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The Dirichlet problem for the Laplace equation in supershaped annuli

D. Caratelli
J. Gielis
Ilia Tavkhelidze
P. E. Ricci
Journal / Anthology

Boundary Value Problems
Year: 2013
Page range: 113

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.

*Science > Physics
*Science > Physics > Electromagnetism