Advanced Scientific Computing Research (ASCR)

# Research

## Applied Mathematics

**New Applied Mathematics Funding Opportunity**

The Department of Energy (DOE) Office of Advanced Scientific Computing Research (ASCR) is pleased to announce a new funding opportunity in Applied Mathematics entitled “Uncertainty Quantification Methodologies for Enabling Extreme-Scale Science”. This announcement is open to universities, industry, non- profit organizations, and Federally Funded Research and Development Centers (FFRDCs), including the DOE National Laboratories.

The university / industry announcement is here:

Under Search Criteria, select “Reference Number” and then enter “DE-FOA-0000895”

The DOE National Laboratory announcement, LAB 13-895, is here:

Scroll down and look to the right.

Pre-applications are required and are due by April 24, 2013, 5:00 PM Eastern Time.

The Applied Mathematics program in ASCR has a long history and focuses on mathematical research and software that impact the future of high-performance computing.

- Numerical methods for solving ordinary and partial differential equations, especially numerical methods for computational fluid dynamics. PDEs solve problems involving unknown relationships between several variables, enabling simulations of things like fluid flow, wave propagation and other phenomena.
- Computational meshes for complex geometrical configurations, which seek to translate domains of mathematical values into discrete points to simulate continuous processes like combustion.
- Numerical methods for solving large systems of linear and nonlinear equations.
- Optimization, which seeks to minimize or maximize mathematical functions and can be used to find the most efficient solutions to engineering problems or to discover physical properties and biological configurations.
- Multiscale computing, which connects varying scales in the same problem, such as relating processes and properties at the tiniest scales of time and space to those at the largest scales.
- Multiphysics computations, which simulate physical processes of different kinds, such as a chemical reaction at its boundary with a material.
- Math software and libraries – modular codes that can be incorporated in programs from diverse science areas, allowing developers to quickly build software that makes difficult calculations efficiently and rapidly.

In the years ahead, Applied Mathematics will focus on algorithms that take advantage of computers capable of up to 1 quadrillion operations per second (1 petaflop). These computers will allow scientists to consider research never thought possible, such as predictive simulation of the physical properties of novel materials.

Applied Mathematics also is devoting more resources to “uncertainty quantification,” which gives a mathematical characterization of the confidence levels for calculations. Algorithms are also being developed to help researchers sift through the mountains of data generated by increasingly detailed simulations and more powerful experiments.

The program also looks to the future by supporting fellowships and other programs to train new computational scientists.

The Applied Mathematics program at DOE has broadly influenced our ability to use computers for scientific discovery. Work done 50 years ago, for example, provided the foundations for modern computational fluid dynamics (CFD), which studies the movement of gases and liquids. New research and continuous refinement of techniques has made modern CFD essential to climate modeling, nuclear reactor design, subsurface flow modeling, and many other applications of critical importance to our nation.

Applied Mathematics projects often take years before they directly contribute to new and better simulations and software. Nonetheless, the fundamental advances these projects provide are essential to maintaining America’s global competitive edge.