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Spherical Harmonic Solution of the Robin Problem for the Helmholtz Equation in a Supershaped Shell
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
- 1 Microwave Sensing, Signals and Systems, Delft University of Technology, Delft, The Netherlands
- 2 Department of Bioscience Engineering, University of Antwerp, Antwerp, Belgium
- 3 Faculty of Exact and Natural Sciences, Tbilisi State University, Tbilisi, Georgia
- 4 Faculty of Engineering, Campus Bio-Medico University, Rome, Italy
Applied Mathematics·Volume 04 (2013)·Pages 263–270·Published 30 January 2013·DOI10.4236/am.2013.41A040
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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.
KeywordsRobin ProblemHelmholtz EquationSpherical Harmonic ExpansionGielis FormulaSupershaped Shell
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