We present hierarchical Krylov methods and nested Krylov methods to overcome the scaling difficulties for extreme-scale computing.We demonstrate the impact at high core counts on the PFLOTRAN subsurface flow application.Because these algorithms can be activated at runtime via the PETSc library, application codes that employ PETSc can easily experiment with such techniques.The principles of hierarchal Krylov methods and nested Krylov methods can be applied to complementary advances insynchronization/communication-avoiding Krylov methods, there by offering potentially multiplicative benefits of combined approaches.We also demonstrate a Scientific Application Web server (SAWs) still under development that assists users in viewing, customizing and assembling the composable solvers.