This article is cited in 1 scientific paper (total in 1 paper)
Transfer of Sommerfeld's radiation conditions to an artificial boundary of a domain, based on a variational principle
I. V. Bezmenov
M. V. Keldysh Institute for Applied Mathematics, Russian Academy of Sciences
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.
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Russian Academy of Sciences. Sbornik. Mathematics, 1995, 81:2, 261–279
MSC: 35J05, 35A05, 35A35
I. V. Bezmenov, “Transfer of Sommerfeld's radiation conditions to an artificial boundary of a domain, based on a variational principle”, Mat. Sb., 185:3 (1994), 3–24; Russian Acad. Sci. Sb. Math., 81:2 (1995), 261–279
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\paper Transfer of Sommerfeld's radiation conditions to an~artificial boundary of a~domain, based on a~variational principle
\jour Mat. Sb.
\jour Russian Acad. Sci. Sb. Math.
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T. Sh. Kalmenov, D. Suragan, “Perenos uslovii izlucheniya Zommerfelda na granitsu ogranichennoi oblasti”, Zh. vychisl. matem. i matem. fiz., 52:6 (2012), 1063–1068
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