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.
机构:
Univ New South Wales, Sch Math & Stat, Sydney, NSW 2052, AustraliaUniv New South Wales, Sch Math & Stat, Sydney, NSW 2052, Australia
Feischl, Michael
Fuhrer, Thomas
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h-index: 0
机构:
Pontificia Univ Catolica Chile, Fac Matemat, Ave Vicuna Mackenna 4860, Santiago, ChileUniv New South Wales, Sch Math & Stat, Sydney, NSW 2052, Australia
Fuhrer, Thomas
Praetorius, Dirk
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h-index: 0
机构:
Vienna Univ Technol, Inst Anal & Sci Comp, Wiedner Hauptstr 8-10, A-1040 Vienna, AustriaUniv New South Wales, Sch Math & Stat, Sydney, NSW 2052, Australia
Praetorius, Dirk
Stephan, Ernst P.
论文数: 0引用数: 0
h-index: 0
机构:
Leibniz Univ Hannover, Inst Appl Math, Welfengarten 1, D-30167 Hannover, GermanyUniv New South Wales, Sch Math & Stat, Sydney, NSW 2052, Australia