A Nonlinear Multigrid Method for the Parameter Identification Problem of Partial Differential Equations with Constraints

In this paper, we consider the parameter identification problem of partial differential equations with constraints. A nonlinear multigrid method is introduced to process inversion. By keeping objective functions on coarse grids consistent those fine grids, proposed reduces dimensions enormously and mitigates risk trapping in local minima effectively. Furthermore, constraints significantly improve convergence ability method. We performed numerical simulation based porosity elastic wave fluid-saturated porous media, which suggests that decreases computational expenditure, suppresses noise, improves inversion results.