2015: New horizons of supercomputer modeling


The MSU physicists (Faculty of Physics) in cooperation with their colleagues from Tomsk Polytechnic University have developed a high-performance solver for solution of 3D time-dependent Schrodinger equation, which is three times faster than other existing solvers.

A parallelized 3Dl time-dependent Schrodinger equation (TDSE) solver for one-electron systems has been developed. The TDSE Solver is based on the finite-difference method 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 106 time-steps on the 1000⋅1000⋅1000 numerical grid (109 points) takes only 16 hours on 16 Tesla M2090 GPUs of Lomonosov supercomputer. The TDSE Solver demonstrates scalability (parallel efficiency) close to 100%. 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 has been applied to the calculation of the resonant charge transfer (RCT) in nanosystems, including several related physical problems, such as electron capture during H+-H0 collision and electron tunneling between H- ion and thin metallic island film.

These results have been published in the paper: I.K. Gainullin, M.A. Sonkin, “High-performance parallel solver for 3D time-dependent Schrodinger equation for large-scale nanosystems,” Computer Physics Communications, 188, 68-75 (2015).