A wavelet multiscale-adaptive homotopy method for the inverse problem of nonlinear diffusion equation

This article considers a permeability estimation problem of nonlinear diffusion equation within multiphase porous media flow. By combining the wavelet multiscale method with the adaptive homotopy method, we shall design a joint inversion method called the wavelet multiscale-adaptive homotopy method. And the adaptive homotopy method provides a simple manner to adapt computational refinement to the choice of the homotopy parameters. Numerical experiments show that the proposed algorithm is globally convergent, computationally efficient, and has the anti-noise and de-noising abilities.