The atomistic simulations of electronic structures, using a tight binding model with millions of atoms, require solution of
very large sparse Hermitian eigenvalue problems. To obtain the eigenpairs of interest in the interior of the spectrum, we
must take advantage of the most efficient parallel numerical algorithms. Several methods have been developed and implemented
in Nanoelectronic Modeling software package NEMO-3D, including (P)ARPACK, (Block) Lanczos and Tracemin. In this paper, the
performance and tradeoffs of these algorithms for realistic models are discussed. The effectiveness of code optimization techniques
such as SSE2 vectorization is also presented.
Keywords Lanczos - PARPACK - Tracemin - Eigenvalues - Atomistic - Tight binding - Quantum dot - NEMO-3D