Quasi-Newton methods for topology optimization using a level-set method

Abstract The ability to efficiently solve topology optimization problems is of great importance for many practical applications. Hence, there a demand efficient solution algorithms. In this paper, we propose novel quasi-Newton methods solving PDE-constrained problems. Our approach based on and extends the popular algorithm Amstutz Andrä (J Comput Phys 216: 573–588, 2006). To do so, introduce new perspective commonly used evolution equation level-set method, which allows us derive our optimization. We investigate performance proposed numerically following examples: Inverse constrained by linear semilinear elliptic Poisson problems, compliance minimization in elasticity, fluids Navier–Stokes flow, where compare them current state-of-the-art methods. results show that algorithms significantly outperform other considered methods: They require substantially less iterations find optimizer while demanding only slightly more resources per iteration. This shows are highly attractive field