Investigation of nonlinear multigrid methods for solving one-phase filtration problem

The paper considers generalizations of geometric multigrid method onto non-linear problems of mathematical physics such as one-phase filtration problem which includes dependence of parameters on pressure. Essential advantage of these methods is that linerization and Jacobian construction are not required. Generalizations were compared against multigrid methods applied to the linearised problem and against Krylov-type methods with ILU preconditioners. The resulting conclusion is applicability of the non-linear full multigrid method. The speed characteristics approximately correspond to those of FGMRes method with ILUT preconditioner.