A sequential coupling of optimal topology and multilevel shape design applied to two-dimensional nonlinear magnetostatics

Author： Lukáš Dalibor

Publisher： Springer Publishing Company

ISSN： 1432-9360

Source： Computing and Visualization in Science, Vol.10, Iss.3, 2007-09, pp. : 135-144

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Abstract

In this paper, a sequential coupling of two-dimensional (2D) optimal topology and shape design is proposed so that a coarsely discretized and optimized topology is the initial guess for the following shape optimization. In between, we approximate the optimized topology by piecewise Bézier shapes via least square fitting. For the topology optimization, we use the steepest descent method. The state problem is a nonlinear Poisson equation discretized by the finite element method and eliminated within Newton iterations, while the particular linear systems are solved using a multigrid preconditioned conjugate gradients method. The shape optimization is also solved in a multilevel fashion, where at each level the sequential quadratic programming is employed. We further propose an adjoint sensitivity analysis method for the nested nonlinear state system. At the end, the machinery is applied to optimal design of a direct electric current electromagnet. The results correspond to physical experiments.