Explore a comprehensive lecture on advanced computational methods for large-scale density functional theory (DFT) calculations in materials modeling. Delve into the development of fast and accurate techniques using adaptive finite-element discretization, forming the basis of the open-source DFT-FE code. Examine the computational efficiency, scalability, and performance of DFT-FE compared to widely used plane-wave DFT codes. Investigate recent studies on the energetics of dislocations in magnesium, their interaction with solute atoms, and implications for c-axis ductility. Learn about spatial adaptivity, non-orthogonal basis, spectral finite elements, and mixed precision errors in DFT calculations. Gain insights into the broad framework of DFT-FE, including PDA constraint optimization and metrics of errors, to enhance understanding of large-scale ab-initio calculations for materials modeling.