Electrostatic Micro-Electro-Mechanical-Systems (MEMS) Devices: A Comparison Among Numerical Techniques for Recovering the Membrane Profile

In this work, numerical techniques based on Shooting procedure, Relaxation scheme and Collocation technique have been used for recovering the profile of the membrane of a 1D electrostatic Micro-Electro-Mechanical-Systems (MEMS) device whose analytic model considers |E| proportional to the membrane curvature. The comparison among these numerical techniques has put in evidence the pros and cons of each numerical procedure. Furthermore, useful convergence conditions which ensure the absence of ghost solutions, and a new condition of existence and uniqueness for the solution of the considered differential MEMS model, are obtained and discussed.