Inverse design of dielectric materials by topology optimization

Progress in Electromagnetics Research

Volumn 127, Issue , 2012, Pages 93-120

  Otomori, M ^a   Andkjaer J ^b   Sigmund, O ^b   Izui, K ^a   Nishiwaki, S ^a  

^a KYOTO UNIVERSITY   (Japan)

^b TECHNICAL UNIVERSITY OF DENMARK   (Denmark)

Author keywords

[No Author keywords available]

Indexed keywords

ANISOTROPY; DESIGN; ELECTROMAGNETS; FINITE ELEMENT METHOD; INVERSE PROBLEMS; OPTICAL ANISOTROPY; OPTIMIZATION; PERMITTIVITY; SENSITIVITY ANALYSIS; TOPOLOGY;

ADJOINT-VARIABLE METHOD; ELECTRIC PERMITTIVITIES; ELECTROMAGNETIC DEVICES; GRADIENT-BASED TOPOLOGY OPTIMIZATION METHOD; OPTIMIZATION ALGORITHMS; OPTIMIZED CONFIGURATION; PERIODIC MICROSTRUCTURE; SYSTEMATIC METHODOLOGY;

DIELECTRIC MATERIALS;

EID: 84860110556     PISSN: 10704698     EISSN: 15598985     Source Type: Journal    
DOI: 10.2528/PIER12020501     Document Type: Article

References (34)

1. Bendsøe, M. P. and N. Kikuchi, "Generating optimal topologies in structural design using a homogenization method," Comput. Methods Appl. Mech. Engrg., Vol. 71, No. 2, 197-224, 1988.
2. Yoo, J., N. Kikuchi, and J. L. Volakis, "Structural optimization in magnetic devices by the homogenization design method," IEEE T. Magn., Vol. 36, No. 3, 574-580, 2000.
3. Nomura, T., S. Nishiwaki, K. Sato, and K. Hirayama, "Topology optimization for the design of periodic microstructures composed of electromagnetic materials," Finite Elem. Anal. Des., Vol. 45, No. 3, 210-226, 2009.
4. Nishiwaki, S., T. Nomura, S. Kinoshita, K. Izui, M. Yoshimura, K. Sato, and K. Hirayama, "Topology optimization for cross-section designs of electromagnetic waveguides targeting guiding characteristics," Finite Elem. Anal. Des., Vol. 45, No. 12, 944-957, 2009.
5. Yamasaki, S., T. Nomura, A. Kawamoto, K. Sato, and S. Nishiwaki, "A level set-based topology optimization method targeting metallic waveguide design problems," Int. J. Numer. Meth. Eng., Vol. 87, No. 9, 844-868, 2011.
6. Borrvall, T. and J. Petersson, "Topology optimization of fluids in stoles flow," Int. J. Numer. Meth. Eng., Vol. 41, No. 1, 77-107, 2003.
7. Sigmund, O. and J. S. Jensen, "Systematic design of phononic band-gap materials and structures by topology optimization," Phil. Trans. R. Soc. Lond. A, Vol. 361, 1001-1019, 2003.
8. Sigmund, O. and S. Torquato, "Design of materials with extreme thermal expansion using a three-phase topology optimization method," J. Mech. Phys. Solids., Vol. 45, No. 6, 1037-1067, 1997.
9. Larsen, U. D., O. Sigmund, and S. Bouwstra, "Design and fabrication of compliant micromechanisms and structures with negative Poisson's ratio," J. Microelectromech. S., Vol. 6, No. 2, 99-106, 1997.
10. Sigmund, O., "Materials with prescribed constitutive parameters: an inverse homogenization problem," INT. J. Solids Struct., Vol. 31, No. 17, 2313-2329, 1994.
11. Choi, J. S. and J. Yoo, "Design and application of layered composites with the prescribed magnetic permeability," Int. J. Numer. Meth. Eng., Vol. 82, No. 1, 1-25, 2010.
12. El-Kahlout, Y. and G. Kiziltas, "Inverse synthesis of electromagnetic materials using homogenization based topology optimization," Progress In Electromagnetics Research, Vol. 115, 343-380, 2011.
13. Sihvola, A., Electromagnetic Mixing Formulas and Applicataions, The Institution of Engineering and Technology, London, 1999.
14. Bensoussan, A., J. L. Lions, and G. Papanicolau, Asymptotic Analysis for Periodic Structures, North-Holland Publishing Company, Amsterdam, 1978.
15. Sanchez-Palencia, E., "Non-homogeneous media and vibration theory," Lecture Notes in Physics, Vol. 127, Springer-Verlag, Berlin, 1980.
16. Hashin, Z., "Analysis of composite materials - A survey," J. Appl. Mech., Vol. 50, No. 3, 481-505, 1983.
17. Milton, G. W., The Theory of Composites, Cambridge University Press, Cambridge, 2001.
18. Sigmund, O., "On the usefulness of non-gradient approaches in topology optimization," Struct. Multidisc. Optim., Vol. 43, No. 5, 589-596, 2011.
19. Bendsøe, M. P. and O. Sigmund, "Material interpolation schemes in topology optimization," Arch. Appl. Mech., Vol. 69, No. 9-10, 635-654, 1999.
20. Guest, J. K., J. H. Prévost, and T. Belytschko, "Achieving minimum length scale in topology optimization using nodal design variables and projection functions," Int. J. Numer. Meth. Eng., Vol. 61, No. 2, 238-254, 2004.
21. Sigmund, O., "Morphology-based black and white filters for topology optimization," Struct. Multidisc. Optim., Vol. 33, No. 4-5, 401-424, 2007.
22. Olesen, L. H., "A high-level programming-language implementation of topology optimization applied to steady-state Navier-Stokes flow," Int. J. Numer. Meth. Eng., Vol. 65, No. 7, 975-1001, 2006.
23. Milton, G. W., "Bounds on the complex permittivity of a two-component composite material," J. Appl. Phys., Vol. 52, No. 8, 5286-5293, 1981.
24. Hashin, Z., "The elastic moduli of heterogeneous materials," J. Appl. Mech., Vol. 29, No. 1, 143-150, 1962.
25. Francfort, G. and F. Murat, "Homogenization and optimal bounds in linear elasticity," Archive for Rational Mechanics and Analysis, Vol. 94, No. 4, 307-334, 1986.
26. Lurie, K. A. and A. V. Cherkaev, "Optimization of properties of multicomponent isotropic composites," J. Optimiz. Theory App., Vol. 46, No. 4, 571-580, 1985.
27. Milton, G. W., Modelling the Properties of Composites by Laminates, Vol. 1 of IMA, 150-174, Springer-Verlag, New York, 1985.
28. Norris, A. N., "A differential scheme for the effective moduli of composites," Mech. Mater., Vol. 4, No. 1, 1-16, 1985.
29. Sigmund, O., "A new class of extremal composites," J. Mech. Phys. Solids, Vol. 48, No. 2, 397-428, 2000.
30. Grabovsky, Y. and R. V. Kohn, "Microstructures minimizing the energy of a two phase elastic composite in two space dimensions. II: the Vigdergauz microstructure," J. Mech. Phys. Solids, Vol. 43, No. 6, 949-972, 1995.
31. Vigdergauz, S., "Energy-minimizing inclusions in a planar elastic structure with macroisotropy," Struct. Optimization, Vol. 17, No. 2-3, 104-112, 1999.
32. Svanberg, K., "A class of globally convergent optimization methods based on conservative convex separable approximations," SIAM J Optimiz., Vol. 12, No. 2, 555-573, 2002.
33. Rayleigh, L., "On the influence of obstacles arranged in rectangular order upon the properties of a medium," Philos. Mag., Vol. 34, No. 211, 481-502, 1892.
34. Wallén, H., H. Kettunen, and A. Sihvola, "Composite near- field superlens design using mixing formulas and simulations," Metamaterials, Vol. 3, No. 3-4, 129-139, 2009.