Numerical parallel algorithms for large-scale nanoelectronics simulations using NESSIE

A new high performance parallel algorithms to enhance the numerical efficiency of the self-consistent procedure was being proposed. In NESSIE, the linear systems are currently solved on a uniprocessor using a preconditioned Krylov subspace iterative method. In order to compute the electron density, one needs to repeat this procedure for all the energy levels (of the order 103+). This can be trivially done independently on each processor of a Linux cluster using MPI directives. One advantage of this parallel procedure is that the communications between the processors are minimal. A significant drawback, however, to this simplistic solution strategy is that it may not be possible for each processor, with its limited local memory, to handle huge linear systems. For very large systems as outlined above, it is essential to adopt a strategy in which all processors of a high-end computing platform, cooperate on solving a single system. Towards the goal the following were developed and applied (i) a parallel hybrid linear solver SPIKE that represents an improvement over the classical direct solvers of ScaLAPACK, (ii) a parallel trace-minimization algorithm TRACEMIN that is superior to Lanczos, subspace iteration, and LAPACK schemes for computing the lowest eigenpairs.