Convergence and discretization characteristics of a staggered algorithm for microelectromechanical system simulation

Microelectromechanical systems have their working principles based in the interaction between two or more physical fields. To design them multi-physics simulation tools are needed. For surface type electromechanical coupling, a staggered procedure can be used to treat the problem. The involved domains are solved separately and the coupling is taken into account by inserting electrostatic pressures coming from an electrical analysis into the structure, and updating the electrical mesh with the deformations originated from a mechanical analysis. The staggered procedure is iterative and the convergence criteria is based in the displacement variation between successive iterations. In this paper, a study about the convergence properties of the staggered algorithm for coupled problems implemented in our finite element code, MefLab, is done. A 0.5% variation in the displacement prooved to be sufficient to reach convergence in the simulation. A second analysis is related to the use of the Finite Element Method to model the electrical domain. A study about mesh dimension and proper boundary conditions to get good results saving computational time is carried out. Although not representing exactly the behavior of an unbounded field, the imposition of a null electric potential gradient on the external limit of the electrical mesh has shown to produce good results in the case of microelectromechanical systems simulation.