A shape optimization method for nonlinear axisymmetric magnetostatics using a coupling of finite and boundary elements

被引:5
|
作者
Lukas, D. [1 ]
Postava, K. [2 ]
Zivotsky, O. [2 ]
机构
[1] VSB Tech Univ Ostrava, Dept Appl Math, Ostrava 70833, Czech Republic
[2] VSB Tech Univ Ostrava, Dept Phys, Ostrava 70833, Czech Republic
关键词
Shape optimization; Nonlinear magnetostatics; Boundary element method; Finite element method; Ad joint sensitivity analysis; LIPSCHITZ POLYHEDRA; EQUATIONS; QUADRATURE; TRACES; BEM;
D O I
10.1016/j.matcom.2011.01.015
中图分类号
TP39 [计算机的应用];
学科分类号
081203 ; 0835 ;
摘要
In this paper we propose a method for constrained shape optimization governed with a nonlinear axisymmetric magnetostatic state problem and we apply it to an optimal shape design of an electromagnet. The state problem is solved via Hiptmair's symmetric coupling of finite elements employed in the interior ferromagnetic domain and boundary elements modelling the exterior air domain as well as current excitations. As a novelty we derive Duffy regularization transforms of the boundary element integrals for the axisymmetric case, which are then evaluated using a tensor-product Gaussian quadrature. Nonlinear ferromagnetic behaviour is resolved by Newton iterations. The optimization method under both linear and nonlinear constraints relies on the active-set steepest-descent search, projections onto the set of linearized constraints, and an adjoint method of shape sensitivity analysis. Shape perturbations influence grid deformation via a solution to an auxiliary torsion-free linear elasticity problem. Finally, numerical results are presented. (c) 2011 1:MACS. Published by Elsevier B.V.. All rights reserved.
引用
收藏
页码:1721 / 1731
页数:11
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