Massively parallel algorithms for computational nanoelectronics based on quantum molecular dynamics

A quantum molecular dynamics (QMD) simulation scheme has been developed which is suitable for the study of highly nonlinear electron dynamics far from equilibrium in semiconducting devices of nanometer size. The core components of the QMD algorithm are: (i) solution of the time-dependent Kohn-Sham or Schrödinger equations; and (ii) solution of the Poisson equation for the direct electron-electron interaction. Efficient parallel algorithms for these components are the space-splitting Schrödinger solver and the dynamical-simulated-annealing Poisson solver. Both algorithms are scalable and require only nearest-neighbor communications. These algorithms are implemented on an 8,192-node MasPar computer. Timing tests are carried out to compare these algorithms with other parallel Schrödinger and Poisson solvers. The timing results on the MasPar are also compared with those on other parallel and vector architectures. © 1994.