TDSE Solver

High-performance parallel solver for 3D time-dependent Schr”odinger equation for large-scale nanosystems. A parallelized three-dimensional (3D) time-dependent Schrödinger equation (TDSE) solver for one-electron systems is presented in this paper. The TDSE Solver is based on the finite-difference method (FDM) in Cartesian coordinates and uses a simple and explicit leap-frog numerical scheme. The simplicity of the numerical method provides very efficient parallelization and high performance of calculations using Graphics Processing Units (GPUs). For example, calculation of 10 6 time-steps on the 1000·1000·1000 numerical grid (10 9 points) takes only 16 hours on 16 Tesla M2090 GPUs. The TDSE Solver demonstrates scalability (parallel efficiency) close to 100% with some limitations on the problem size. The TDSE Solver is validated by calculation of energy eigenstates of the hydrogen atom (13.55 eV) and affinity level of H - ion (0.75 eV). The comparison with other TDSE solvers shows that a GPU-based TDSE Solver is 3 times faster for the problems of the same size and with the same cost of computational resources. The usage of a non-regular Cartesian grid or problem-specific non-Cartesian coordinates increases this benefit up to 10 times. The TDSE Solver was applied to the calculation of the resonant charge transfer (RCT) in nanosystems, including several related physical problems, such as electron capture during H + -H 0 collision and electron tunneling between H - ion and thin metallic island film.

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  1. Gainullin, I.K.; Sonkin, M.A.: High-performance parallel solver for 3D time-dependent Schrödinger equation for large-scale nanosystems (2015)