Skip to main content

Abstract

In order that the sensitivity formulas derived in the previous chapters are used for design optimization of electromagnetic systems, the optimization algorithms and the geometry modeling for evolving shapes are both required.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 129.00
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 169.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 169.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

References

  1. Sethian, J.A.: Level Set Methods and Fast Marching Methods: Evolving Interfaces in Computational Geometry, Fluid Mechanics, Computer Vision, and Materials Science. Cambridge University Press, Cambridge (1999)

    MATH  Google Scholar 

  2. Osher, S., Fedkiw, R.: Level Set Methods and Dynamic Implicit Surfaces. Springer-Verlag, New York (2003)

    Book  Google Scholar 

  3. Dorn, O., Miller, E.L., Rappaport, C.M.: A shape reconstruction method for electromagnetic tomography using adjoint fields and level sets. Inverse Probl. 16, 1119–1156 (2000)

    Article  MathSciNet  Google Scholar 

  4. Allaire, G.: Shape Optimization by the Homogenization Method. Springer-Verlag, New York (2002)

    Book  Google Scholar 

  5. Allaire, G., Jouve, F., Toader, A.-M.: Structural optimization using sensitivity analysis and a level-set method. J. Comput. Phys. 194, 363–393 (2004)

    Article  MathSciNet  Google Scholar 

  6. Bendsøe, M.P., Sigmund, O.: Topology Optimization: Theory. Springer-Verlag, Berlin, Methods and Applications (2004)

    Book  Google Scholar 

  7. Wang, Y., Luo, Z., Kang, Z., Zhang, N.: A multi-material level set-based topology and shape optimization method. Comput. Methods Appl. Mech. Engrg. 283, 1570–1586 (2015)

    Article  MathSciNet  Google Scholar 

  8. Liu, Z., Korvink, J.G., Huang, R.: Structure topology optimization: fully coupled level set method via FEMLAB. Struct. Multidiscip. Optim. 29, 407–417 (2005)

    Article  MathSciNet  Google Scholar 

  9. Kim, Y.S., Byun, J.K., Park, I.H.: A level set method for shape optimization of electromagnetic systems. IEEE Trans. Magn. 45, 1466–1469 (2009)

    Article  Google Scholar 

  10. Kim, Y.S., Park, I.H.: Topology optimization of rotor in synchronous reluctance motor using level set method and shape design sensitivity. IEEE Trans. Appl. Supercond. 20, 1093–1096 (2010)

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Il Han Park .

Rights and permissions

Reprints and permissions

Copyright information

© 2019 Springer Nature Singapore Pte Ltd.

About this chapter

Check for updates. Verify currency and authenticity via CrossMark

Cite this chapter

Park, I. (2019). Level Set Method and Continuum Sensitivity. In: Design Sensitivity Analysis and Optimization of Electromagnetic Systems. Mathematical and Analytical Techniques with Applications to Engineering. Springer, Singapore. https://doi.org/10.1007/978-981-13-0230-5_7

Download citation

  • DOI: https://doi.org/10.1007/978-981-13-0230-5_7

  • Published:

  • Publisher Name: Springer, Singapore

  • Print ISBN: 978-981-13-0229-9

  • Online ISBN: 978-981-13-0230-5

  • eBook Packages: EngineeringEngineering (R0)

Publish with us

Policies and ethics