Skip to main content

Parallel Procedure Based on the Swarm Intelligence for Solving the Two-Dimensional Inverse Problem of Binary Alloy Solidification

  • Conference paper
  • First Online:
Parallel Processing and Applied Mathematics

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 9574))

Abstract

In the paper an application of Ant Colony Optimization algorithm for solving the two-dimensional inverse solidification problem of binary alloy is presented. Aim of the considered problem lies in reconstruction of the boundary condition on the basis of temperature values measured in selected points of the cast. Presented approach is grounded on two procedures: the finite difference method with application of the generalized alternating phase truncation method and the parallelized Ant Colony Optimization algorithm serving for minimization of a functional representing the important part of the procedure.

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 39.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 54.99
Price excludes VAT (USA)
  • Compact, lightweight 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. Gottlieb, A., Almasi, G.S.: Highly Parallel Computing. Benjamin-Cummings Publishing Co., Menlo Park (1989)

    MATH  Google Scholar 

  2. Eberhart, R.C., Shi, Y., Kennedy, J.: Swarm Intelligence. Morgan Kaufmann, San Francisco (2001)

    Google Scholar 

  3. Toksari, M.D.: Ant colony optimization for finding the global minimum. Appl. Math. Comput. 176, 308–316 (2006)

    MathSciNet  MATH  Google Scholar 

  4. Dorigo, M., Blumb, C.: Ant colony optimization theory: a survey. Theor. Comput. Sci. 344, 243–278 (2005)

    Article  MathSciNet  MATH  Google Scholar 

  5. Duan, H.: Ant colony optimization: principle, convergence and application. Adapt. Learn. Optim. 8, 373–388 (2011)

    Article  MATH  Google Scholar 

  6. Hetmaniok, E., Słota, D., Zielonka, A.: Using the swarm intelligence algorithms in solution of the two-dimensional inverse Stefan problem. Comput. Math. Appl. 69(4), 347–361 (2015)

    Article  MathSciNet  Google Scholar 

  7. Hetmaniok, E., Słota, D., Zielonka, A.: Experimental verification of selected artificial intelligence algorithms used for solving the inverse Stefan problem. Numer. Heat Transf. B. 66(4), 343–359 (2014)

    Article  Google Scholar 

  8. Ionescu, D., Ciobanu, I., Munteanu, S.I., Crisan, A., Monescu, V.: 2D mathematical model for the solidification of alloys within a temperature interval. Metal. Int. 16(4), 39–44 (2011)

    Google Scholar 

  9. Piasecka Belkhayat, A.: Numerical modelling of solidification process using interval boundary element method. Arch. Foundry Eng. 8(4), 171–176 (2008)

    MATH  Google Scholar 

  10. Mochnacki, B., Suchy, J.S.: Numerical Methods in Computations of Foundry Processes. PFTA, Cracow (1995)

    Google Scholar 

  11. Rogers, J.C.W., Berger, A.E., Ciment, M.: The alternating phase truncation method for numerical solution of a Stefan problem. SIAM J. Numer. Anal. 16, 563–587 (1979)

    Article  MathSciNet  MATH  Google Scholar 

  12. Słota, D.: Restoring boundary conditions in the solidification of pure metals. Comput. Struct. 89, 48–54 (2011)

    Article  Google Scholar 

Download references

Acknowledgements

This project has been financed from the funds of the National Science Centre granted on the basis of decision DEC-2011/03/B/ST8/06004.

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Edyta Hetmaniok .

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2016 Springer International Publishing Switzerland

About this paper

Cite this paper

Hetmaniok, E., SÅ‚ota, D., Zielonka, A. (2016). Parallel Procedure Based on the Swarm Intelligence for Solving the Two-Dimensional Inverse Problem of Binary Alloy Solidification. In: Wyrzykowski, R., Deelman, E., Dongarra, J., Karczewski, K., Kitowski, J., Wiatr, K. (eds) Parallel Processing and Applied Mathematics. Lecture Notes in Computer Science(), vol 9574. Springer, Cham. https://doi.org/10.1007/978-3-319-32152-3_27

Download citation

  • DOI: https://doi.org/10.1007/978-3-319-32152-3_27

  • Published:

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-32151-6

  • Online ISBN: 978-3-319-32152-3

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics