Some mathematical and numerical issues in multiscale modeling

Weinan E

To put multiscale modeling on a solid foundation, we need to study the following problems:

1. The connection between different physical models, e.g., how continuum elasticity models can be derived from quantum mechanics models
2. How to impose general, non-periodic boundary conditions for different physical models?
3. How to interface the different models so that the coupled model is uniformly accurate?
4. In general, how to develop sub-linear scaling algorithms that use higher levels of adaptivity?

I will discuss some recent progress that has been made on these issues, using both classical atomistic models and electronic structure models as examples.

[Joint work with Carlos Garcia-Cevera, Xiantao Li, Jianfeng Lu and Pingbing Ming]