Parallel computing in TDBEM in Elastodynamics with mCCSR Sparse Storage

  • Zhou, Weiyu (Tsinghua University)
  • Zhang, Haixiang (Tsinghua University)
  • Chen, Yongqiang (Peking University)

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This study presents a high-performance CPU-based parallel strategy for the elastodynamic time-domain boundary element method (TDBEM) using the mixed cell compressed sparse row (mCCSR) format. A quantitative task-load model is developed to account for element integration costs, enabling a dynamic super-row partitioning scheme that effectively balances workload across threads during matrix generation. For the solution phase, a unified, multi-step parallel scheme is introduced for convolution computations, while GMRES iterative solving employs mCCSR-based sparse matrix–vector multiplication. The proposed framework fully exploits the cell-based sparsity of the mCCSR format and minimizes thread scheduling and synchronization overhead. Numerical examples—including rectangular, spherical, T-beam, and complex mechanical components—demonstrate substantial improvements in parallel efficiency, achieving up to 64% efficiency with 48 threads for large-scale problems. The dynamic partitioning approach consistently outperforms conventional average partitioning, particularly for asymmetric geometries, while maintaining stable and physically accurate results. The method provides a scalable and robust solution for large-scale elastodynamic simulations, with potential extensions to hybrid MPI–GPU implementations.