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Zh. Vychisl. Mat. Mat. Fiz., 2020, Volume 60, Number 11, Pages 1915–1932 (Mi zvmmf11161)  

Mathematical physics

Recovery of boundary functions on external and internal open boundaries in an open sea hydrodynamic problem

V. I. Agoshkovab, N. R. Lezinaa, T. O. Sheloputa

a Marchuk Institute of Numerical Mathematics, Russian Academy of Sciences, Moscow, 119333 Russia
b Lomonosov Moscow State University

Abstract: The inverse problem of recovering boundary functions on external and internal open boundaries for an open sea hydrodynamic model based on the linearized shallow water equations is considered. The external open boundary is meant as the boundary separating the considered water area from the world ocean. The internal open boundary is introduced to use the domain decomposition method. The inverse problem is studied theoretically, including the proof of its unique and dense solvability. An iterative algorithm for its solution is formulated, which combines variational data assimilation with the domain decomposition method. The theoretical study is illustrated by numerical results obtained for a test problem.

Key words: mathematical modeling, numerical methods, inverse problems, open boundaries, open sea areas, domain decomposition method, variational data assimilation, methods of adjoint equations, regularization.

Funding Agency Grant Number
Russian Science Foundation 19-71-20035
Russian Foundation for Basic Research 19-01-00595
This work was supported in part by the Russian Science Foundation (project no. 19-71-20035, the general formulation of the inverse problem) and by the Russian Foundation for Basic Research (project no. 19-01-00595, the study of the formulated problems).


DOI: https://doi.org/10.31857/S0044466920110010


English version:
Computational Mathematics and Mathematical Physics, 2020, 60:11, 1855–1871

Bibliographic databases:

UDC: 519.6
Received: 31.07.2019
Revised: 16.01.2020
Accepted:07.07.2020

Citation: V. I. Agoshkov, N. R. Lezina, T. O. Sheloput, “Recovery of boundary functions on external and internal open boundaries in an open sea hydrodynamic problem”, Zh. Vychisl. Mat. Mat. Fiz., 60:11 (2020), 1915–1932; Comput. Math. Math. Phys., 60:11 (2020), 1855–1871

Citation in format AMSBIB
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\paper Recovery of boundary functions on external and internal open boundaries in an open sea hydrodynamic problem
\jour Zh. Vychisl. Mat. Mat. Fiz.
\yr 2020
\vol 60
\issue 11
\pages 1915--1932
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\crossref{https://doi.org/10.31857/S0044466920110010}
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