| Abstract: |
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One of the central computations in atomistic, quantum transport simulation consists in solving the Schroedinger equation several thousand times using the non-equilibrium Green's function equations which is one of the most efficient techniques to perform this task. The computational challenge consists in computing all the diagonal entries of the retarded Green's functions, which represent the inverse of the electron Hamiltonian matrix including open-boundary conditions. This is usually achieved with a so-called recursive Green's function algorithm or, more recently, using a selected inversion algorithm which is an efficient method for computing certain selected elements of the inverse of a sparse matrix. In both methods the computed inverse elements correspond to all or some nonzero elements of the LU factors of a sparse matrix. In this work we review a highly scalable stochastic estimator as an alternative approach for this selected inversion of the retarded Green's function in nano-electronic device simulations. We not only illustrate the impact of the stochastic estimator by comparing its accuracy against existing methods, but also demonstrate its scalability and performance on various supercomputing architectures. We describe its implementation and its performance by focusing on a scalable discretization of the retarded Green's function and testing and evaluating its parallel efficiency, preparing for post-petascale three-dimensional nanoscale calculations.
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