# Space-time simulation and shape optimizationfor moving domains

## Dipl.-Ing. Peter Gangl

**April 13, 2021, 3:30 p.m. ZOOM**

This talk is motivated by the numerical simulation and optimization of rotating electric machines which we consider in a space-time framework, rather than solving the magneto-(quasi-)static problems sequentially. We consider time-dependent problems on spatially two-dimensional domains, resulting in three-dimensional space-time geometries.

On the one hand, we present and analyse a space-time finite element method for moving domains and show numerical results. We present two ways of creating moving space-time geometries: It can either be done by hand using a meshing tool or, alternatively, the moving geometry can be encoded in a level set function. In the latter case, the geometry is resolved by the space-time mesh using a local mesh modification method.

On the other hand, we consider the optimization of the shape of a moving object, which is subject to a parabolic partial differential equation (PDE) constraint on the moving domain. We compute the shape derivative for a model problem where we exploit the automatic differentiation capabilities of the finite element software NGSolve. We present a way to compute a feasible descent direction and show numerical results for an academic model problem and a rotating electric machine.

This presentation is based on joint work with Olaf Steinbach, Alessio Cesarano, Mario Gobrial and Christian Köthe.