A Numerical Descent Method for an Inverse Problem of a Scalar Conservation Law Modelling Sedimentation

R. Bürger (), A. Coronel () and M. Sepúlveda ()
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R. Bürger: Universidad de Concepción, Departamento de Ingeniería Matemática
A. Coronel: Universidad del Bío-Bío, Departamento de Ciencias Básicas, Facultad de Ciencias
M. Sepúlveda: Universidad de Concepción, Departamento de Ingeniería Matemática

A chapter in Numerical Mathematics and Advanced Applications, 2008, pp 225-232 from Springer

Abstract: Abstract This contribution presents a numerical descent method for the identification of parameters in the flux function of a scalar nonlinear conservation law when the solution at a fixed time is known. This problem occurs in a model of batch sedimentation of an ideal suspension. We formulate the identification problem as a minimization problem of a suitable cost function and derive its formal gradient by means of a first-order perturbation of the solution of the direct problem, which yields a linear transport equation with source term and discontinuous coefficients. for the numerical approach, we assume that the direct problem is discretized by the Engquist-Osher scheme and obtain a discrete first order perturbation associated to this scheme. The discrete gradient is used in combination with the conjugate gradient and coordinate descent methods to find numerically the flux parameters.

Keywords: Inverse Problem; Direct Problem; Degenerate Parabolic Equation; Adjoint State; Discrete Gradient (search for similar items in EconPapers)
Date: 2008
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-540-69777-0_26

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DOI: 10.1007/978-3-540-69777-0_26

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