Open Access
WINTER 2014 Active manipulation of fields modeled by the Helmholtz equation
Daniel Onofrei
J. Integral Equations Applications 26(4): 553-572 (WINTER 2014). DOI: 10.1216/JIE-2014-26-4-553


In this paper we extend the results proposed in \cite{Onofrei-S} and study the problem of active control in the context of a scalar Helmholtz equation. Given a source region $D_a$ and $\{v_0,v_1,\ldots,v_n\}$, a set of solutions of the homogeneous scalar Helmholtz equation in $n$ mutually disjoint ``control" regions $\{D_0,D_1,\ldots,D_n\}$ of $\RR^2$ or $\RR^3$, respectively, the main objective of this paper is to characterize the necessary boundary data on $\partial D_a$ so that the solution to the corresponding exterior scalar Helmholtz problem will closely approximate $v_i$ in $D_i$, respectively, for each $i\in\{0,\ldots,n\}$. Building up on the previous ideas presented in \cite{Onofrei-S} we show the existence of a class of solutions to the problem, provide numerical support of the results in 2D and 3D and discuss the existence of a minimal energy solution and its stability.


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Daniel Onofrei. "Active manipulation of fields modeled by the Helmholtz equation." J. Integral Equations Applications 26 (4) 553 - 572, WINTER 2014.


Published: WINTER 2014
First available in Project Euclid: 9 January 2015

zbMATH: 1305.78011
MathSciNet: MR3299831
Digital Object Identifier: 10.1216/JIE-2014-26-4-553

Keywords: active exterior cloaking , Active manipulation , Helmholtz equation , integral equation , Layer potentials

Rights: Copyright © 2014 Rocky Mountain Mathematics Consortium

Vol.26 • No. 4 • WINTER 2014
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