A preconditioner for hybrid matrices arising in RF MEMS switch analysis

Despite the excellent characteristics of RF MEMS switches, they generally suffer from low power-handling capability. This limitation is due to the complex interactions among electromagnetic losses, heat transfer, and mechanical deformations associated with the switches. To understand these failure mechanisms, we proposed a multiphysics model (Jensen, B.D. et al., IEEE Microwave and Wireless Components Letters, vol.13, no.9, p.364-66, 2003). This model is based on an extended finite element-boundary integral (EFE-BI) model that allows efficient modeling of the boundary (MEMS beam for our case) exterior to the volumetric region modeled by the standard FE-BI method. The condition number of the resulting EFE-BI matrix system increases rapidly as the frequency decreases. The matrix condition number required at 2 GHz warrants computational accuracy beyond the capability of normal CPUs. For this reason, our EFE-BI analysis and validation of the code were limited to high frequency cases. We propose a preconditioning approach that lowers the condition number of the system. The proposed approach allows for fast, efficient analysis of RF MEMS switches at practical RF frequencies as low as 500 MHz, which will enable the desired multiphysics modeling.