Gradient-based estimation of Manning's friction coefficient from noisy data

Type
Article
Authors
Calo, Victor M. cc
Collier, Nathan
Gehre, Matthias
Jin, Bangti
Radwan, Hany G.
Santillana, Mauricio
KAUST Department
Applied Mathematics and Computational Science Program
Earth Science and Engineering Program
Physical Sciences and Engineering (PSE) Division
Environmental Science and Engineering Program
Numerical Porous Media SRI Center (NumPor)
Date
2013-01
Permanent link to this record
http://hdl.handle.net/10754/562559

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Abstract
We study the numerical recovery of Manning's roughness coefficient for the diffusive wave approximation of the shallow water equation. We describe a conjugate gradient method for the numerical inversion. Numerical results for one-dimensional models are presented to illustrate the feasibility of the approach. Also we provide a proof of the differentiability of the weak form with respect to the coefficient as well as the continuity and boundedness of the linearized operator under reasonable assumptions using the maximal parabolic regularity theory. © 2012 Elsevier B.V. All rights reserved.
Sponsors
This work was initiated while V.M.C. was a Visiting Professor at the Institute for Applied Mathematics and Computational Science (IAMCS), Texas A&M University, College Station. The work of M.G. was carried out during his visit at IAMCS. They would like to thank the institute for the kind hospitality and support. The work of B.J. is supported by Award No. KUS-C1-016-04, made by King Abdullah University of Science and Technology (KAUST).
Publisher
Elsevier
Journal
Journal of Computational and Applied Mathematics
ISSN
03770427
DOI
10.1016/j.cam.2012.08.004
arXiv
arXiv:1204.1709
Additional Links
http://arxiv.org/abs/arXiv:1204.1709v1
Collections
Articles; Environmental Science and Engineering Program; Applied Mathematics and Computational Science Program; Physical Sciences and Engineering (PSE) Division; Earth Science and Engineering Program