Major Goals: The overarching objective of the proposed work is to develop the formulation and implementation of large-scale time dependent DFT (TDDFT) calculations. The aim is to develop methods for both pseudopotential as well as all-electron calculations. The specific goals include: 1. Development of a real-space formulation of TDDFT that is applicable to both psuedopotential as well as all-electron calculations. 2. Finite element discretization of the formulation with basis adaptation informed by numerical analysis. 3. An adaptive coarse-graining of the temporal evolution of the wave functions informed by numerical analysis. 4. Development of subspace projection techniques that will significantly improve the efficiency and computational complexity of TDDFT calculations. 5. Develop a scalable implementation of the algorithms on massive parallel computing platforms.