Fast and scalable multi-GPU sliced FFT solvers for asymptotically compatible discretizations of 3D nonlocal diffusion problems
Abstract
Large-scale 3D peridynamic transient diffusion simulations are constrained by the computational cost and memory requirements of nonlocal interactions. We propose a fast and scalable multi-GPU sliced FFT algorithm based on the recently developed asymptotically compatible finite difference (ACFD) scheme. By exploiting the discrete operator's structure and finite interaction range, the algorithm combines FFT acceleration with local inter-GPU communication. It preserves the ACFD scheme while avoiding the global data redistribution required by full 3D FFTs. We build a matrix-free GPU conjugate gradient (CG) solver, use multigrid preconditioning to reduce iteration counts, and introduce a human-audited configuration agent for efficient cross-level configuration. Strong-scaling tests show that sliced FFT-CG achieves 93.2% parallel efficiency on eight GPUs, compared with 28.2% for full FFT-CG on the same problem and hardware. The framework supports approximately 10.29 billion degrees of freedom on eight RTX 4090 GPUs with 24 GB of memory each. The insulated penny-shaped cutout benchmark demonstrates transient simulation with approximately 8.58 billion degrees of freedom. Three-dimensional star-shaped interface evolution further demonstrates convergence toward the local solution in a nonlinear phase-field problem. These results demonstrate that sliced FFT provides a scalable multi-GPU approach for fast computation of 3D peridynamic diffusion.
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BibTeX
@misc{li2026fast,
title = {{Fast and scalable multi-GPU sliced FFT solvers for asymptotically compatible discretizations of 3D nonlocal diffusion problems}},
author = {Yulong Li and Jiale Meng and Zhenlin Guo and Jiwei Zhang},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.28372},
eprint = {2610.28372},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.28372},
}
RIS
TY - UNPB
TI - Fast and scalable multi-GPU sliced FFT solvers for asymptotically compatible discretizations of 3D nonlocal diffusion problems
AU - Yulong Li
AU - Jiale Meng
AU - Zhenlin Guo
AU - Jiwei Zhang
PY - 2026
DA - 2026/10/20
PB - arXiv
DO - 10.48550/arxiv.2610.28372
UR - https://arxiv.org/abs/2610.28372
AB - Large-scale 3D peridynamic transient diffusion simulations are constrained by the computational cost and memory requirements of nonlocal interactions. We propose a fast and scalable multi-GPU sliced FFT algorithm based on the recently developed asymptotically compatible finite difference (ACFD) scheme. By exploiting the discrete operator's structure and finite interaction range, the algorithm combines FFT acceleration with local inter-GPU communication. It preserves the ACFD scheme while avoiding the global data redistribution required by full 3D FFTs. We build a matrix-free GPU conjugate gradient (CG) solver, use multigrid preconditioning to reduce iteration counts, and introduce a human-audited configuration agent for efficient cross-level configuration. Strong-scaling tests show that sliced FFT-CG achieves 93.2% parallel efficiency on eight GPUs, compared with 28.2% for full FFT-CG on the same problem and hardware. The framework supports approximately 10.29 billion degrees of freedom on eight RTX 4090 GPUs with 24 GB of memory each. The insulated penny-shaped cutout benchmark demonstrates transient simulation with approximately 8.58 billion degrees of freedom. Three-dimensional star-shaped interface evolution further demonstrates convergence toward the local solution in a nonlinear phase-field problem. These results demonstrate that sliced FFT provides a scalable multi-GPU approach for fast computation of 3D peridynamic diffusion.
ER -