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A stochastic Lagrangian approach for geometrical uncertainties in electrostatics

Summary: A stochastic Lagrangian approach for geometrical
uncertainties in electrostatics
Nitin Agarwal, N.R. Aluru *
Department of Mechanical Science and Engineering, Beckman Institute for Advanced Science and Technology,
University of Illinois at Urbana-Champaign, 405 N. Mathews Avenue, Urbana, IL 61801, United States
Received 18 September 2006; received in revised form 20 March 2007; accepted 29 March 2007
Available online 7 April 2007
This work proposes a general framework to quantify uncertainty arising from geometrical variations in the electrostatic
analysis. The uncertainty associated with geometry is modeled as a random field which is first expanded using either poly-
nomial chaos or Karhunen≠Loe`ve expansion in terms of independent random variables. The random field is then treated
as a random displacement applied to the conductors defined by the mean geometry, to derive the stochastic Lagrangian
boundary integral equation. The surface charge density is modeled as a random field, and is discretized both in the random
dimension and space using polynomial chaos and classical boundary element method, respectively. Various numerical
examples are presented to study the effect of uncertain geometry on relevant parameters such as capacitance and net elec-
trostatic force. The results obtained using the proposed method are verified using rigorous Monte Carlo simulations. It has
been shown that the proposed method accurately predicts the statistics and probability density functions of various rele-
vant parameters.
” 2007 Elsevier Inc. All rights reserved.
Keywords: Spectral stochastic boundary element method (SSBEM); Polynomial chaos; Lagrangian electrostatic analysis; Geometrical


Source: Aluru, Narayana R. - Department of Mechanical and Industrial Engineering, University of Illinois at Urbana-Champaign


Collections: Engineering; Materials Science