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

The Robin problem for the Helmholtz equation in normal-polar shells is addressed by using a suitable spherical har-monic expansion technique. Attention is in particular focused on the wide class of domains whose boundaries are de-fined 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 obtainedMicroelectronicsElectrical Engineering, Mathematics and Computer Scienc