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

Type

Article

Authors

Calo, Victor M.

Collier, Nathan
Gehre, Matthias
Jin, Bangti
Radwan, Hany G.
Santillana, Mauricio

KAUST Department

Applied Mathematics and Computational Science Program
Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division
Earth Science and Engineering Program
Environmental Science and Engineering Program
Numerical Porous Media SRI Center (NumPor)
Physical Science and Engineering (PSE) Division

KAUST Grant Number

Date

2013-01

Preprint Posting Date

2012-04-08

Permanent link to this record

http://hdl.handle.net/10754/562559

Metadata

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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

Journal

Journal of Computational and Applied Mathematics

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 Science and Engineering (PSE) Division; Earth Science and Engineering Program; Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division