Computational Method Development Matrix-Free Algorithms for Higher-Order Finite-Element Discretized Matrix Multivector Products Non-Collinear Magnetism and SOC a scalable finite-element framework for ab-initio modelling of Non-Collinear Magnetism and Spin-Orbit Coupling in pseudopotential DFT GW methods Scalable finite-element based methodologies for DFT+GW methods. Novel Applications Platinum Clustering Influence of excess charge on Platinum Clustering on graphene substrate