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

2013 ◽  
Vol 04 (01) ◽  
pp. 263-270
Author(s):  
Diego Caratelli ◽  
Johan Gielis ◽  
Ilia Tavkhelidze ◽  
Paolo Emilio Ricci
Keyword(s):  
Helmholtz Equation ◽  
Spherical Harmonic ◽  
Robin Problem ◽  
Harmonic Solution

scholarly journals CORRELATED AND ZONAL ERRORS OF GLOBAL ASTROMETRIC MISSIONS: A SPHERICAL HARMONIC SOLUTION

2012 ◽  
Vol 144 (1) ◽  
pp. 22 ◽  
Author(s):  
V. V. Makarov ◽  
B. N. Dorland ◽  
R. A. Gaume ◽  
G. S. Hennessy ◽  
C. T. Berghea ◽  
...  
Keyword(s):  
Spherical Harmonic ◽  
Harmonic Solution

scholarly journals Fourier-Hankel solution of the Robin problem for the Helmholtz equation in supershaped annular domains

2013 ◽  
Vol 2013 (1) ◽  
pp. 253 ◽  
Author(s):  
Diego Caratelli ◽  
Johan Gielis ◽  
Ilia Tavkhelidze ◽  
Paolo E Ricci
Keyword(s):  
Helmholtz Equation ◽  
Robin Problem ◽  
Annular Domains

The Robin problem for the Helmholtz equation in a starlike planar domain

2011 ◽  
Vol 18 (3) ◽  
pp. 465-479
Author(s):  
Diego Caratelli ◽  
Johan Gielis ◽  
Pierpaolo Natalini ◽  
Paolo Emilio Ricci ◽  
Ilia Tavkhelidze
Keyword(s):  
Fourier Series ◽  
Helmholtz Equation ◽  
Series Expansion ◽  
Computer Algebra ◽  
Computer Algebra System ◽  
Numerical Procedure ◽  
Fourier Series Expansion ◽  
Robin Problem ◽  
Planar Domains ◽  
Good Agreement

Abstract The interior and exterior Robin problems for the Helmholtz equation in starlike planar domains are addressed by using a suitable Fourier-like technique. Attention is in particular focused on normal-polar domains whose boundaries are defined by the so-called “superformula” introduced by J. Gielis. A dedicated numerical procedure based on the computer algebra system Mathematica© is developed in order to validate the proposed approach. In this way, highly accurate approximations of the solution, featuring properties similar to the classical ones, are obtained. The computed results are found to be in good agreement with the theoretical findings on Fourier series expansion presented by L. Carleson.

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