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A multi-GPU enabled solver in Kronecker product form for multiphysics problems.

Wenpeng Ma1, Siyuan Zhao2, Xiaofan Le2

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This study introduces an optimized parallel GMRES solver for Kronecker product linear systems, significantly accelerating multiphysics simulations on multi-GPU systems. The new solver enhances Sparse Matrix-Vector Multiplication (SpMV) and communication efficiency for fluid dynamics problems.

Keywords:
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Area of Science:

  • Scientific Computing
  • High-Performance Computing
  • Numerical Analysis

Background:

  • Solving sparse linear systems is crucial for multiphysics problems in engineering and scientific computing.
  • Space-time parallel methods are effective for fluid dynamics on parallel architectures.
  • Kronecker product forms arise in domain decomposition methods for these simulations.

Purpose of the Study:

  • To design and implement a parallel, multi-GPU enabled GMRES solver for Kronecker product linear systems.
  • To optimize Sparse Matrix-Vector Multiplication (SpMV) for Kronecker products on GPUs.
  • To accelerate communication phases using GPU-Direct.

Main Methods:

  • Developed a parallel, multi-GPU GMRES solver tailored for Kronecker product matrices.
  • Implemented SpMV optimizations: enhancing Compute-to-Memory Access Ratio (CMAR) and parallel buffering with pre-mapping for GPU-Direct.
  • Conducted experiments on V100 and A100 GPUs across 1 to 8 GPU configurations.

Main Results:

  • The Kronecker product SpMV achieved significant speedups (e.g., up to 7.1x on 8 V100 GPUs).
  • Communication time was reduced, with speedups up to 3.0x on 8 A100 GPUs.
  • Overall solver runtime showed substantial speedups, up to 4.7x on 8 V100 GPUs and 4.8x on 8 A100 GPUs.

Conclusions:

  • The proposed OKP-Solver demonstrates superior performance compared to cuSPARSE implementations.
  • Optimization strategies effectively leverage GPU capabilities for both computation and communication.
  • The solver is highly efficient for large-scale multiphysics simulations using space-time parallel methods.