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Recovery of Boundary Functions on External and Internal Open Boundaries in an Open Sea Hydrodynamic Problem

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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.

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ACKNOWLEDGMENTS

We are grateful to V.P. Shutyaev for discussion of this work and helpful comments.

Funding

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).

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Authors and Affiliations

  1. Marchuk Institute of Numerical Mathematics, Russian Academy of Sciences, 119333, Moscow, Russia

    V. I. Agoshkov, N. R. Lezina & T. O. Sheloput

  2. Faculty of Computational Mathematics and Cybernetics, Lomonosov Moscow State University, 119991, Moscow, Russia

    V. I. Agoshkov

Authors
  1. V. I. Agoshkov
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  2. N. R. Lezina
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  3. T. O. Sheloput
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Correspondence to N. R. Lezina or T. O. Sheloput.

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Translated by I. Ruzanova

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Agoshkov, V.I., Lezina, N.R. & Sheloput, T.O. Recovery of Boundary Functions on External and Internal Open Boundaries in an Open Sea Hydrodynamic Problem. Comput. Math. and Math. Phys. 60, 1855–1871 (2020). https://doi.org/10.1134/S0965542520110019

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