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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Published in:SC24: International Conference for High Performance Computing, Networking, Storage and Analysis pp. 1 - 16
Main Authors: Lu, Yuechen, Zeng, Lijie, Wang, Tengcheng, Fu, Xu, Li, Wenxuan, Cheng, Helin, Yang, Dechuang, Jin, Zhou, Casas, Marc, Liu, Weifeng
Format: Conference Proceeding
Language:English
Published: IEEE 17.11.2024
Subjects:
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
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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.
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
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  surname: Lu
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  organization: China University of Petroleum,Super Scientific Software Laboratory,Dept. of CST,Beijing,China
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  givenname: Dechuang
  surname: Yang
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  email: dechuang.yang@student.cup.edu.cn
  organization: China University of Petroleum,Super Scientific Software Laboratory,Dept. of CST,Beijing,China
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  givenname: Zhou
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  organization: China University of Petroleum,Super Scientific Software Laboratory,Dept. of CST,Beijing,China
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  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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