In this chapter we describe some computational techniques to approximate the evolution of gypsum crusts on marble monuments. Mathematical models of this phenomenon are typically based on partial differential equations and here we deliberately consider a quite simple one, so that we can focus on the numerical techniques that can be used to overcome the main difficulties of this kind of computations, namely the efficiency of the timestepping procedure and the complexity of the computational domains in real-world cases. First, the design of optimal preconditioners for Cartesian grid discretizations is reviewed. Then, we illustrate a technique to deal with non Cartesian domains by described via a level-set function. The chapter ends with a study of the influence of the surface curvature on the growth of the gypsum crust, that generalizes earlier analytical one-dimensional results.