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 andoptimization of rotating electric machines which we consider in aspace-time framework, rather than solving themagneto-(quasi-)static problems sequentially. We considertime-dependent problems on spatially two-dimensional domains,resulting in three-dimensional space-time geometries.
On the one hand, we present and analyze a space-time finiteelement method for moving domains and show numerical results. Wepresent two ways of creating moving space-time geometries: It caneither be done by hand using a meshing tool or, alternatively, themoving geometry can be encoded in a level set function. In thelatter case, the geometry is resolved by the space-time mesh usinga local mesh modification method.
On the other hand, we consider the optimization of the shape of amoving object, which is subject to a parabolic partialdifferential equation (PDE) constraint on the moving domain. Wecompute the shape derivative for a model problem where we exploitthe automatic differentiation capabilities of the finite elementsoftware NGSolve. We present a way to compute a feasible descentdirection and show numerical results for an academic model problemand a rotating electric machine.
This presentation is based on joint work with Olaf Steinbach,Alessio Cesarano, Mario Gobrial and Christian Köthe.