# Tools for Solution of Algebraic Systems

Solution of systems of algebraic equations is undoubtedly one of the most common computational kernels in scientific applications of interest to the Department of Energy. Efficient, scalable, and reliable algorithms are crucial for the success of large-scale simulations. FASTMath work focuses on both iterative and direct linear solution methods, and eigensolvers. Our work in the first half of the project in these areas centered around two primary themes. First, we are developing new algorithms and using them to better solve physics problems including advanced multigrid techniques, improved preconditioners, and new eigensystem solvers. Second, we are creating efficient many-core solution methodologies using hybrid programming techniques, communication-reducing strategies, and intelligent task-mapping methods. This work has application to fusion, nuclear structure calculation, quantum chemistry, accelerator modeling, climate, and dislocation dynamics research.