Modeling and simulation of Micro Electro Mechanical Systems has become increasingly important as the complexity of MEMS devices increases. In particular, thermal effects on MEMS devices has become a growing topic of interest. Through the FEA, detailed solutions can be obtained to investigate the multiphysics coupling and the transient behavior of a MEMS device at the component level. For system-level integration and simulation, the FEA discretization often results in large full-scale models, which can be computationally demanding or even prohibitive to solve. Model order reduction (MOR) was investigated in this study to reduce problem size for complex dynamic system modeling. The Arnoldi method was implemented for MOR to improve the computational efficiency while preserving the input-output behavior of coupled MEMS simulation. Using this method, a low dimensional Krylov subspace was extracted from the full-scale system model. Reduced order solution of the transient temperature distributions was then determined by projecting the system onto the extracted Krylov subspace and solving the reduced system. An electro thermal MEMS actuator was studied for various inputs. To compare results, the full-scale analyses were performed using the commercial FEA program ANSYS. It was found that the computational time of MOR was only a fraction of the full-scale solution time, with the relative errors ranging from 1.1% to 4.5% at different positions on the actuator. Our results show that the reduced order modeling via Alnoldi can significantly decrease the transient analysis solution time without much loss in accuracy for coupled-field MEMS simulation.
Efficient optimization of transient dynamic problems in MEMS devices using model order reduction
