Numerical simulation of hydrocarbon flow in porous media and turbulent flow in combustion engines initiated our interest in iterative solvers for large, sparse systems of linear equations. We investigate multilevel incomplete factorizations of matrices arising from finite-difference discretizations. Our interest lies in hierarchical ordering strategies and estimates for resulting condition numbers. These methods are closely related to algebraic multigrid methods. Promising coarsening strategies based on minimum spanning trees in the grid are considered. We also use eigenvalue methods for recursive spectral decomposition of graphs. These methods are implemented for domain decomposition on distributed-memory parallel computers. Here we deal with additional constraints like load-balance conditions or edge sets that must not be cut. The modeling of flow and transport, and discretication of the resulting partial differential equations is another area of interest. For example, discretization strategies in regions where a moving grid glides along stationary grid cells were developed. The practical application behind this task was to simulate air flow in rotating fans to optimize the performance of laundry dryers. Current activities also include the drying of porous refractory bricks and thermal monitoring of steel slabs.