveness of the proposed algorithm as a reliable and computationally
affordable design tool, both in two- and three-dimensional contexts.
