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Zh. Vychisl. Mat. Mat. Fiz., 2018, Volume 58, Number 8, Pages 138–147 (Mi zvmmf10769)  

An algorithm for source reconstruction in nonlinear shallow-water equations

S. I. Kabanikhinab, O. I. Krivorotkoab

a Institute of Computational Mathematics and Mathematical Geophysics, Siberian Branch, Russian Academy of Sciences, Novosibirsk, Russia
b Novosibirsk State University, Novosibirsk, Russia

Abstract: A numerical algorithm is proposed to solve the source reconstruction problem for a system of nonlinear shallow-water equations using the dynamics of water surface perturbation measured at a finite number of spatial points and/or over a part of the surface at a fixed time. The combined inverse problem under study is reduced to the minimization of an objective functional characterizing the quadratic deviation of simulated data from measured data (a misfit function). An explicit expression for the gradient of the misfit function is obtained. The direct and conjugate problems within the framework of shallow-water equations are solved by the finite volume method. The numerical results are analyzed and compared with experimental data.

Key words: nonlinear shallow-water equations, finite volume method, inverse problem, source reconstruction, regularization, optimization, gradient of objective functional, conjugate gradient method.

Funding Agency Grant Number
Ministry of Education and Science of the Russian Federation
Russian Foundation for Basic Research 16-31-00189_мол_а
16-29-15120_офи_м


DOI: https://doi.org/10.31857/S004446690002008-9

References: PDF file   HTML file

English version:
Computational Mathematics and Mathematical Physics, 2018, 58:8, 1334–1343

Bibliographic databases:

UDC: 519.63
Received: 05.03.2018

Citation: S. I. Kabanikhin, O. I. Krivorotko, “An algorithm for source reconstruction in nonlinear shallow-water equations”, Zh. Vychisl. Mat. Mat. Fiz., 58:8 (2018), 138–147; Comput. Math. Math. Phys., 58:8 (2018), 1334–1343

Citation in format AMSBIB
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\by S.~I.~Kabanikhin, O.~I.~Krivorotko
\paper An algorithm for source reconstruction in nonlinear shallow-water equations
\jour Zh. Vychisl. Mat. Mat. Fiz.
\yr 2018
\vol 58
\issue 8
\pages 138--147
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\crossref{https://doi.org/10.31857/S004446690002008-9}
\elib{https://elibrary.ru/item.asp?id=36283437}
\transl
\jour Comput. Math. Math. Phys.
\yr 2018
\vol 58
\issue 8
\pages 1334--1343
\crossref{https://doi.org/10.1134/S0965542518080109}
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  • Журнал вычислительной математики и математической физики Computational Mathematics and Mathematical Physics
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