Inverse problem of groundwater modeling by iteratively regularized Gauss–Newton method with a nonlinear regularization term

A nonlinear minimization problem ‖F(d)−u‖⟶min‖F(d)−u‖⟶min, ‖u−uδ‖≤δ‖u−uδ‖≤δ, is a typical mathematical model of various applied inverse problems. In order to solve this problem numerically in the lack of regularity, we introduce iteratively regularized Gauss–Newton procedure with a nonlinear regularization term (IRGN–NRT). The new algorithm combines two very powerful features: iterative regularization and the most general stabilizing term that can be updated at every step of the iterative process. The convergence analysis is carried out in the presence of noise in the data and in the modified source condition. Numerical simulations for a parameter identification ill-posed problem arising in groundwater modeling demonstrate the efficiency of the proposed method.

► Iteratively regularized Gauss–Newton procedure with a nonlinear penalty term is suggested. ► The most general stabilizing term that can be updated at every step of the iterative process is used. ► The convergence analysis is done in the presence of noise in the data and in the source condition. ► Numerical simulations for an ill-posed problem in groundwater modeling are presented.