Newton-type method for the variational discretization of topology optimization problems

We present a locally quadratically convergent optimization algorithm for solving topology optimization problems. The distinguishing feature of the algorithm is to treat the design as a smooth function of the state and not vice versa as in the traditional nested approach to topology optimization, which we achieve by inverting a part of perturbed optimality conditions for the problem. In this way, the computational bottleneck is conveniently shifted from evaluating the merit function to a direction finding subproblem. The latter involves solving certain linearized PDEs, and the computational effort is similar to that of finding a gradient of the merit function in the traditional nested approach. We illustrate the performance of the algorithm on benchmark topology optimized problems in fluid mechanics.