Argonne National Laboratory

Applied Mathematics

Applied Mathematics

SPOTLIGHT: Managing dynamic datastructures. The Indexed Parallel Programming (IPM) model is a post-MPI parallel programming where the runtime system, rather than the programmer, manages the placement and movement of all the simulation data. The user provides graphs representing the data dependencies of each phase of the simulation; the runtime ensures that the needed data is available for each computational kernel when it is launched. The goal of this project is to refine the programming model, provide a prototype implementation, and provide a full adaptive mesh refinement simulation demonstrating the programming model.

OVERVIEW: 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 software on leading-edge computing platforms. We explore three main areas:

  • State-of-the-art techniques that will fully exploit high-performance computing and will lay the groundwork for new scientific insights, including compiler decision algorithms, automatic differentiation, and performance tuning.
  • 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.
  • Incorporation of new numerical methods into portable, high-performance software and testing of that software in large-scale simulations of interest to the scientific community, including the areas of data analysis and optimization.

We also administer the J. H. Wilkinson Prize for Numerical Software.