Applied Mathematics
SPOTLIGHT: Managing dynamic datastructures. The Indexed Parallel Programming (IPM) model is a postMPI 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 leadingedge computing platforms. We explore three main areas:
 Stateoftheart techniques that will fully exploit highperformance 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, highperformance software and testing of that software in largescale 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.
Active Projects

January 17, 2013

January 17, 2013

January 17, 2013

March 19, 2013

November 12, 2014

March 19, 2013

January 17, 2013

May 14, 2013

June 24, 2013

January 17, 2013

May 17, 2013

May 9, 2013

January 17, 2013

November 11, 2014

November 7, 2014

January 17, 2013

January 17, 2013

May 10, 2013