Eigenvalue Solvers for Atomistic Simulations of Electronic Structures with NEMO-3D

In the atomistic simulation of electronic structures (e.g. quantum dots, Fig. 1), it is imperative to take advantage of the most efficient parallel numerical algorithms. In order to determine the energy levels and corresponding wave functions of interest, we need to find few of the interior eigenvalues of a large sparse standard Hermitian eigenvalue problem. Several algorithms have been devised for such problems, including (P)ARPACK [1], (Block) Lanczos [2] and Tracemin [3]. In this paper, the tradeoffs of these algorithms for the solution of eigenvalue problems arising in Nanoelectronic Modeling tool NEMO-3D [4], [5] will be discussed. The effectiveness of code optimization techniques, such as the use of SSE3 instruction set and explicit inlining in the Hamiltonian construction for Intel-based machines will also be presented