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Open Access Research

The Dirichlet problem for the Laplace equation in supershaped annuli

Diego Caratelli1, Johan Gielis2*, Ilia Tavkhelidze3 and Paolo E Ricci4

Author Affiliations

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

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Boundary Value Problems 2013, 2013:113  doi:10.1186/1687-2770-2013-113

Published: 3 May 2013

Abstract

The Dirichlet problem for the Laplace equation in normal-polar annuli is addressed by using a suitable Fourier-like technique. Attention is in particular focused on the wide class of domains whose boundaries are defined by 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.