Skip to main content
SpringerLink
Log in

A Fast Algorithm to Determine the Flux Around Closely Spaced Non-overlapping Disks

  • Conference paper
  • First Online:
New Trends in Analysis and Interdisciplinary Applications

Part of the book series: Trends in Mathematics ((RESPERSP))

  • 1028 Accesses

Abstract

This paper is devoted to application of the fast algorithm to determine the flux around closely spaced non-overlapping disks on the conductive plane. This method is based on successive approximations applied to functional equations. When the distances between the disks are sufficiently small, convergence of the classical method of images fails numerically. In this talk, the limitations on geometric parameters are described.

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

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 149.00
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 199.99
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. G.W. Milton, The Theory of Composites (Cambridge University Press, Cambridge, 2002)

    Book  MATH  Google Scholar 

  2. V. Mityushev, Y. Obnosov, E. Pesetskaya, S. Rogosin, Analytical Methods for Heat Conduction. Math. Model. Anal. 13 (1), 67–78 (2008)

    Article  MathSciNet  MATH  Google Scholar 

  3. V. Mityushev, N. Rylko, A fast algorithm for computing the flux around non-overlapping disks on the plane. Math. Comput. Model. 57, 1350–1359 (2013)

    Article  MathSciNet  Google Scholar 

  4. A.A. Kolpakov, A.G. Kolpakov, Capacity and Transport in Contrast Composite Structures: Asymptotic Analysis and Applications (CRC Press, Boca Raton, 2009)

    Book  MATH  Google Scholar 

  5. V. Mityushev, S. Rogosin, Constructive Methods to Linear and Non-linear Boundary Value Problems of the Analytic Function. Theory and Applications. Monographs and Surveys in 2000, Pure and Applied Mathematics (Chapman & Hall/CRC, Boca Raton, 2000)

    Google Scholar 

  6. L.D. Landau, E.M. Lifshitz, Electrodynamics of Continuous Media. Course of Theoretical Physics S, vol. 8 (Pergamon Press, Oxford, 1960)

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. The Pedagogical University of Cracow, ul. Podchoraążych 2, 30-084, Kraków, Poland

    Olaf Bar

Authors
  1. Olaf Bar
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Olaf Bar .

Editor information

Editors and Affiliations

  1. Faculty of Information Technology, Macau University of Science and Technology, Taipa, Macao

    Pei Dang

  2. Department of Mathematics, University of Aveiro, Aveiro, Portugal

    Min Ku

  3. Faculty of Science and Technology, Department of Mathematics, University of Macau, Taipa, Macao

    Tao Qian

  4. Department of Mathematics, University of Torino, Torino, Italy

    Luigi G. Rodino

Rights and permissions

Reprints and permissions

Copyright information

© 2017 Springer International Publishing AG

About this paper

Cite this paper

Bar, O. (2017). A Fast Algorithm to Determine the Flux Around Closely Spaced Non-overlapping Disks. In: Dang, P., Ku, M., Qian, T., Rodino, L. (eds) New Trends in Analysis and Interdisciplinary Applications. Trends in Mathematics(). Birkhäuser, Cham. https://doi.org/10.1007/978-3-319-48812-7_2

Download citation

Publish with us

Policies and ethics

Search

Navigation