Topology Optimization of Electric Machines based on Topological Sensitivity Analysis

Topological sensitivities are a very useful tool for determining optimal designs. The topological derivative of a domain-dependent functional represents the sensitivity with respect to the insertion of an infinitesimally small hole. In the gradient-based ON/OFF method, proposed by M. Ohtake, Y. Okamoto and N. Takahashi in 2005, sensitivities of the functional with respect to a local variation of the material coefficient are considered. We show that, in the case of a linear state equation, these two kinds of sensitivities coincide. For the sensitivities computed in the ON/OFF method, the generalization to the case of a nonlinear state equation is straightforward, whereas the computation of topological derivatives in the nonlinear case is ongoing work. We will show numerical results obtained by applying the ON/OFF method in the nonlinear case to the optimization of an electric motor.Comment: 20 pages, 7 figure

Functional a posteriori error estimates for parabolic time-periodic boundary value problems

The paper is concerned with parabolic time-periodic boundary value problems which are of theoretical interest and arise in different practical applications. The multiharmonic finite element method is well adapted to this class of parabolic problems. We study properties of multiharmonic approximations and derive guaranteed and fully computable bounds of approximation errors. For this purpose, we use the functional a posteriori error estimation techniques earlier introduced by S. Repin. Numerical tests confirm the efficiency of the a posteriori error bounds derived

Functional a posteriori error estimates for time-periodic parabolic optimal control problems

This paper is devoted to the a posteriori error analysis of multiharmonic finite element approximations to distributed optimal control problems with time-periodic state equations of parabolic type. We derive a posteriori estimates of functional type, which are easily computable and provide guaranteed upper bounds for the state and co-state errors as well as for the cost functional. These theoretical results are confirmed by several numerical tests that show high efficiency of the a posteriori error bounds