Focal Themes
Focal Themes
Homogenization is a mathematical framework used to analyze the behavior of multi-scale media. Broadly speaking, homogenization provides a way to approximate macroscopic properties of a heterogeneous media by an equivalent homogeneous model.
It plays a crucial role in various applications across engineering and medical sciences, including composite materials, metamaterials, thin structures, and porous media.
Theoretical aspects of Homogenization
The asymptotic analysis of solutions to partial differential equations (PDEs), leading to limit equations that describe the effective or bulk behavior of the medium, free from microscopic heterogeneities. These limit models are not only easier to solve but also capture the essential macroscopic features of the material.
Numerical methods for Homogenization
Developing efficient computational methods for approximating effective coefficients, solving limit equations, and simulating multi-scale behavior.
Control problems in multiscale setting
Understanding how systems governed by PDEs can be steered towards desired states, and how control strategies can be optimized in multi-scale settings.
Inverse problems in Homogenization
Reconstruction of fine-scale information or material properties from macroscopic data, which has practical implications in imaging, non-destructive testing, and material design.