Volume 44 Issue 1
Jan.  2023
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ZHEN Yujie, XU Kang, JIANG Tao, REN Jinlian. GPU Parallelization Computation of High-Dimensional Multi-Phase Separation in Complex Domains Based on the Corrected FPM[J]. Applied Mathematics and Mechanics, 2023, 44(1): 93-104. doi: 10.21656/1000-0887.430147
Citation: ZHEN Yujie, XU Kang, JIANG Tao, REN Jinlian. GPU Parallelization Computation of High-Dimensional Multi-Phase Separation in Complex Domains Based on the Corrected FPM[J]. Applied Mathematics and Mechanics, 2023, 44(1): 93-104. doi: 10.21656/1000-0887.430147

GPU Parallelization Computation of High-Dimensional Multi-Phase Separation in Complex Domains Based on the Corrected FPM

doi: 10.21656/1000-0887.430147
  • Received Date: 2022-04-26
  • Rev Recd Date: 2022-06-13
  • Available Online: 2023-01-06
  • Publish Date: 2023-01-01
  • Based on the corrected finite pointset method (CFPM) with CPU-GPU heteroid parallelization (CFPM-GPU), a high-efficiency, accurate and fast parallel algorithm was developed for the high-dimensional phase separation phenomena governed by the multi-component Cahn-Hilliard (C-H) equation in complex domains. The proposed parallel algorithm with the CFPM-GPU was built in a process like: ① introduce the Wendland weight function into the discretization of the finite pointset method (FPM) scheme for the 1st/2nd spatial derivatives, based on the Taylor series and the weighted least square concept; ② use the above FPM scheme twice to approximate the 4th spatial derivative in the C-H equation, which is called the CFPM method; ③ for the first time establish an accelerating parallel algorithm for the CFPM with local matrices by means of a single GPU card based on the CUDA programming. Two benchmark problems of 2D radially and 3D spherically symmetric C-H equations were first solved to test the accuracy and high-efficiency of the proposed CFPM-GPU, and the acceleration ratio of the GPU parallelization to the single CPU computation is about 160. Subsequently, the proposed CFPM-GPU was used to predict the 2D/3D multi-phase separation phenomena in complex domains, and the prediction was compared with other numerical results. The numerical results show that, the proposed CFPM-GPU is valid and high-efficiency to simulate the 2D/3D multi-phase separation cases in complex domains.

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