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Bathymetry Reconstruction Using Inverse ShallowWater Models : Finite Element Discretization and Regularization

Title data

Hajduk, Hennes ; Kuzmin, Dmitri ; Aizinger, Vadym:
Bathymetry Reconstruction Using Inverse ShallowWater Models : Finite Element Discretization and Regularization.
In: van Brummelen, Harald ; Corsini, Alessandro ; Perotto, Simona ; Rozza, Gianluigi (ed.): Numerical Methods for Flows : FEF 2017 Selected Contributions. - Cham : Springer , 2020 . - pp. 223-230
ISBN 978-3-030-30705-9
DOI: https://doi.org/10.1007/978-3-030-30705-9_20

Abstract in another language

In the present paper, we use modified shallow water equations (SWE) to reconstruct the bottom topography (also called bathymetry) of a flow domain without resorting to traditional inverse modeling techniques such as adjoint methods. The discretization in space is performed using a piecewise linear discontinuous Galerkin (DG) approximation of the free surface elevation and (linear) continuous finite elements for the bathymetry. Our approach guarantees compatibility of the discrete forward and inverse problems: for a given DG solution of the forward SWE problem, the underlying continuous bathymetry can be recovered exactly. To ensure well-posedness of the modified SWE and reduce sensitivity of the results to noisy data, a regularization term is added to the equation for the water height. A numerical study is performed to demonstrate the ability of the proposed method to recover bathymetry in a robust and accurate manner.

Further data

Item Type: Article in a book
Refereed: Yes
Institutions of the University: Faculties > Faculty of Mathematics, Physics und Computer Science > Department of Mathematics > Chair Scientific Computing
Faculties > Faculty of Mathematics, Physics und Computer Science > Department of Mathematics > Chair Scientific Computing > Chair Scientific Computing - Univ.-Prof. Dr. Mario Bebendorf
Faculties > Faculty of Mathematics, Physics und Computer Science > Department of Mathematics > Professor Numerics of Partial Differential Equations
Faculties > Faculty of Mathematics, Physics und Computer Science > Department of Mathematics > Professor Numerics of Partial Differential Equations > Professor Numerics of Partial Differential Equations - Univ.-Prof. Dr. Vadym Aizinger
Research Institutions > Research Centres > Forschungszentrum für Modellbildung und Simulation (MODUS)
Research Institutions > Research Centres > Forschungszentrum für Wissenschaftliches Rechnen an der Universität Bayreuth - HPC-Forschungszentrum
Result of work at the UBT: No
DDC Subjects: 000 Computer Science, information, general works > 004 Computer science
500 Science > 510 Mathematics
500 Science > 550 Earth sciences, geology
Date Deposited: 25 Feb 2020 07:31
Last Modified: 25 Feb 2020 07:31
URI: https://eref.uni-bayreuth.de/id/eprint/54426