# Advanced Computing, Mathematics and Data Division

Research Highlights

January 2008

## School Grooming Next Generation of Researchers in Multiscale Mathematics

Multiscale mathematics are critical to solving complex problems facing society today. DOE's Office of Advanced Scientific Computing Research (ASCR) is helping to spur continuing advances in multiscale mathematics through its Summer School in Multiscale Mathematics and High-Performance Computing.

The annual summer school is a week-long workshop that seeks to develop and equip early career researchers in advancing the understanding of the mathematics of complex physical processes that occur on a wide range of interacting length and time scales. These objectives are achieved by providing technical resources, such as lecture notes and laboratory content, to the participants. The summer school also serves to test curriculum content that will be the basis for expanding graduate mathematics and science curriculum.

The summer school is aimed at graduate and post-doctoral students in mathematics, scientific computing, materials sciences, geophysics, computational physics, and mechanical engineering. To spur the development of new methods, the summer school includes research discussions, tutorials on parallel computing, and instructor-led laboratory activities that explore the lecture concepts in advanced computing environments. The summer school features lectures on the mathematical and computational methods commonly used to model physical systems at various scales and on the approaches under development for bridging the scales between current methods.

Participants in the 2007 Multiscale Mathematics Summer School.

**Summer Schools in Session**

The Northwest Consortium of Multiscale Mathematics and Applications, which organizes the workshops, has held two summer school workshops. The first workshop was held in May 2006 in Tacoma, WA, drew more than 40 participants and focused on critical issues forefront to multiscale modeling. The second annual workshop was held June 29-July 3, 2007 at Oregon State University in Corvallis, Oregon, and attracted 30 students from universities across the U.S. and instructors from over 15 universities and national laboratories.

The particular components of the 2007 school included:

- Tutorials on parallel computing and MPI
- Introductions to the mathematical and computational methods commonly used to model physical systems at various scales: continuum methods, discrete methods, statistical methods, network methods for Multiscale Mathematics and Applications
- Surveys of developing mathematical and computational approaches for bridging the scales between current methods
- Instructor-led laboratory activities that led the participants' exploration of the lecture concepts in parallel computing environments, discrete particle dynamics, solvers, and continuum methods
- Research discussions to motivate the development of new methods.

The lectures from these activities are available on the web at http://multiscale.emsl.pnl.gov/. In 2008, the summer school will be held at Pacific Northwest National Laboratory.

**About the Northwest Consortium for Multiscale Mathematics and Applications**

The consortium is a collaborative effort among the Pacific Northwest National Laboratory, Washington State University, and Oregon State University. Its mission is to address critical problems in multiscale modeling, to enhance modeling in engineering and science by bringing mathematical and computational tools to bear on practical problems, to create a continuous communication between relevant disciplines, and to enhance engineering and science education to meet the requirements of the 21st century.