An adaptive homotopy method for permeability estimation of a nonlinear diffusion equation

We investigate the problem of estimating the permeability function in a nonlinear diffusion equation, which plays an important role in promoting the permeability estimation within multiphase porous media flow. The forward problem is discretized using finite-difference methods and the parameter estimation is formulated as a least-square minimization problem with a regularization term. To overcome the weakness of the local convergence of traditional methods, a homotopy method is applied to solve this inverse problem. By introducing the Tikhonov regularization and adaptively choosing the homotopy parameters, a new and globally convergent algorithm is constructed. Finally, many numerical simulations are presented to show the global convergence, computational efficiency and anti-noise ability of the proposed algorithm.