Active control of scalar Helmholtz fields in the presence of known impenetrable obstacles

Author:

Besabe Lander,Onofrei Daniel

Abstract

In this paper, we consider the question of actively manipulating scalar Helmholtz fields radiated by a given source that is supported on a compact domain. We claim that the field radiated by the source approximates given scalar fields in prescribed exterior regions while maintaining desired far field patterns in prescribed directions in the presence of exterior known impenetrable obstacles. For simplicity of the exposition, we consider a simplified geometry with only one obstacle, one region of control, and a finite number of far field directions and present a theoretical argument for our claim stated above. Afterwards, we also show how it can be elementarily extended to the general case. Further, we construct a numerical scheme to compute these boundary inputs using the method of moments, the addition theorem, Tikhonov regularization, and Laplace spherical functions.

Publisher

American Mathematical Society

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