joint work with Anders Bernland, André Massing, Eddie Wadbro
When applying shape optimization to design certain acoustic devices, a challenge is to account for effects of the visco–thermal boundary layers that appear in narrow channels and cavities. An accurate model of this phenomenon uses a so-called Wentzell boundary condition together with the Helmholtz equation for the acoustic pressure. For the first time, this model is here used to successfully design such a device, a compression driver feeding a loudspeaker horn. The computations make use of a level-set description of the geometry and the CutFEM framework implemented in the FEniCS platform.
joint work with Andreas Vogel
In this talk we present a mesh deformation technique for PDE constrained shape optimization. Introducing a gradient penalization to the inner product for linearized shape spaces, mesh degeneration can be prevented and the scalability of employed solvers can be retained. We illustrate the approach by a shape optimization for cellular composites with respect to linear elastic energy under tension. The influence of the gradient penalization is evaluated and the parallel scalability of the approach demonstrated employing a geometric multigrid solver on hierarchically distributed meshes.
joint work with Volker Schulz
Shape optimization has been proven useful for identifying interfaces in models governed by partial differential equations. For instance, shape calculus can be exploited for parameter identification of problems where the diffusivity is structured by piecewise constant patches. On the other hand, nonlocal models, which are governed by integral operators instead of differential operators, have attracted increased attention in recent years. We bring together these two fields by considering a shape optimization problem which is constrained by a nonlocal convection-diffusion equation.