The Alternating Direction Method of Multipliers (ADMM) can be applied to time-decomposition formulations of optimal control problems to exploit parallelism. However, ADMM alone converges slowly and the subproblem solves, while done in parallel, are relatively expensive. Instead ADMM is used as a preconditioner. This approach inherits parallelism, but reduces the number of iterations and allows coarser subproblems solves. Approach, theoretical and numerical results will be presented.
In Topology Optimization the goal is to find the ideal material distribution in a domain subject to external forces. The structure is optimal if it has the highest possible stiffness. A volume constraint ensures filigree structures, which are controlled via a Ginzburg-Landau term. During 3D Printing overhangs lead to instabilities, which have only been tackled unsatisfactorily. The novel idea is to incorporate an Additive Manufacturing Constraint into the phase field method. Stability during 3D Printing is assured, which solves a common additive manufacturing problem.
joint work with Manuel Arenas, Robert Lasarzik
We consider a mathematical model for the flame cutting of steel. It is known that for high-strength steel grades this technology is prone to develop cracks at the cutting surface. To mitigate this effect new strategies for inductive pre-heating have been investigated within the European Industrial Doctorate project "MIMESIS - Mathematics and Materials Science for Steel Production and Manufacturing". In the talk we formulate a quasi-stationary optimal control problem for this problem, derive the optimality system and discuss preliminary numerical results.