  Micro-Electro-Mechanical Systems (MEMS) normally have fixed or moving
structures (plates or array of thin beams) with cross-sections of the order of
microns and lengths of the order of tens or hundreds of microns. Electrostatic
forces play a very major role in maneuvering these devices, and hence, a
thorough understanding of the electrostatic properties of these structures is
of critical importance. Recently, a nearly exact boundary element method
(neBEM) solver has been developed and used to solve difficult problems related
to electrostatics of various devices. Because of the exact foundation
expressions, this solver has been found to be very accurate while solving
critical problems which normally necessitate special formulations involving
elegant, but difficult mathematics. In this work, we investigate the effects of
various possible approximations on the 3D electrostatic solutions obtained for
MEMS structures. In particular, we investigate the effects of discretization,
omission of surfaces with small amount of charge accumulation on the final
results such as the charge distribution on various surfaces or capacitance of a
given MEMS structure.
