Numerical recipes in FORTRAN (2nd ed.): the art of scientific computing
Numerical recipes in FORTRAN (2nd ed.): the art of scientific computing
LAPACK Users' guide (third ed.)
LAPACK Users' guide (third ed.)
Algorithm 582: The Gibbs-Poole-Stockmeyer and Gibbs-King Algorithms for Reordering Sparse Matrices
ACM Transactions on Mathematical Software (TOMS)
Parallel implementation of the recursive Green's function method
Journal of Computational Physics
PT-Scotch: A tool for efficient parallel graph ordering
Parallel Computing
A hybrid method for the parallel computation of Green's functions
Journal of Computational Physics
Optimal block-tridiagonalization of matrices for coherent charge transport
Journal of Computational Physics
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The efficient calculation of the Green's function is a central issue for assessing electronic transport at the nanoscale. In a near-to-equilibrium description, it can be obtained from a matrix inversion, combined with iterative algorithms developed in the 80s. However, this procedure becomes computationally challenging when dealing with very large systems. A set of algorithms (known as knitting and sewing) based on the recursive application of Dyson's equation were recently proposed, where the Green's function elements are obtained in a selective way and without the need of explicit matrix inversion, by including one matrix element at a time. Here we propose a variation of these algorithms adapted to parallel computing. The approach is based on the division of the system in a set of domains whose individual Green's functions are computed independently. The domains are then merged to yield the necessary elements of the Green's function for subsequent evaluation of the electronic transport properties. Promising scaling behavior is found, depending on the details of the domain decomposition.