Parallel implementation of the recursive Green's function method

TL;DR

This paper presents a parallel algorithm for the recursive Green's function method, enabling efficient domain decomposition and recursive elimination to improve computational scalability in quantum scattering simulations.

Contribution

It introduces a novel parallel implementation with domain decomposition and recursive elimination, analyzing its performance and identifying bottlenecks for scalable quantum transport calculations.

Findings

Linear scaling of complexity with number of processors

Identification of cyclic reduction as a computational bottleneck

Performance analysis on numerical benchmarks

Abstract

A parallel algorithm for the implementation of the recursive Green's function technique, which is extensively applied in the coherent scattering formalism, is developed. The algorithm performs a domain decomposition of the scattering region among the processors participating in the computation and calculates the Schur's complement block in the form of distributed blocks among the processors. If the method is applied recursively, thereby eliminating the processors cyclically, it is possible to arrive at a Schur's complement block of small size and compute the desired block of the Green's function matrix directly. The numerical complexity due to the longitudinal dimension of the scatterer scales linearly with the number of processors, though, the computational cost due to the processors' cyclic reduction, establishes a bottleneck to achieve efficiency 100%. The proposed algorithm is accompanied by a performance analysis for two numerical benchmarks, in which the dominant sources of computational load and parallel overhead as well as their competitive role in the efficiency of the algorithm will be demonstrated.