A sparse grid based collocation method for model order reduction of finite element approximations of passive electromagnetic devices under uncertainty

Prasad S. Sumant, Hong Wu, Andreas C. Cangellaris, Narayana R. Aluru

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Abstract

A methodology is proposed for the model order reduction of finite element approximations of passive electromagnetic 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 languageEnglish (US)
Title of host publication2010 IEEE MTT-S International Microwave Symposium, MTT 2010
Pages1652-1655
Number of pages4
DOIs
StatePublished - Oct 15 2010
Event2010 IEEE MTT-S International Microwave Symposium, MTT 2010 - Anaheim, CA, United States
Duration: May 23 2010May 28 2010

Publication series

NameIEEE MTT-S International Microwave Symposium Digest
ISSN (Print)0149-645X

Other

Other2010 IEEE MTT-S International Microwave Symposium, MTT 2010
CountryUnited States
CityAnaheim, CA
Period5/23/105/28/10

Keywords

  • Finite element
  • Krylov based
  • Model order reduction
  • Random input
  • Stochastic

ASJC Scopus subject areas

  • Electrical and Electronic Engineering
  • Radiation
  • Condensed Matter Physics

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    Sumant, P. S., Wu, H., Cangellaris, A. C., & Aluru, N. R. (2010). A sparse grid based collocation method for model order reduction of finite element approximations of passive electromagnetic devices under uncertainty. In 2010 IEEE MTT-S International Microwave Symposium, MTT 2010 (pp. 1652-1655). [5517633] (IEEE MTT-S International Microwave Symposium Digest). https://doi.org/10.1109/MWSYM.2010.5517633