مقاله A shape optimization method for nonlinear axisymmetric magnetostatics using a coupling of finite and boundary elements : تی پی بین

خلاصه مقاله

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.

نویسندگان

D. Lukáš [ Department of Applied Mathematics, VŠB-Technical University of Ostrava, 17. listopadu 15, 708 33 Ostrava-Poruba, Czech Republic ]

K. Postava [ Department of Physics, VŠB-Technical University of Ostrava, 17. listopadu 15, 708 33 Ostrava-Poruba, Czech Republic ]

O. Životský [ Department of Physics, VŠB-Technical University of Ostrava, 17. listopadu 15, 708 33 Ostrava-Poruba, Czech Republic ]

کلمات کلیدی

Shape optimization Nonlinear magnetostatics Boundary element method Finite element method Adjoint sensitivity analysis

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Mathematics and Computers in Simulation

About conference: The aim of the journal is to provide an international forum for the dissemination of up-to-date information in the fields of the mathematics and computers, in particular (but not exclusively) as they apply to the dynamics of systems, their simulation and scientific computation in general. Published material ranges from short, concise research papers to more general tutorial articles. Mathematics and Computers in Simulation, published monthly, is the official organ of IMACS, the International Association for Mathematics and Computers in Simulation (Formerly AICA). This Association, founded in 1955 and legally incorporated in 1956 is a member of FIACC (the Five International Associations Coordinating Committee), together with IFIP, IFAV, IFORS and IMEKO.

حوزه های تحت پوشش : ریاضی و کامپیوتر در شبیه سازی