Our work in applied mathematics ranges from algorithm design, to development of software tools and technology, to advanced simulations in applications of interest to the U.S. Department of Energy. MCS is formulating rigorous theory leading to fast algorithms, deployed in portable software on leading-edge computing platforms. We explore three main areas along with their interactions::
- New approaches for mathematical modeling and numerical simulations to study complex, multiphysics, multiscale phenomena that arise in scientific and engineering problems, focusing on PDE and ODE solvers, discretizations, uncertainty quatification, and stochastic approaches.
- State-of-the-art techniques that fully exploit high-performance computing and beyond-Moore computing and lay the groundwork for new scientific insights, including automatic differentiation, verification, and performance modeling, tuning, and productivity.
- Algorithms and models for analysis, design, decision, and control problems that incorporate novel data fusion, machine learning, optimization, statistics, and uncertainty quantification methodology.
We also administer the J. H. Wilkinson Prize for Numerical Software.