This paper proposes a multiple level set method for multi-material shape optimization in an electromagnetic system. This method enables the handling of multi-material interfaces simultaneously. The sign combination of the level set functions is used for identifying the different material regions and their interfaces. The continuum sensitivity formula for the multi-material interfaces is adopted for the velocity field in the multiple level set equations. Numerical examples are tested to show the usefulness of the proposed method.
van DijkN.P.MauteK.LangelaarM. and van KeulenF., Level-set method for structural topology optimization: a review, Structural and Multidisciplinary Optimization48 (2013), 437–472.
2.
DeatonJ.D. and GrandhiR.V., A survey of structural and multidisciplinary continuum topology optimization: post 2000, Structural and Multidisciplinary Optimization49 (2014), 1–38.
3.
KimY.S.LeeS.-H.ChoiH.S. and H.ParkI., Shape formation of ferrofluid under external magnetic fields using level set method, Journal of Applied Physics105 (2009), 07D539.
4.
KimY.S.BaekM.K. and ParkI.H., Design sensitivity and LSM for topology and shape optimization in electromagnetic system, COMPEL – International Journal for Computation and Mathematics in Electrical and Electronic Engineering31 (2012), 803–815.
5.
ParkS. and MinS., Optimal topology design of magnetic devices using level-set method, IEEE Transactions on Magnetics45 (2009), 1610–1613.
6.
LeeK.H. et al., Adaptive level set method for accurate boundary shape in optimization of electromagnetic systems, COMPEL – International Journal for Computation and Mathematics in Electrical and Electronic Engineering33 (2014), 809–820.
7.
LeeK.H. et al., Alleviation of electric field intensity in high-voltage system by topology and shape optimization of dielectric material using continuum design sensitivity and level set method, IEEE Transactions on Magnetics51 (2015), 9400404.
8.
WangM.Y. and WangX., “Color” level sets: a multi-phase method for structural topology optimization with multiple materials, Computer Methods in Applied Mechanics and Engineering193 (2004), 469–496.
9.
WangM.Y.ChenS.WangX. and MeiY., Design of multimaterial compliant mechanisms using level-set methods, Journal of Mechanical Design127 (2005), 941–956.
10.
AllaireG.DapognyC.DelgadoG. and MichailidisG., Multi-phase structural optimization via a level set method, ESAIM: Control, Optimisation and Calculus of Variations20 (2014), 576–611.
11.
OsherS. and FedkiwR., Level Set Methods and Dynamic Implicit Surfaces, Springer (2003), 17–45.
12.
SlemonG.R. and StraughenA., Electric Machines, Addison Wesley (1980), 19–27.
