NUMERICAL SOLUTIONS OF THE DIFFUSION COEFFICIENT IDENTIFICATION PROBLEM

Tóm tắt

In this paper, we investigate several numerical algorithms to find the numerical solutions of the diffusion coefficient identification problem. Normally, in order to solve this problem, one uses the least squares function together with a regularization method, butwe here use the energy functional with parsity regularization method. Our approach leads to the study of a minimum convexproblem (but not differentiable). Therefore, we can apply some fast and efficient algorithms, which has been proposed recently. The main results presented in the paper is to give the new approach and to implement the efficient algorithms to find the numerical solutions of the diffusion coefficient identification problem. The effectiveness of the algorithms and the numerical solutions are illustrated and presented in a specific example.