# Shape Calculus for Multi-Domain Formulation of Elliptic Problems and its Application to Electrical Machines

## DI Armin Fohler

April 24, 2018, 3:30 p.m. S2 416-1

This work is driven by requirements from applications in the framework of rotating electrical machines. For the simulation of electrical machines we have to solve a non-linear PDE in each rotation step of the motor. This is done via a Newton scheme. To reduce the computational costs of such a scheme one can construct a good initial guess in each rotation step. From an abstract point of view we are dealing with a parametrized family of PDEs with the rotation angle $\varphi$ as our
parameter. The construction of the initial guess comes down to computing the derivative of the solution with respect to
$\varphi$ - the so called Euler predictor. For this we have to extend the ideas of shape calculus presented in the book of
Sokolowski and Zolesio 'Introduction to shape optimization: shape sensitivity analysis' to the multidomain case with
different transformations acting on the individual parts.