# ASCR Applied Mathematics Base Program

The goal of this DoE ASCR Applied Math project is to develop new algorithms for simulating complex systems that are represented by solutions to partial differential equations (PDE). Such systems are characterized by the presence of multiple physical processes, complex geometries, and multiple length and time scales. In our previous work, we have developed a number of new methods that are required to simulate a variety of complex systems. These include methods for treating problems with multiple time scales; accurate and robust finite-volume discretizations; methods for adaptively concentrating computational effort where it is most needed; general, flexible methods for representing complex geometries; and high-performance scalable parallel solvers for elliptic PDE. The focus for our research will be provided by the requirements for simulation in the applications areas of importance to the DOE. Current work includes the fundamental algorithmic research required to support such applications, including high-order methods for adaptive grids, both in Cartesian and spherical geometries; higher-order accurate embedded boundary methods; and highly scalable methods for Poisson's equation.

#### ANAG members

- Phil Collela (co-PI)
- Hans Johansen (co-PI)
- Christos Kavouklis
- Chris Chaplin
- Sven Chilton
- Genia Vogman