Electron transfer activities of metal clusters are fundamentally significant and have promising potential in catalysis, charge or energy storage, sensing, biomedicine and other applications. Strong resonance coupling between the metal core energy states and the ligand molecular orbitals has not been established experimentally, albeit exciting progress has been achieved in the composition and st...

Most research on preconditioners for time-dependent PDEs has focused implicit multi-step or diagonally-implicit multi-stage temporal discretizations. In this paper, we consider monolithic multigrid fully-implicit Runge-Kutta (RK) time integration methods. These discretizations have very attractive accuracy and stability properties, but they couple the spatial degrees of freedom across multiple ...