Multi-parameter homotopy for the numerical analysis of mems

The configuration space of electromechanical microdevices inherently includes areas of unstable operation, the analysis of which requires appropriate numerical techniques. Homotopy methods have proven to be suitable for rigid as well as for flexible device structures [Sens. Actuat. A 76 (1999) 9]. In many cases, the electric charge Q located on the actuating electrodes may be used as proper control variable to trace the device characteristics by path continuation. However it shows that, in certain cases, this choice can lead to an undesired, but unavoidable wide spacing of the calculated operating points and, hence, to a rather poor resolution of the device characteristics. We identify the cause of this phenomenon, introduce alternative homotopy parameters and present a new multi-parameter homotopy scheme, which switches automatically and smoothly to the locally most suitable homotopy parameter and, thus, allows for arbitrarily small spacing between the simulated operating points.