An adaptive multigrid conjugate gradient method for the inversion of a nonlinear convection-diffusion equation

This paper considers the problem of estimating the permeability in a nonlinear convection-diffusion equation. To overcome the large calculation burden of conventional methods, we apply an adaptive multigrid conjugate gradient method to solve this inverse problem. This new method combines the multigrid multiscale idea with the conjugate gradient method, and adopts the necessary condition that the optimum solution should be the fixed point of the multigrid inversion method. Some numerical results verify that the proposed method both dramatically reduces the required computations and improves the inversion quality.