A comprehensive study of popular eigenvalue methods employed for quantum calculation of energy eigenstates in nanostructures using GPUs

In this work, we concentrate on the graphics processing unit (GPU) implementation of three different methods that are common among peers in the electronic computational domain. We calculate the energy eigenstates of GaN/AlGaN quantum dots on GPU using the tight-binding approach with a $$ sp^3d^5s^* $$s + spin-orbit parametrization for structures ranging from 8039 atoms to 351,600 atoms corresponding to a Hamiltonian matrix size of around 160,780-7,032,000. We perform an analysis for timing, memory occupancy and convergence on a multi-GPU workstation and a high performance computing (HPC) cluster. We also present comparisons between the multi-GPU system having 4 Nvidia Kepler graphic cards and a HPC cluster where the algorithms are benchmarked on up to 256 CPU cores.