FlashMP: Fast Discrete Transform-Based Solver for Preconditioning Maxwell's Equations on GPUs
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arXiv
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| Main Authors: | , , , , , , , , , , , |
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866917035149099008 |
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| author | Zhang, Haoyuan Gao, Yaqian Zhang, Xinxin Li, Jialin Jin, Runfeng Chen, Yidong Zhang, Feng Yuan, Wu Ma, Wenpeng Liang, Shan Zhang, Jian Lu, Zhonghua |
| author_facet | Zhang, Haoyuan Gao, Yaqian Zhang, Xinxin Li, Jialin Jin, Runfeng Chen, Yidong Zhang, Feng Yuan, Wu Ma, Wenpeng Liang, Shan Zhang, Jian Lu, Zhonghua |
| contents | Efficiently solving large-scale linear systems is a critical challenge in electromagnetic simulations, particularly when using the Crank-Nicolson Finite-Difference Time-Domain (CN-FDTD) method. Existing iterative solvers are commonly employed to handle the resulting sparse systems but suffer from slow convergence due to the ill-conditioned nature of the double-curl operator. Approximate preconditioners, like Successive Over-Relaxation (SOR) and Incomplete LU decomposition (ILU), provide insufficient convergence, while direct solvers are impractical due to excessive memory requirements. To address this, we propose FlashMP, a novel preconditioning system that designs a subdomain exact solver based on discrete transforms. FlashMP provides an efficient GPU implementation that achieves multi-GPU scalability through domain decomposition. Evaluations on AMD MI60 GPU clusters (up to 1000 GPUs) show that FlashMP reduces iteration counts by up to 16x and achieves speedups of 2.5x to 4.9x compared to baseline implementations in state-of-the-art libraries such as Hypre. Weak scalability tests show parallel efficiencies up to 84.1%. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2508_07193 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | FlashMP: Fast Discrete Transform-Based Solver for Preconditioning Maxwell's Equations on GPUs Zhang, Haoyuan Gao, Yaqian Zhang, Xinxin Li, Jialin Jin, Runfeng Chen, Yidong Zhang, Feng Yuan, Wu Ma, Wenpeng Liang, Shan Zhang, Jian Lu, Zhonghua Distributed, Parallel, and Cluster Computing Efficiently solving large-scale linear systems is a critical challenge in electromagnetic simulations, particularly when using the Crank-Nicolson Finite-Difference Time-Domain (CN-FDTD) method. Existing iterative solvers are commonly employed to handle the resulting sparse systems but suffer from slow convergence due to the ill-conditioned nature of the double-curl operator. Approximate preconditioners, like Successive Over-Relaxation (SOR) and Incomplete LU decomposition (ILU), provide insufficient convergence, while direct solvers are impractical due to excessive memory requirements. To address this, we propose FlashMP, a novel preconditioning system that designs a subdomain exact solver based on discrete transforms. FlashMP provides an efficient GPU implementation that achieves multi-GPU scalability through domain decomposition. Evaluations on AMD MI60 GPU clusters (up to 1000 GPUs) show that FlashMP reduces iteration counts by up to 16x and achieves speedups of 2.5x to 4.9x compared to baseline implementations in state-of-the-art libraries such as Hypre. Weak scalability tests show parallel efficiencies up to 84.1%. |
| title | FlashMP: Fast Discrete Transform-Based Solver for Preconditioning Maxwell's Equations on GPUs |
| topic | Distributed, Parallel, and Cluster Computing |
| url | https://arxiv.org/abs/2508.07193 |