| Microelectromechanical systems (MEMS) depend on the interaction between electrical, mechanical and fluidic forces. Since most MEMS devices are innately three-dimensional and geometrically complicated, simulating these coupled domain problems involves many challenges. This thesis presents a methodology to simulate MEMS. Reduced order dynamic macromodels are automatically generated from three-dimensional, domain-specific, physical simulations. Specifically, the Arnoldi method for model order reduction, commonly used for high-speed circuit interconnect problems, is extended to microelectromechanical system (MEMS) problems. Linear models are used to simulate single and coupled domain MEMS problems. The automatic extraction of reduced order models is demonstrated. The model order reduction algorithm is applied to a representative set of MEMS operating in a linear region. The results show that very-low order reduced models can capture the dynamics of the large linear systems. The nonlinear behavior of MEMS is also addressed. Waveform relaxation techniques for self-consistent analysis of three-dimensional MEMS are presented. Finally, techniques for nonlinear model order reduction of MEMS are discussed. |
