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Parametric Simulation of MEMS Based on Automatic Differentiation of Finite Element Codes

V.A. Kolchuzhin, J.E. Mehner, T. Gessner and W. Doetzel
Chemnitz University of Technology, DE

Keywords:
parametric models, reduced order model, variational technologies, finite element method

Abstract:
The key idea of the presented approach, which account for parameter variations in a single finite element run, is to compute not only the governing system matrices of the FE problem but also their partial derivatives with regard to design variables. In contrast to symbolic differentiation which propagates mathematical functions, novel approaches make use automatic differentiation algorithms which process numerical values extracted at the initial position. Finally, Taylor vectors of the goal function can be expanded covering the system response in the vicinity of the initial position with regard to design parameters.
This article extends the approach to design of coupled domain systems where strain energy and capacitance functions relate interactions between electrostatic and structural domains. Benefits of variational technologies for shape optimization; sensitivity analyses and data sampling needed for ROM of MEMS become obvious for multi-parameter problems. The algorithms have been implemented in MATLAB. Numerical details, stability and observed problems will be discussed on several examples.

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