Geodesic
Recovery of a~boundary function from observation data for the surface wave propagation problem in an open basin
Sibirskij žurnal industrialʹnoj matematiki, Tome 16 (2013) no. 1, pp. 10-20.

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The iterative numerical method of recovery of the unknown boundary function describing the ocean influence on the open boundary of a computational domain is proposed. The algorithm is based on the method for solving inverse problems by adjoint equations and optimal control methods. The algorithm is tested on a model problem for the basin of the Sea of Okhotsk.
Keywords: shallow water equations, finite element method, inverse problem. 
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E. V. Dementyeva; E. D. Karepova; V. V. Shaidurov. Recovery of a~boundary function from observation data for the surface wave propagation problem in an open basin. Sibirskij žurnal industrialʹnoj matematiki, Tome 16 (2013) no. 1, pp. 10-20. http://geodesic.mathdoc.fr/item/SJIM_2013_16_1_a1/

[1] Marchuk G. I., Kagan B. A., Dinamika okeanskikh prilivov, Gidrometizdat, L., 1983

[2] Gill A., Dinamika atmosfery i okeana, v. 1, Mir, M., 1986

[3] Kowalik Z., Polyakov I., “Tides in the Sea of Okhotsk”, J. Phys. Oceanogr., 28:7 (1998), 1389–1409 | 2.0.CO;2 class='badge bg-secondary rounded-pill ref-badge extid-badge'>DOI

[4] Agoshkov V. I., “Inverse problems of the mathematical theory of tides: boundary-function problem”, Russian J. Numer. Anal. Math. Modelling, 20:1 (2005), 1–18 | DOI | MR | Zbl

[5] Kamenshchikov L. P., Karepova E. D., Shaidurov V. V., “Simulation of surface waves in basins by the finite element method”, Russian J. Numer. Anal. Math. Modelling, 21:4 (2006), 305–320 | DOI | MR | Zbl

[6] Karepova E. D., Shaidurov V. V., “Parallelnaya realizatsiya MKE dlya nachalno-kraevoi zadachi melkoi vody”, Vychisl. tekhnologii, 14:6 (2009), 45–57 | Zbl

[7] Dementeva E. V., Karepova E. D., Malyshev A. V., “Effektivnost chislennogo modelirovaniya na klasternykh sistemakh rasprostraneniya poverkhnostnykh voln”, Vestn. NGU. Ser. Informatsionnye tekhnologii, 9:1 (2011), 11–20

[8] Tikhonov A. N., Arsenin V. Ya., Metody resheniya nekorrektnykh zadach, Nauka, M., 1979 | MR

[9] Kabanikhin S. I., Obratnye i nekorrektnye zadachi, Ucheb. dlya studentov vysshikh uchebnykh zavedenii, Sib. nauch. izd-vo, Novosibirsk, 2009

[10] Agoshkov V. I., Metody optimalnogo upravleniya i sopryazhennykh uravnenii v zadachakh matematicheskoi fiziki, Izd. IVM RAN, M., 2003 | MR

[11] Alekseev G. V., Tereshko D. A., Analiz i optimizatsiya v gidrodinamike vyazkoi zhidkosti, Dalnauka, Vladivostok, 2008

[12] Alekseev G. V., “Obratnye ekstremalnye zadachi dlya statsionarnykh uravnenii teorii massoperenosa”, Zhurn. vychisl. matematiki i mat. fiziki, 42:3 (2002), 380–394 | MR | Zbl

[13] Alekseev G. V., Kalinina E. A., “Identifikatsiya mladshego koeffitsienta dlya statsionarnogo uravneniya konvektsii-diffuzii-reaktsii”, Sib. zhurn. industr. matematiki, 10:1(29) (2007), 3–16 | MR | Zbl

[14] Kireev I. V., Pyataev C. F., “Pikselnaya tekhnologiya diskretizatsii akvatorii Mirovogo okeana”, Vychisl. tekhnologii, 14:5 (2009), 30–39 | Zbl