Spherical Harmonic Solution of the Robin Problem for the Helmholtz Equation in a Supershaped Shell

Affiliation(s)

Microwave Sensing, Signals and Systems, Delft University of Technology, Delft, The Netherlands.

Department of Bioscience Engineering, University of Antwerp, Antwerp, Belgium.

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

Faculty of Engineering, Campus Bio-Medico University, Rome, Italy.

Microwave Sensing, Signals and Systems, Delft University of Technology, Delft, The Netherlands.

Department of Bioscience Engineering, University of Antwerp, Antwerp, Belgium.

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

Faculty of Engineering, Campus Bio-Medico University, Rome, Italy.

Abstract

The Robin problem for the Helmholtz 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^{?} 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.

Keywords

Robin Problem; Helmholtz Equation; Spherical Harmonic Expansion; Gielis Formula; Supershaped Shell

Robin Problem; Helmholtz Equation; Spherical Harmonic Expansion; Gielis Formula; Supershaped Shell

Cite this paper

D. Caratelli, J. Gielis, I. Tavkhelidze and P. Ricci, "Spherical Harmonic Solution of the Robin Problem for the Helmholtz Equation in a Supershaped Shell,"*Applied Mathematics*, Vol. 4 No. 1, 2013, pp. 263-270. doi: 10.4236/am.2013.41A040.

D. Caratelli, J. Gielis, I. Tavkhelidze and P. Ricci, "Spherical Harmonic Solution of the Robin Problem for the Helmholtz Equation in a Supershaped Shell,"

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