Mathematical approaches to some hyperbolic problems in multiscale materials science
Abstract
The presence of several length-scales in material science problems represents a daunting challenge for numerical simulation. The proposed research program is a continuation of previous projects completed in the same context and funded by AFOSR and ONR. On the theoretical side, these past projects were mainly focused on the multiscale diffusion equation, and in particular they focused on the consideration of defects embedded in an otherwise periodic microstructure and how the presence of the defects may affect the homogenization limit. The numerical aspects, on the other hand, were focused on studying, developing, and extending a well-established computational approach, the multi-scale finite element method, in order to address some new cases of multiscale media modeled by a diffusive equation. The diffusion equation is not only interesting and practically relevant, but it is also particularly useful as a test-bed for new ideas regarding modeling of defects and uncertainties in the idealized materials, which can help bridge the gap between ideal materials and actual materials. But, as is well-known, other equations other than the diffusion equation are relevant in the engineering sciences. Consequently, this study will focus on multiscale hyperbolic equations, and more precisely, that of hyperbolic conservation laws.
Document Details
- Document Type
- DoD Grant Award
- Publication Date
- Feb 05, 2025
- Source ID
- FA86552417057
Entities
People
- Claude Le Bris
Organizations
- Air Force Office of Scientific Research
- United States Air Force
- École des Ponts ParisTech