A Primer on Homogenization of Elliptic PDEs with Stationary and Ergodic Random Coefficient Functions
Alen Alexanderian
TL;DR
This paper introduces the mathematical theory of homogenization for elliptic PDEs with stationary and ergodic random coefficients, supported by numerical examples to illustrate the concepts.
Contribution
It provides a comprehensive introduction to the homogenization of elliptic PDEs with random coefficients, combining theoretical insights with numerical demonstrations.
Findings
Effective properties can be characterized using homogenization theory.
Numerical examples validate the theoretical results.
Homogenization provides a way to understand complex random media.
Abstract
We study the problem of characterizing the effective (homogenized) properties of materials whose diffusive properties are modeled with random fields. Focusing on elliptic PDEs with stationary and ergodic random coefficient functions, we provide a gentle introduction to the mathematical theory of homogenization of random media. We also present numerical examples to elucidate the theoretical concepts and results.
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Taxonomy
TopicsAdvanced Mathematical Modeling in Engineering · Composite Material Mechanics · Advanced Numerical Methods in Computational Mathematics