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. c`c 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.

Mathematical modelling in actual problems of science and technics