The thesis is concerned with efficient numerical algorithms for solving linear systems originating from singular problems or problems where equations prescribed on domains with different topological dimensions are coupled. The former problem arises e.g. in planetology while the latter has numerous applications in biomedicine. Therein introducing the domain with lower topological dimension is a mean to meet the challenge of a wide range of spatial scales that are present in the physical system. Upon discretization the problems yield large linear systems, which can only be solved efficiently provided that an iterative method is used with a suitable preconditioner. Establishing the preconditioner is then the main challenge. In the thesis preconditioners for both problems are constructed within the framework of operator preconditioning.