Seminar in Numerical Analysis: Florian Loos (Universität der Bundeswehr München)
The number of electrical devices in modern cars supplied by high currents grows continuously. In order to avoid hot spot generation and overheating on the one hand, but to save weight and material on the other hand, electrical connecting structures have to be dimensioned appropriately. The heat transfer in current carrying multicables with consideration of the rise of electrical resistivity for higher temperatures is described by a system of semilinear equations with discontinuous coefficients. The effects of convection and radiation are taken into account by a nonlinear boundary condition.
Simulation results and experimental studies show that the positioning of the single cables has important influence on the maximum temperatures. In order to find an optimal cable design, i.e. to arrange the single cables with fixed cross section and current such that the maximum temperature is minimized, a shape optimization problem is formulated. We derive an adjoint system and the shape gradient using the formal Lagrange approach. The effect of the discontinuity of some coefficients on the shape gradient is shown. By application of different (nonlinear) optimizers combined with the finite element solver COMSOL Multiphysics, a solution is obtained numerically. In this talk, we present the modeling of the problem, the derivation of the shape gradient and numerical results.
This is joint work with Helmut Harbrecht and Thomas Apel.
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