TY - JOUR

T1 - An Algorithm for Source Reconstruction in Nonlinear Shallow-Water Equations

AU - Kabanikhin, S. I.

AU - Krivorotko, O. I.

N1 - Funding Information: ACKNOWLEDGMENTS This study was supported by the Ministry of Education and Science of the Russian Federation and the Russian Foundation for Basic Research, project nos. 16-31-00189 and 16-29-15120. Publisher Copyright: © 2018, Pleiades journals. All rights reserved.

PY - 2018/8

Y1 - 2018/8

N2 - 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.

AB - 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.

KW - nonlinear shallow-water equations

KW - finite volume method

KW - inverse problem

KW - source reconstruction

KW - regularization

KW - optimization

KW - gradient of objective functional

KW - conjugate gradient method

KW - TSUNAMI WAVE-FORMS

KW - INVERSION

KW - AMPLITUDES

KW - RUNUP

KW - source recon-struction

UR - http://www.scopus.com/inward/record.url?scp=85117327843&partnerID=8YFLogxK

U2 - 10.1134/S0965542518080109

DO - 10.1134/S0965542518080109

M3 - Article

VL - 58

SP - 1334

EP - 1343

JO - Computational Mathematics and Mathematical Physics

JF - Computational Mathematics and Mathematical Physics

SN - 0965-5425

IS - 8

ER -