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
Principal Investigator: Professor George Karniadakis, PNNL / Brown University.
- Michael L. Parks, Sandia National Laboratories
- Professor Martin R. Maxey, Brown University
- Professor Panos Stinis, University of Minnesota
- Professor Eric Darve, Stanford University
- Professor Weinan E, Princeton University
- Professor Paul J. Atzberger, University of California - Santa Barbara
- Professor Jinchao Xu, Penn State University
Research team members
- PNNL: Nathan Baker, Jaehun Chun, Guang Lin, Chris Mundy, Kenny Roche, Wenxiao Pan, Bruce Palmer, Greg Schenter, TP Straatsma, Alex Tartakovsky, Jay Xu
- SNL: Pavel Bochev, Jonathan Hu, Christopher Siefert
- Brown: Professor Bruce Caswell
- Penn State: Xiaozhe Hu
- Coarse Graining - Mori-Zwanzig (task lead Panos Stinis) focuses on making the MZ formalism computationally manageable to open new avenues of application for coarse-graining methods.
- Particle-Based Methods (task lead George Karniadakis) focuses on extending the spectrum of Lagrangian DPD-SDPD-SPH methods for modeling and making connections to the MZ formalism.
- Grid-Based Methods (task lead Martin R. Maxey) focuses on develop grid-based high-order methods that are efficient for multi-phase dynamics and scale well at the system level while also capturing dominant fluctuations at mesoscale.
- Stochastic Methods (task lead Guang Lin) focuses on developing methods to quantify the uncertainty in Hamiltonian systems, and calibrate the model parameters using data obtained from experimental measurements or from simulations of systems at a higher resolution.
- Concurrent Coupling (task lead Michael L. Parks) focuses on developing concurrent multi-model coupling methods to address the challenge of bridging the spatial and temporal regimes that are individually described by distinct mathematical models and computational models.
- Fast Solvers (task lead Jinchao Xu) focuses on developing new physics-based Schur complements and preconditions for multiscale dynamics within the algebraic multigrid.
- Scalable Algorithms and Applications (task lead TP Straatsma) focuses on developing scalable method implementations within a software infrastructure that facilitates coupling with existing scalable simulation codes to allow method validation and verification based on simulations of real problems.
George Karniadakis is the co-organizer for the first-ever U.S. workshop on Fractional Partial Differential Equations. The conference will be held in June in Newport, Rhode Island and will focus on sharing international advances in the methodology and applications of FPDEs as well as on introducing young U.S. postdocs in simulation science to these emerging computational methods. More information
PAST WORKSHOPSThe kick-off meeting for the Modeling Mesoscale Processes of Scalable Synthesis Project was held in Seattle, WA on September 10-11, 2012. The focus of this meeting was to produce a defined research plan, a technical roadmap, and a path forward in an effort to collectively produce a document for the client that will include milestones and metrics of success.
Coryann Newsom (509) 371-7812
SUPPORTThis work is supported by the Applied Mathematics Program within the Department of Energy (DOE) Office of Advanced Scientific Computing Research (ASCR) as part of the Collaboratory on Mathematics for Mesoscopic Modeling of Materials (CM4). DOE Program Manager: Sandy Landsberg