  Topology Optimization (TO), which maximizes structural robustness under
material weight constraints, is becoming an essential step for the automatic
design of mechanical parts. However, existing TO algorithms use the Finite
Element Analysis (FEA) that requires massive computational resources. We
present a novel TO algorithm that incurs a much lower iterative cost. Unlike
conventional methods that require exact inversions of large FEA system matrices
at every iteration, we reformulate the problem as a bilevel optimization that
can be solved using a first-order algorithm and only inverts the system matrix
approximately. As a result, our method incurs a low iterative cost, and users
can preview the TO results interactively for fast design updates. Theoretical
convergence analysis and numerical experiments are conducted to verify our
effectiveness. We further discuss extensions to use high-performance
preconditioners and fine-grained parallelism on the Graphics Processing Unit
(GPU).
