APPLIED MATHEMATICS

The Bridge between Physical Reality and Simulations

“Mathematics is the bridge between physical reality and computer simulations of physical reality. The starting point for a computer simulation is a mathematical model, expressed in terms of a system of equations and based on scientific understanding of the problem being investigated, such as the knowledge of forces acting on a particle or a parcel of fluid.”¹

One of the challenges facing many model developers is managing model complexity. Many physical systems have processes that operate on length and time scales that vary over many orders of magnitude. These systems require multiscale modeling, which represents physical interactions on multiple scales so that the results of interest can be recovered without the unaffordable expense of representing all behaviors at uniformly fine scales. This section describes the award-winning work of two research groups specializing in multiscale modeling.

Algorithms in the Service of Science

¹"A Science-Based Case for Large-Scale Simulation," report to the DOE Office of Science, July 30, 2003, p.31.