Parameter estimation with the multigrid-homotopy method for a nonlinear diffusion equation

Abstract

This paper is concerned with the numerical identification of the piecewise constant permeability function for a nonlinear diffusion equation within the two-phase porous media flow. A novel iteration scheme based on the multigrid idea and homotopy method, named as the multigrid-homotopy method, has been developed for solving this problem. Numerical results indicate that this method can overcome the numerical instability and be robust to data noise. In addition, compared with the multigrid method, the multigrid-homotopy method expands the convergence domain; compared with the homotopy method, this method improves the convergence rate. The results are promising.