The Office of Science has funded a new effort jointly lead by Sandia National Laboratories (SNL) and Oak Ridge National Laboratories (ORNL) to explore scalable algorithms for the next generation of hardware architectures. As DOE moves towards the Leadership-class machines of the next 5-10 years, algorithms are going to face significant challenges due to: extreme concurrency, complex memory hierarchies, costly data movement, a steep rise in fault rates, and heterogeneous processor architectures. In the face of these challenges, major innovations in algorithm design will be required just to achieve acceptable productivity on future DOE Leadership computers, let alone realize their full promise. The resulting solver algorithms will provide a breakthrough in state-of-the-art algorithm design for the next generation of high-performance computers, providing support for hybrid systems, and significantly exceeding the performance of currently available solutions. This project is an outgrowth of a three year Office of Science funded Math/CS Institute project started in 2009. This project will be funded for three years and includes collaboration with three universities: University of Illinois, University of California, and University of Tennessee.