Abstract
AbstractIn the operation of high frequency resonators in micro electromechanical systems(MEMS), there is a strong need to be able to accurately determine the energy loss rates or alternatively the quality of resonance. The resonance quality is directly related to a designers ability to assemble a high fidelity system response for signal filtering, for example. This has implications on robustness and quality of electronic communication and also strongly influences overall rates of power consumption in such devices – i.e. battery life. An index of the quality of resonance Q is inversely proportional to the amount of energy loss existing in the system, and can be defined in terms of the complex‐valued eigenvalues ω of the system as, . In this presentation, we examine methods for accurately simulating energy loss using the direct modeling of acoustic radiation via perfectly matched layer (PML) technology for 3‐D structures, which results in complex‐symmetric mass and stiffness matrices. Thus it is crucial that one is able to accurately compute eigenvalues of a complex‐symmetric system. 3‐D modeling increases the number of degrees of freedom and complexity in obtaining the solution, resulting in a requirement for more computing power and memory which can only be supplied by parallel computing methods. The simulations are conducted through the MEMS simulation software HiQLab in combination with the parallel numerical libraries PETSc and Trilinos. A modified smoothed aggregation algebraic multigrid method for solving a linear system of equations is combined with a Jacobi‐Davidson method to solve for desired eigenvalues. (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)
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