At the heart of many scientific applications is the solution of algebraic systems, such as linear systems of equations, eigenvalue problems, and optimization problems, to name a few. TOPS, which stands for Towards Optimal Petascale Simulations, is a SciDAC applied math center focused on the development of solvers for tackling these algebraic systems, as well as the deployment of such technologies in large-scale scientific applications of interest to the U.S. Department of Energy. In this paper, we highlight some of the solver technologies we have developed in optimization and matrix computations. We also describe some accomplishments achieved using these technologies in UNEDF, a SciDAC application project on nuclear physics.

}, author = {E. Ng and J. Sarich and S. M. Wild and T. S. Munson and H. M. Aktulga and C. Yang and P. Maris and J. P. Vary and M. Kortelainen and W. Nazarewicz and T. Papenbrock and N. Schunck and M. V. Stoitsov and M. Bertolli} }