Estimation and Control of Modeling Error: A General Approach to Multiscale Modeling

J. T. Oden*, S. Prudhomme, P. T. Bauman, L. Chamoin

*Corresponding author for this work

Research output: Chapter in Book/Report/Conference proceedingChapterpeer-review


This chapter describes a class of computational methods designed to handle multiscale modeling of large atomistic or molecular systems. The key to this approach is the estimation of relative modeling error in which errors in quantities of interest produced by averaging or homogenization are computed using a posteriori error estimates. The error is judged to be the relative error between the fine-scale base model and any number of surrogates produced by homogenization. Features of modeling the atomistic to continuum interface are also addressed. Specific applications of the methodology are described that involve analyzing polymer etch barriers that are used in nano-manufacturing of semi-conductors. The basic adaptive modeling strategy employs goal-oriented adaptation in which fine-scale information is systematically added to hybrid molecular-continuum models until the appropriate level of accuracy in certain quantities of interest is achieved.

Original languageEnglish (US)
Title of host publicationMultiscale Methods
Subtitle of host publicationBridging the Scales in Science and Engineering
PublisherOxford University Press
ISBN (Electronic)9780191715532
ISBN (Print)9780199233854
StatePublished - Oct 1 2009
Externally publishedYes

Bibliographical note

Publisher Copyright:
© Oxford University Press 2009. All rights reserved.


  • Adaptive modeling
  • Error estimation
  • Molecular systems
  • Nanomanufacturing

ASJC Scopus subject areas

  • General Mathematics


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