The performance of micro-electro-mechanical systemsdepends on the interaction between electrical, mechanical,and fluidic forces. Simulating this coupled problem is made moredifficult by the fact that most MEMS devices are innately three-dimensionaland geometrically complicated. It is possible to simulateefficiently these devices using domain-specific solvers, providedthe coupling betweendomains can be handled effectively. Inthis paper we will survey recent developments in coupled-domainsimulation, and give computational comparisons between relaxation,multi-level Newton, and Newton-Iterative methods for 3-Delectromechanical analysis.