An efficient black-box algorithm for self-consistent analysis of three-dime
nsional (3-D) microelectromechanical systems (MEMS) is described. The algor
ithm is matrix-free based and employs a multilevel Newton technique to solv
e the coupled electromechanical equations. The new approach is shown to con
verge very rapidly and is much faster than relaxation algorithm for tightly
coupled cases. While this paper focuses on coupled electromechanical analy
sis, the proposed algorithm can be extended to include several coupled doma
ins typically encountered in MEMS.