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A controllability method with an artificial boundary condition for the exterior Helmholtz problem

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Abstract

The exterior Helmholtz problem is solved by a controllability method with a new artificial boundary condition for a time-periodic wave equation. The condition uses the Dirichlet-to-Neumann operator associated with the Helmholtz problem. A semi-discrete problem is derived for the time-periodic wave equation, and a necessary and sufficient condition is proved for the uniqueness of the discrete problem. A typical example where the condition is satisfied is shown. Some numerical examples are also presented.

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Authors and Affiliations

  1. Department of Computer Science, Faculty of Electro-Communications, The University of Electro-Communications, 1-5-1, Chofugaoka, Chofu-shi, 182-8585, Tokyo, Japan

    Daisuke Koyama

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  1. Daisuke Koyama
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Correspondence to Daisuke Koyama.

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Koyama, D. A controllability method with an artificial boundary condition for the exterior Helmholtz problem. Japan J. Indust. Appl. Math. 20, 117 (2003). https://doi.org/10.1007/BF03167466

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  • DOI: https://doi.org/10.1007/BF03167466

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