Parallel Quadratic Selected Inversion in Quantum Transport Simulation

TL;DR

This paper presents a distributed, GPU-accelerated method for parallel selected inversion and quadratic matrix solutions in quantum transport simulations, enabling larger device modeling with improved speed.

Contribution

The authors develop distributed algorithms based on recursive Green's function techniques that enable parallel selected inversion and quadratic solutions, extending to arrowhead matrices for multi-terminal devices.

Findings

Achieved 5.2x speedup over PARDISO on 16 GPUs

Enabled simulation of larger nano-devices with improved efficiency

Extended methods to handle arrowhead matrices for complex transistor structures

Abstract

Driven by Moore's Law, the dimensions of transistors have been pushed down to the nanometer scale. Advanced quantum transport (QT) solvers are required to accurately simulate such nano-devices. The non-equilibrium Green's function (NEGF) formalism lends itself optimally to these tasks, but it is computationally very intensive, involving the selected inversion (SI) of matrices and the selected solution of quadratic matrix (SQ) equations. Existing algorithms to tackle these numerical problems are ideally suited to GPU acceleration, e.g., the so-called recursive Green's function (RGF) technique, but they are typically sequential, require block-tridiagonal (BT) matrices as inputs, and their implementation has been so far restricted to shared memory parallelism, thus limiting the achievable device sizes. To address these shortcomings, we introduce distributed methods that build on RGF and enable parallel selected inversion and selected solution of the quadratic matrix equation. We further extend them to handle BT matrices with arrowhead, which allows for the investigation of multi-terminal transistor structures. We evaluate the performance of our approach on a real dataset from the QT simulation of a nano-ribbon transistor and compare it with the sparse direct package PARDISO. When scaling to 16 GPUs, our fused SI and SQ solver is 5.2x faster than the SI module of PARDISO applied to a device 16x shorter. These results highlight the potential of our method to accelerate NEGF-based nano-device simulations.