Finite element compatible matrix interpolation for parametric model order reduction of electrothermal microgripper

Abstract

Abstract Electrothermal microgrippers are nowadays commonly used as they are small in size, low cost, and easy to manufacture. The microgripper is modeled through partial differential equations, which are discretized by the finite element method (FEM), producing a large number of ordinary differential equations. This makes model order reduction (MOR) a fruitful proposition. Moreover, in design applications, the microgripper needs to be simulated repeatedly, with varying values of certain parameters. When these parameters are geometric in nature, matrix interpolation-based parametric model order reduction (pMOR) is the most suited method. However, in finite element applications, the sizes of the FE matrices change for varying geometrical parameters. The conventional matrix interpolation-based pMOR method becomes inapplicable for such cases, which remains a major drawback of this otherwise powerful algorithm. In this paper, this major hurdle is removed, and a new finite element compatible matrix interpolation (FEMI) for pMOR is proposed. A three-dimensional electrothermal microgripper is modeled parametrically using this proposed methodology. The effectiveness of the proposed method is shown through simulation results.