The Computational Science effort focuses on the development, analysis, and verification and validation (V&V) of numerical solution techniques for physical models embodied within large-scale multi-physics simulation tools designed to address today’s leading problems in science and engineering. Key applications currently include the predictive simulation of weapons manufacturing and performance as supported by the DOE Advanced Simulation and Computing (ASC) Program and global climate modeling as supported by the DOE Scientific Discovery Through Advanced Computing (SciDAC) Program. The computational science effort can be divided into three principal research thrust areas: algorithms and models for specific physical phenomena of interest, numerical methods for the algorithmic coupling of these physical phenomena, and metrics for correctness and robustness of these models and algorithms. The thrust areas are:

1. Numerical Solution of Partial Differential Equations for Continuum Dynamics, Energy Transport, and Materials Science;
2. Linear and Nonlinear Solvers; and
3. Methodologies for V&V, Sensitivity, and Uncertainty Quantification.

A key product of this effort, both in the long and short term, is verified and validated software components constructed with defensible (demonstrable) software quality engineering practices. These components must instantiate robust and accurate solution techniques for the physical models required by the multi-physics simulation tools. The computational science effort devoted to “multi-physics coupling” algorithm research is necessary for the faithful simulation of multiple, simultaneously-occurring physical phenomena.

Long-term goals.  Ensuring computational science follows the fundamental principles of the scientific method requires long term investigation of numerical methods and algorithms and careful software development.  For example, a physicist or engineering analyst using these simulation tools should be able to generate high fidelity three-dimensional simulations, attain similar answers with two different numerical techniques, and be assured that each technique has been verified and validated.  Because the transformation of physical principles into software can take many different paths, long-term research focuses on the investigation of new, possibly high-risk, methods along with new ideas for the improvement of classical methods that are parallel and scalable.
Experience shows investigation of new methods must be built upon the foundation of good software quality engineering. Unit-testing and component-based designs for even one-dimensional tests are necessary to assess the impact of this long-term research on next-generation simulation tools.

Long-term goals of the computational sciences effort include:

• Understanding the physics and mathematics of the phenomena to be simulated so that improved numerical methods can be devised that are both robust and accurate;
• Developing new algorithms for the resulting physical models that possess good single processor performance as well as being parallel and scalable;
• Instantiating these algorithms into component-based software as guided by sound software quality engineering practices. Unit-testing is of primary importance compared to reusability;
• Developing improved and automated methodologies for the verification of the algorithms and the software and the validation of the models; and
• Devising strategies for successful team software development of large-scale simulation tools