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Spherical Harmonic Solution of the Robin Problem for the Laplace Equation in Supershaped Shells

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Modeling in Mathematics

Part of the book series: Atlantis Transactions in Geometry ((ATLANTIS,volume 2))

Abstract

The Robin problem for the Laplace equation in normal-polar shells is addressed by using a suitable spherical harmonic expansion technique. Attention is in particular focused on the wide class of domains whose boundaries are defined by a generalized version of the so-called “superformula” introduced by Gielis. A dedicated numerical procedure based on the computer algebra system Mathematica\(^{\copyright }\) is developed in order to validate the proposed methodology. In this way, highly accurate approximations of the solution, featuring properties similar to the classical ones, are obtained.

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Acknowledgements

This study has been partly carried out in the framework of the research and development program running at The Antenna Company. For further information, please visit the web site: http://www.antennacompany.com/.

Author information

Authors and Affiliations

  1. The Antenna Company Nederland B.V., High Tech Campus, 5656, Eindhoven, AE, The Netherlands

    Diego Caratelli

  2. Tomsk Polytechnic University, 84/3 Sovetskaya Street, 634050, Tomsk, Russia

    Diego Caratelli

  3. Department of Mathematics and Physics, Roma Tre University, Largo San Leonardo Murialdo, 1, 00146, Rome, Italy

    Pierpaolo Natalini

  4. International Telematic University UniNettuno, Corso Vittorio Emanuele II, 39, 00186, Rome, Italy

    Paolo Emilio Ricci

Authors
  1. Diego Caratelli
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  2. Pierpaolo Natalini
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  3. Paolo Emilio Ricci
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Corresponding author

Correspondence to Diego Caratelli .

Editor information

Editors and Affiliations

  1. Bio-Engineering Sciences, University of Antwerp, Antwerp, Belgium

    Johan Gielis

  2. International Telematic University UniNettuno, Roma, Italy

    Paolo Emilio Ricci

  3. Faculty of Exact and Natural Sciences, Ivane Javakhishvili Tbilisi State University, Tbilisi, Georgia

    Ilia Tavkhelidze

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Caratelli, D., Natalini, P., Ricci, P.E. (2017). Spherical Harmonic Solution of the Robin Problem for the Laplace Equation in Supershaped Shells. In: Gielis, J., Ricci , P., Tavkhelidze, I. (eds) Modeling in Mathematics . Atlantis Transactions in Geometry, vol 2. Atlantis Press, Paris. https://doi.org/10.2991/978-94-6239-261-8_2

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