GPU acceleration of non-equilibrium Green's function calculation using OpenACC and CUDA FORTRAN

TL;DR

This paper develops GPU-accelerated methods using OpenACC and CUDA FORTRAN for solving the computationally intensive non-equilibrium Green's function equations, achieving significant speedups and scalability on modern hardware.

Contribution

It introduces optimized GPU implementations of NEGF calculations with detailed performance comparisons, highlighting the advantages of CUDA FORTRAN over OpenACC.

Findings

GPU approaches outperform CPU implementations significantly

Both CPU and GPU methods show excellent scalability

CUDA FORTRAN offers more advanced control and better performance

Abstract

The numerical solution of the Kadanoff-Baym nonlinear integro-differential equations, which yields the non-equilibrium Green's functions (NEGFs) of quantum many-body systems, poses significant computational challenges due to its high computational complexity. In this work, we present efficient implementations of a numerical method for solving these equations on distributed-memory architectures, including many-core CPUs and multi-GPU systems. For CPU-based platforms, we adopt a hybrid MPI/OpenMP programming model to exploit both inter-node and intra-node parallelism. On GPU-accelerated systems, we implement the method using two distinct approaches: MPI/OpenACC and MPI/CUDA FORTRAN. Several optimization strategies are employed to enhance GPU performance, including techniques to maximize computational resource utilization and minimize the overhead associated with kernel launches and memory management. Although OpenACC is easy to use, CUDA FORTRAN provides more advanced features for configuring and managing multiple levels of concurrency, while also simplifying memory allocation and data movement between host and device. This flexibility translates into significant performance improvements. We compare the performance of the three implementations and demonstrate that the GPU-based approaches achieve substantial speedups over CPU-based implementations. Furthermore, both CPU and GPU versions exhibit excellent strong and weak scaling, confirming the scalability and efficiency of our approach for large-scale NEGF computations.