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A three-dimensional active cloaking strategy for the Helmholtz equation that exploits the symmetry of the platonic
Cheuk-Him Yeung1, William J Parnell1, Tom Shearer1
1Department of Mathematics, University of Manchester, Manchester, M13 9PL, United Kingdomcheukhim.yeung@manchester.ac.uk, william.parnell@manchester.ac.uk, tom.shearer@manchester.ac.uk.
Abstract:
An active cloaking strategy for the scalar Helmholtz equation in three dimensions is developed by placing active sources at the vertices of Platonic solids. In each case, a "silent zone" is created interior to the Platonic solid and only the incident field remains in a defined region exterior to this zone. This distribution of sources ensures that implementation of the cloaking strategy is efficient: once the multipole source amplitudes at a single source location are determined, the other amplitudes are calculated by multiplying the multipole source vector by a rotation matrix. The technique is relevant to any scalar wave field.
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