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Sparse matrix LU factorization is a critical method in direct solvers, playing a significant role in the field of first-principles materials simulation. Matrices in quantum chemistry problems often exhibit locally dense properties, yet their spatial structural characteristics have been overlooked in previous efforts. This paper proposes a novel LU factorization algorithm that leverages application-specific locally dense structures by partitioning sparse matrices into uniform dense blocks. Through systematic integration of level-3 BLAS kernels, the method transforms traditionally memory-bound LU operations into compute-intensive tasks, achieving significant improvements in both computational efficiency and CPU utilization. We conducted performance tests on CPUs from three different vendors, including the x86-based Intel Xeon Platinum 8375C and AMD EPYC 7543, as well as the ARM-based Kunpeng 920. Experimental results demonstrate significant performance improvements compared to the state-of-the-art sparse direct solvers.

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Uniform Dense Blocking for Efficient Sparse LU Factorization in First-Principles Materials Simulation

  • 会议论文

  • 发表日期：

    2026年

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  • Chao Wang,
  • Junshi Chen,
  • Longsheng Song,
  • Haijie Hou,
  • Dongdong Tan,
  • Yueqiang He,
  • Wentiao Wu,
  • Sihan Lu,
  • Hong An

摘要

Sparse matrix LU factorization is a critical method in direct solvers, playing a significant role in the field of first-principles materials simulation. Matrices in quantum chemistry problems often exhibit locally dense properties, yet their spatial structural characteristics have been overlooked in previous efforts. This paper proposes a novel LU factorization algorithm that leverages application-specific locally dense structures by partitioning sparse matrices into uniform dense blocks. Through systematic integration of level-3 BLAS kernels, the method transforms traditionally memory-bound LU operations into compute-intensive tasks, achieving significant improvements in both computational efficiency and CPU utilization. We conducted performance tests on CPUs from three different vendors, including the x86-based Intel Xeon Platinum 8375C and AMD EPYC 7543, as well as the ARM-based Kunpeng 920. Experimental results demonstrate significant performance improvements compared to the state-of-the-art sparse direct solvers.