1,071 research outputs found
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
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