### Abstract

A methodology is proposed for the model order reduction of finite element approximations of MEMS devices under random input conditions. In this approach, the reduced order system matrices are represented in terms of their convergent orthogonal polynomial expansions of input random variables. The coefficients of these polynomials, which are matrices, are obtained by repeated, deterministic model order reduction of finite element models generated for specific values of the input random variables. These values are chosen efficiently in a multi-dimensional grid using a Smolyak algorithm. The stochastic reduced order model is represented in the form of an augmented system which can be used for generating the desired statistics of the specific system response. The proposed method provides for significant improvement in computational efficiency over standard Monte Carlo.

Original language | English (US) |
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Title of host publication | Nanotechnology 2010 |

Subtitle of host publication | Electronics, Devices, Fabrication, MEMS, Fluidics and Computational - Technical Proceedings of the 2010 NSTI Nanotechnology Conference and Expo, NSTI-Nanotech 2010 |

Pages | 577-580 |

Number of pages | 4 |

State | Published - Nov 9 2010 |

Event | Nanotechnology 2010: Electronics, Devices, Fabrication, MEMS, Fluidics and Computational - 2010 NSTI Nanotechnology Conference and Expo, NSTI-Nanotech 2010 - Anaheim, CA, United States Duration: Jun 21 2010 → Jun 24 2010 |

### Publication series

Name | Nanotechnology 2010: Electronics, Devices, Fabrication, MEMS, Fluidics and Computational - Technical Proceedings of the 2010 NSTI Nanotechnology Conference and Expo, NSTI-Nanotech 2010 |
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Volume | 2 |

### Other

Other | Nanotechnology 2010: Electronics, Devices, Fabrication, MEMS, Fluidics and Computational - 2010 NSTI Nanotechnology Conference and Expo, NSTI-Nanotech 2010 |
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Country | United States |

City | Anaheim, CA |

Period | 6/21/10 → 6/24/10 |

### Keywords

- Finite element
- Mems
- Model order reduction
- Random
- Stochastic

### ASJC Scopus subject areas

- Hardware and Architecture
- Electrical and Electronic Engineering

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## Cite this

*Nanotechnology 2010: Electronics, Devices, Fabrication, MEMS, Fluidics and Computational - Technical Proceedings of the 2010 NSTI Nanotechnology Conference and Expo, NSTI-Nanotech 2010*(pp. 577-580). (Nanotechnology 2010: Electronics, Devices, Fabrication, MEMS, Fluidics and Computational - Technical Proceedings of the 2010 NSTI Nanotechnology Conference and Expo, NSTI-Nanotech 2010; Vol. 2).