A wavelet multiscale-homotopy method for the parameter identification problem of partial differential equations

By introducing the wavelet multiscale method and the homotopy method to the inversion process for the parameter identification problem of partial differential equations, a joint inversion method called the wavelet multiscale-homotopy method is proposed, which is globally convergent, computationally efficient, and has the anti-noise ability. As a practical problem, the parameter identification problem of the saturation equation in the fractional flow formulation of the two-phase porous media flow equations is solved. Numerical results validate the method’s merits.