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Active exterior cloaking for the 2D Laplace and Helmholtz equations
Fernando Guevara Vasquez1, Graeme W Milton, Daniel Onofrei
1Department of Mathematics, University of Utah, Salt Lake City, Utah 84112, USA.
Abstract:
A new cloaking method is presented for 2D quasistatics and the 2D Helmholtz equation that we speculate extends to other linear wave equations. For 2D quasistatics it is proven how a single active exterior cloaking device can be used to shield an object from surrounding fields, yet produce very small scattered fields. The problem is reduced to finding a polynomial which is close to 1 in a disk and close to 0 in another disk, and such a polynomial is constructed. For the 2D Helmholtz equation it is numerically shown that three exterior cloaking devices placed around the object suffice to hide it.
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