The Dirichlet problem for the Laplace equation in supershaped annuliThe Dirichlet problem for the Laplace equation in supershaped annuli
Faculty of Sciences. Bioscience Engineering
Environmental Ecology & Microbiology (ENdEMIC)
2013New York, N.Y., 2013
Engineering sciences. Technology
Boundary value problems. - New York, N.Y.
(2013), p. 1-10
University of Antwerp
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.