AmgT: Algebraic Multigrid Solver on Tensor Cores
Algebraic multigrid (AMG) methods are particularly efficient to solve a wide range of sparse linear systems, due to their good flexibility and adaptability. Even though modern parallel devices, such as GPUs, brought massive parallelism to AMG, the latest major hardware features, i.e., tensor core un...
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| Vydáno v: | SC24: International Conference for High Performance Computing, Networking, Storage and Analysis s. 1 - 16 |
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IEEE
17.11.2024
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| Abstract | Algebraic multigrid (AMG) methods are particularly efficient to solve a wide range of sparse linear systems, due to their good flexibility and adaptability. Even though modern parallel devices, such as GPUs, brought massive parallelism to AMG, the latest major hardware features, i.e., tensor core units and their low precision compute power, have not been exploited to accelerate AMG. This paper proposes AmgT, a new AMG solver that utilizes the tensor core and mixed precision ability of the latest GPUs during multiple phases of the AMG algorithm. Considering that the sparse general matrix-matrix multiplication (SpGEMM) and sparse matrix-vector multiplication (SpMV) are extensively used in the setup and solve phases, respectively, we propose a novel method based on a new unified sparse storage format that leverages tensor cores and their variable precision. Our method improves both the performance of GPU kernels, and also reduces the cost of format conversion in the whole data flow of AMG. To better utilize the algorithm components in existing libraries, the data format and compute kernels of the AmgT solver are incorporated into the HYPRE library. The experimental results on NVIDIA A100, H100 and AMD MI210 GPUs show that our AmgT outperforms the original GPU version of HYPRE by a factor of on geomean 1.46 \times, 1.32 \times and 2.24 \times (up to 2.10 \times, 2.06 \times and 3.67 \times), respectively. |
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| AbstractList | Algebraic multigrid (AMG) methods are particularly efficient to solve a wide range of sparse linear systems, due to their good flexibility and adaptability. Even though modern parallel devices, such as GPUs, brought massive parallelism to AMG, the latest major hardware features, i.e., tensor core units and their low precision compute power, have not been exploited to accelerate AMG. This paper proposes AmgT, a new AMG solver that utilizes the tensor core and mixed precision ability of the latest GPUs during multiple phases of the AMG algorithm. Considering that the sparse general matrix-matrix multiplication (SpGEMM) and sparse matrix-vector multiplication (SpMV) are extensively used in the setup and solve phases, respectively, we propose a novel method based on a new unified sparse storage format that leverages tensor cores and their variable precision. Our method improves both the performance of GPU kernels, and also reduces the cost of format conversion in the whole data flow of AMG. To better utilize the algorithm components in existing libraries, the data format and compute kernels of the AmgT solver are incorporated into the HYPRE library. The experimental results on NVIDIA A100, H100 and AMD MI210 GPUs show that our AmgT outperforms the original GPU version of HYPRE by a factor of on geomean 1.46 \times, 1.32 \times and 2.24 \times (up to 2.10 \times, 2.06 \times and 3.67 \times), respectively. |
| Author | Li, Wenxuan Cheng, Helin Jin, Zhou Wang, Tengcheng Liu, Weifeng Lu, Yuechen Casas, Marc Fu, Xu Yang, Dechuang Zeng, Lijie |
| Author_xml | – sequence: 1 givenname: Yuechen surname: Lu fullname: Lu, Yuechen email: yuechenlu@student.cup.edu.cn organization: China University of Petroleum,Super Scientific Software Laboratory,Dept. of CST,Beijing,China – sequence: 2 givenname: Lijie surname: Zeng fullname: Zeng, Lijie email: lijie.zeng@student.cup.edu.cn organization: China University of Petroleum,Super Scientific Software Laboratory,Dept. of CST,Beijing,China – sequence: 3 givenname: Tengcheng surname: Wang fullname: Wang, Tengcheng email: tengcheng.wang@student.cup.edu.cn organization: China University of Petroleum,Super Scientific Software Laboratory,Dept. of CST,Beijing,China – sequence: 4 givenname: Xu surname: Fu fullname: Fu, Xu email: xu.fu@student.cup.edu.cn organization: China University of Petroleum,Super Scientific Software Laboratory,Dept. of CST,Beijing,China – sequence: 5 givenname: Wenxuan surname: Li fullname: Li, Wenxuan email: wenxuan.li@student.cup.edu.cn organization: China University of Petroleum,Super Scientific Software Laboratory,Dept. of CST,Beijing,China – sequence: 6 givenname: Helin surname: Cheng fullname: Cheng, Helin email: helin.cheng@student.cup.edu.cn organization: China University of Petroleum,Super Scientific Software Laboratory,Dept. of CST,Beijing,China – sequence: 7 givenname: Dechuang surname: Yang fullname: Yang, Dechuang email: dechuang.yang@student.cup.edu.cn organization: China University of Petroleum,Super Scientific Software Laboratory,Dept. of CST,Beijing,China – sequence: 8 givenname: Zhou surname: Jin fullname: Jin, Zhou email: jinzhou@cup.edu.cn organization: China University of Petroleum,Super Scientific Software Laboratory,Dept. of CST,Beijing,China – sequence: 9 givenname: Marc surname: Casas fullname: Casas, Marc email: marc.casas@bsc.es organization: Barcelona Supercomputing Center,Spain – sequence: 10 givenname: Weifeng surname: Liu fullname: Liu, Weifeng email: weifeng.liu@cup.edu.cn organization: China University of Petroleum,Super Scientific Software Laboratory,Dept. of CST,Beijing,China |
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| Snippet | Algebraic multigrid (AMG) methods are particularly efficient to solve a wide range of sparse linear systems, due to their good flexibility and adaptability.... |
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| SubjectTerms | AMG Costs Graphics processing units Hardware High performance computing Kernel Libraries Linear systems mixed precision Parallel processing Sparse matrices SpGEMM SpMV tensor core unit Tensors |
| Title | AmgT: Algebraic Multigrid Solver on Tensor Cores |
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