20170508
We investigate methods of topology and shape optimization for an optimal design problem from electrical engineering which is constrained by the quasilinear PDE of twodimensional magnetostatics.
We derive the topological derivative of the objective function, i.e., its sensitivity with respect to a topological perturbation of the domain, and compare it to other topological sensitivities used in the literature. Moreover, we compute the shape derivative, i.e., the sensitivity of a domaindependent functional with respect to a smooth variation of a boundary or material interface. These sensitivities are exploited to obtain optimal designs using gradient descent methods.
In the course of the optimization algorithm, the material interface between different subdomains evolves and has to be taken into account in order to obtain accurate finite element solutions. We present a local mesh modification strategy for triangular meshes which yields smoother designs and show optimal order of convergence of the obtained finite element solution to the true solution.
Finally, we combine these three techniques and apply them to a design optimization problem for an electric motor.
Category: CE SeminarTechnische Universität Darmstadt
Graduate School CE
Dolivostraße 15
D64293 Darmstadt

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