Wednesday, 28 April 2017, 9.30 a.m. (sharp),
Prof. Dietmar Hömberg, WIAS, Berlino
at the conference room of IMATI-CNR in Pavia, will give a lecture titled:
ON A ROBUST PHASE FIELD APPROACH TO TOPOLOGY OPTIMIZATION
as part of the Applied Mathematics Seminar (IMATI-CNR e Dipartimento di Matematica, Pavia).
At the end a refreshment will be organized.
The goal in topology optimization is to partition a given domain into regions occupied by either void or material by minimizing a given cost functional J_1 (typically a combination of compliance and tracking type) such that the displacement u solves a mechanical equilibrium problem. Here, the material distribution is described with the help of a phase field variable phi taking values in [0,1], corresponding to the phases void and material, respectively. To avoid homogenised microstructures, usually a perimeter penalisation is added to the cost functional. In the phase field approach to topology optimization the latter is relaxed by replacing it with a Ginzburg-Landau energy J_2, which can be shown to Gamma-converge to the perimeter functional.
In the presentation I will explain the phase field approach and include the effect of uncertainties in coefficients and loading data. I will present a numerical scheme and show numerical results in 2 and 3 D.