Session: Recent Advances in Shape and Topology Optimization
Chair: Volker Schulz
Cluster: PDE-constrained Optimization
Talk 1: Approaches to Boundary-Effect-Dominated Topology Optimization
Speaker: Eddie Wadbro
Abstract: In classical design optimization using the material distribution method (density-based topology optimization), a material indicator function represents the presence or absence of material within the domain. To use this approach for boundary-effect-dominated problems, it is necessary to identify the boundary of the design at each iteration; this talk explores two methods to achieve this. The first involves using a boundary strip indicator function defined on the elements of the computational mesh. The second involves using a boundary indicator function defined on the mesh faces (edges in 2D and facets in 3D). The first method is applied to model a coated structure in a minimum heat compliance problem. The second method optimizes a heat sink, modeled by the Poisson equation with a Newtonian cooling boundary condition. The talk will cover the main ideas behind both approaches and showcase results from both model problems.
Talk 2: Topology optimization of the first truly wave focusing sonic black hole
Speaker: Martin Berggren
Abstract: We apply density-based topology optimization to design an acoustic waveguide possessing broadband wave focusing properties. Although effective as absorbers, previous suggestions of such devices — labeled sonic or acoustic black holes — have been unable to create the focusing effect. The optimization objective is a broadband maximization of the dissipated energy in a small absorbing area towards the end of the waveguide. A challenge with this application is that it is necessary to accurately model viscothermal boundary-layer losses associated with material boundaries. Here we rely on recent progress in the use of density-based topology optimization approaches for boundary-effect-dominated problems. Using such a procedure, we have been able to successfully design what seems to be the first truly broadband wave-focusing sonic black hole.
Talk 3: Shape Optimization Using the Total Generalized Variation of the Normal as Prior
Speaker: Stephan Schmidt
Abstract: The talk discusses how to use a total variation semi-norm on shapes as a prior. The idea is to concentrate curvature changes to edges, which is of great help when non-smooth shapes are to be reconstructed in inverse problems. Unsurprisingly, classical total variation keeps all typical downsides such as stair-casing when applied to manifolds. To this end, the concept of total generalized variation (TGV) by Bredies/Kunisch/Pock is extended to shapes. To implement TGV for shapes, the required separation of the linear component of a geometric variables necessitates non-standard finite elements on the tangent space of manifolds. The methodology is exemplified with applications stemming from geo-electric impedance tomography and mesh inpainting as well as texture denoising.
