A Multigrid Method for Coupled Optimal Topology and Shape Design in Nonlinear Magnetostatics

Dalibor Lukáš ()
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Dalibor Lukáš: VŠB-Technical University of Ostrava, Department of Applied Mathematics

A chapter in Numerical Mathematics and Advanced Applications, 2006, pp 1015-1022 from Springer

Abstract: Abstract Topology optimization searches for an optimal distribution of material and void without any restrictions on the structure of the design geometry. Shape optimization tunes the shape of the geometry, while the topology is fixed. In the paper we propose a sequential coupling so that a coarsely optimized topology is the initial guess for the following shape optimization. We aim at making this algorithm fast by using the adjoint sensitivity analysis to the Newton-method for the governing nonlinear state equation and a multigrid approach for the shape optimization. A finite element discretization method is employed. Numerical results are given for a 2-dimensional optimal design of a direct electric current electromagnet.

Keywords: Element Discretization Method; Shape Optimization; Conjugate Gradient Method; Direct Electric Current; Optimal Shape Design (search for similar items in EconPapers)
Date: 2006
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-540-34288-5_101

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DOI: 10.1007/978-3-540-34288-5_101

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