A NUMERICAL DESCENT METHOD FOR AN INVERSE PROBLEM OF A SCALAR CONSERVATION LAW MODELLING SEDIMENTATION

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