While slightly increasing the "risk" level of the solver, it is possible to switch to an iterative strategy where a combination of solvers is used via the AMF direct solver + Incomplete L-U factorization (ILU) method. In this case, terms are being dropped in the system matrix (but not in the Right Hand Side so that the solution remains identical) and the AMF direct solver is used as a preconditioner. The terms that are dropped are decided based on block descriptions and problem formulation. Of course, the resulting system is cheaper to solve, but dropping those terms prevents the solution from being computed in one step, and it is then necessary to embed the process in a global iterative strategy represented by a Generalized Minimal Residual Method (GmRes) [28]. This strategy is most efficient in systems involving many blocks, such as moving coordinates or multimode viscoelastic problems, but is unfortunately inefficient in simple cases such as fixed domain, velocity/pressure systems, because opportunities to discover weak couplings in such systems are limited. In most cases, the ILU solver requires less memory than a pure direct solver.