Fast Methods for Computing Selected Elements of the Green's Function in Massively Parallel Nanoelectronic Device Simulations

The central computation in atomistic, quantum transport simulation consists in solving the Schrödinger equation several thousand times with non-equilibrium Green’s function (NEGF) equations. In the NEGF formalism, a numerical linear algebra problem is identified related to the computation of a sparse inverse subset of general sparse unsymmetric matrices. The computational challenge consists in computing all the diagonal entries of the Green’s functions, which represent the inverse of the electron Hamiltonian matrix. Parallel upward and downward traversals of the elimination tree are used to perform these computations very efficiently and reduce the overall simulation time for realistic nanoelectronic devices. Extensive large-scale numerical experiments on the CRAY-XE6 Monte Rosa at the Swiss National Supercomputing Center and on the BG/Q at the Argonne Leadership Computing Facility are presented.