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GPU-Portable Real-Space Density Functional Theory Implementation on Unified-Memory Architectures

Atsushi M. Ito

TL;DR

The compute-bound kernels, which are fast Fourier transforms (FFT), dense matrix-matrix multiplications (GEMM) and eigenvalue solver, show substantial acceleration on both GPUs, indicating that the present GPU-portable approach can benefit a wide range of plasma-fusion simulation codes beyond DFT.

Abstract

We present a GPU-portable implementation of a real-space density functional theory (DFT) code ``QUMASUN'' and benchmark it on the new Plasma Simulator featuring Intel Xeon 6980P CPUs, and AMD MI300A GPUs. Additional tests were performed on an NVIDIA GH200 GPU. In particular MI300A supports unified memory and GH200 supports coherent memory interconnect, simplifying GPU porting. A lightweight C++ lambda-based layer enables CPU, CUDA, and HIP execution without OpenMP/OpenACC preprocessor directives. For diamond (216 atoms) and tungsten (128 atoms) systems, MI300A and GH200 achieve 2.0-2.8 $\times$ and 2.3-2.4 $\times$ speedups over a 256-core Xeon node. The compute-bound kernels, which are fast Fourier transforms (FFT), dense matrix-matrix multiplications (GEMM) and eigenvalue solver, show substantial acceleration on both GPUs, indicating that the present GPU-portable approach can benefit a wide range of plasma-fusion simulation codes beyond DFT.

GPU-Portable Real-Space Density Functional Theory Implementation on Unified-Memory Architectures

TL;DR

The compute-bound kernels, which are fast Fourier transforms (FFT), dense matrix-matrix multiplications (GEMM) and eigenvalue solver, show substantial acceleration on both GPUs, indicating that the present GPU-portable approach can benefit a wide range of plasma-fusion simulation codes beyond DFT.

Abstract

We present a GPU-portable implementation of a real-space density functional theory (DFT) code ``QUMASUN'' and benchmark it on the new Plasma Simulator featuring Intel Xeon 6980P CPUs, and AMD MI300A GPUs. Additional tests were performed on an NVIDIA GH200 GPU. In particular MI300A supports unified memory and GH200 supports coherent memory interconnect, simplifying GPU porting. A lightweight C++ lambda-based layer enables CPU, CUDA, and HIP execution without OpenMP/OpenACC preprocessor directives. For diamond (216 atoms) and tungsten (128 atoms) systems, MI300A and GH200 achieve 2.0-2.8 and 2.3-2.4 speedups over a 256-core Xeon node. The compute-bound kernels, which are fast Fourier transforms (FFT), dense matrix-matrix multiplications (GEMM) and eigenvalue solver, show substantial acceleration on both GPUs, indicating that the present GPU-portable approach can benefit a wide range of plasma-fusion simulation codes beyond DFT.

Paper Structure

This paper contains 1 equation, 4 figures.

Figures (4)

  • Figure 1: Calculation time of SCF loop on RS-DFT for just solving 100 times eigenvalue problems for (a) diamond and (b) tungsten.
  • Figure 2: The performance of GEMM on Xeon 6980P, MI300A, and GH200 for (a) square matrix cases and (b) non-square matrix cases. The problem size $N = 2^p$ or $N = 2^p \pm 1$ ($p=7,8,9,\cdots$) for both cases, and $K/N = 250$ for non-square matrix cases.
  • Figure 3: The performance of eigenvalue solver with divide-and-conquer routine on Xeon 6980P, MI300A, and GH200 for (a) real-symmetric matrix and (b) Hermitian matrix.
  • Figure 4: Performance of three-dimensional FFTs for complex wave functions on the Xeon 6980P, MI300A, and GH200. Both single FFT (N = 1) and batched FFT (N = 512) cases were measured on the GPUs. On the Xeon 6980P, the batched case is parallelized over P = 256 CPU cores, where each core processes N/P = 2 wave functions. All results are shown as the execution time per wave function.