Multiscale Materials Science: A Mathematical Approach to the Role of Defects and Uncertainty

Abstract

We focus on developing affordable numerical methods in the context of stochastic homogenization. Our aim is to compute the homogenized coefficients that represent the behavior of the material at a macroscopic scale. Such computations are usually very expensive. To decrease their cost, we consider a variance reduction technique, namely the control variate technique, and numerically demonstrate its efficiency. We also address questions related to non-periodic modelling of multiscale materials. A typical example is that of a periodic material with a superimposed defect in one periodic cell.

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Document Details

Document Type
Technical Report
Publication Date
Mar 01, 2015
Accession Number
ADA622870

Entities

People

  • Claude Le Bris
  • Frederic Legoll
  • William Minvielle

Organizations

  • ParisTech

Tags

Communities of Interest

  • C4I

DTIC Thesaurus Topics

  • Algorithms
  • Coefficients
  • Computations
  • Differential Equations
  • Equations
  • Estimators
  • Inverse Problems
  • Law
  • Materials
  • Materials Science
  • Military Research
  • Partial Differential Equations
  • Probability
  • Probability Distributions
  • Random Variables
  • Two Dimensional
  • Uncertainty

Fields of Study

  • Mathematics

Readers

  • Computational Fluid Dynamics (CFD)
  • Regression Analysis.