AMG preconditioning for nonlinear degenerate parabolic equations on nonuniform grids with application to monument degradation

Motivated by the modelling of marble degradation by chemical pollutants, we consider the ap- proximation by implicit finite differences schemes of nonlinear degenerate parabolic equations in which sharp boundary layers naturally occur. The latter suggests to consider various types of nonuniform griddings, when defining suitable approximation schemes. The resulting large nonlinear systems are treated by Newton methods, while the locally Toeplitz linear systems aris- ing from the Jacobian have to be solved efficiently. To this end, we propose the use of AMG preconditioners and we study the related convergence issues, together with the associated spec- tral features. We present some numerical experiments supporting our theoretical results on the spectrum of the coefficient matrix of the linear systems, alongside others regarding the numerical simulations in the case of the specific model.