Interior point multigrid methods for topology optimization

In this paper, a new multigrid interior point approach to topology optimization problems in the context of the homogenization method is presented. The key observation is that nonlinear interior point methods lead to linear-quadratic subproblems with structures that can be favourably exploited within multigrid methods. Primal as well as primal-dual formulations are discussed. The multigrid approach is based on the transformed smoother paradigm. Numerical results for an example problem are presented.