# Collaboratory on Mathematics for Mesoscopic Modeling of Materials (CM4)

The Collaboratory on Mathematics for Mesoscopic Modeling of Materials (CM4) focuses on developing rigorous mathematical foundations for understanding and controlling fundamental mechanisms in mesoscale processes to enable scalable synthesis of complex materials, through the design of efficient modeling methods and corresponding scalable algorithms.

**Specific areas of focus include: **

- Developing particle-based, grid-based and stochastic methods
- Concurrent coupling between these methods
- Applying rigorous theoretical approaches to derive new governing equations for coarse graining
- Developing general algorithmic frameworks that involve optimization algorithms on multilayer overlapped domains with heterogeneous discretizations to facilitate disparate spatio-temporal scales
- Investigating the numerical stiffness induced by multiscale phenomena
- Exploring new fast solution techniques that are effective at the exascale level
- Integrating these mathematical and computational tools for applications relevant to scalable synthesis of materials.

**CONTACT**

Sheila Kirk (509) 371-7305

**SUPPORT**