Geodesic
Transfer of Sommerfeld's radiation conditions to an~artificial boundary of a~domain, based on a~variational principle
Sbornik. Mathematics, Tome 81 (1995) no. 2, pp. 261-279

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To solve the Helmholtz equation interior to a bounded domain with artificial boundary, a new formulation of variational type is proposed for boundary conditions which have the property of suppressing waves reflected from the boundary. This formulation is based on the minimization of a functional constructed in a special way. Existence and uniqueness theorems are proved for a classical solution of the problem in the proposed variational formulation. It is proved that the solution of the interior problem converges uniformly to a solution of the problem posed in an unbounded domain with Sommerfeld's radiation conditions at infinity as the size of the domain increases without limit. 
@article{SM_1995_81_2_a0,
     author = {I. V. Bezmenov},
     title = {Transfer of {Sommerfeld's} radiation conditions to an~artificial boundary of a~domain, based on a~variational principle},
     journal = {Sbornik. Mathematics},
     pages = {261--279},
     publisher = {mathdoc},
     volume = {81},
     number = {2},
     year = {1995},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SM_1995_81_2_a0/}
}
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I. V. Bezmenov. Transfer of Sommerfeld's radiation conditions to an~artificial boundary of a~domain, based on a~variational principle. Sbornik. Mathematics, Tome 81 (1995) no. 2, pp. 261-279. http://geodesic.mathdoc.fr/item/SM_1995_81_2_a0/