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Summary: JOURNAL OF MICROELECTROMECHANICAL SYSTEMS, VOL. 8, NO. 3, SEPTEMBER 1999 299
A Multilevel Newton Method for Mixed-Energy
Domain Simulation of MEMS
N. R. Aluru and Jacob White, Member, IEEE
Abstract--An efficient black-box algorithm for self-consistent
analysis of three-dimensional (3-D) microelectromechanical sys-
tems (MEMS) is described. The algorithm is matrix-free based
and employs a multilevel Newton technique to solve the cou-
pled electromechanical equations. The new approach is shown
to converge very rapidly and is much faster than relaxation
algorithm for tightly coupled cases. While this paper focuses
on coupled electromechanical analysis, the proposed algorithm
can be extended to include several coupled domains typically
encountered in MEMS. [355]
Index Terms--MEMS modeling, mixed-energy domain simula-
tion, multilevel Newton method, relaxation technique.
I. INTRODUCTION
ALTHOUGH there are many microelectromechanical sys-
tem (MEMS) designs that use piezoelectric, thermal,
pneumatic, and magnetic actuation, the most popular approach
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