Abstract
A class of radiation problems is considered for the Helmholtz equation in exterior domains bounded by a smooth surface on which Dirichlet, Neumann, or Robin boundary conditions are imposed. The problem of finding the boundary data which maximizes far field power in a restricted subset of far field directions is formulated as a constrained maximization problem. Existence of an optimal solution in a variety of control domains is established. The particular case when the boundary is circular and the control domain is the unit ball inL 2 is treated in detail. An algorithm for constructing the optimal solution is derived and used to obtain explicit numerical results.
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Communicated by L. Cesari
This work was supported by the US Air Force under Grant No. AFOSR 81-0156. The work was completed while the first author was on leave to the Institut für Numerische und Angewandte Mathematik, Universität Göttingen, Göttingen, BRD.
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Angell, T.S., Kleinman, R.E. Generalized exterior boundary-value problems and optimization for the Helmholtz equation. J Optim Theory Appl 37, 469–497 (1982). https://doi.org/10.1007/BF00934952
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DOI: https://doi.org/10.1007/BF00934952