The neumann problem for the helmholtz equation in a starlike planar domain

Journal article (2010)

Authors

D. Caratelli International Research Centre for Telecommunication and Radar

P Natalini External organisation

PE Ricci External organisation

Alexander Yarovoy Microwave Technology and Systems for Radar

Research Group

International Research Centre for Telecommunication and Radar

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Published Date

2010

Language

English

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Research Group

International Research Centre for Telecommunication and Radar

Abstract

The interior and exterior Neumann 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 Gielis. A dedicated numerical procedure based on a computer algebra system is developed in order to validate the proposed approach. In this way, highly accurate approximations of the solution, featuring properties similar to classical ones, are obtained. Computed results are found to be in good agreement with theoretical findings on Fourier series expansion presented by Carleson.