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首页> 外文期刊>Computational Mechanics >An automatic adaptive refinement procedure for the reproducing kernel particle method. Part II: Adaptive refinement
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An automatic adaptive refinement procedure for the reproducing kernel particle method. Part II: Adaptive refinement

机译：用于复制核粒子方法的自动自适应细化过程。第二部分：自适应细化

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摘要

In Part II of this study, an automatic adaptive refinement procedure using the reproducing kernel particle method (RKPM) for the solution of 2D linear boundary value problems is suggested. Based in the theoretical development and the numerical experiments done in Part I of this study, the Zienkiewicz and Zhu (Z–Z) error estimation scheme is combined with a new stress recovery procedure for the a posteriori error estimation of the adaptive refinement procedure. By considering the a priori convergence rate of the RKPM and the estimated error norm, an adaptive refinement strategy for the determination of optimal point distribution is proposed. In the suggested adaptive refinement scheme, the local refinement indicators used are computed by considering the partition of unity property of the RKPM shape functions. In addition, a simple but effective variable support size definition scheme is suggested to ensure the robustness of the adaptive RKPM procedure. The performance of the suggested adaptive procedure is tested by using it to solve several benchmark problems. Numerical results indicated that the suggested refinement scheme can lead to the generation of nearly optimal meshes for both smooth and singular problems. The optimal convergence rate of the RKPM is restored and thus the effectivity indices of the Z–Z error estimator are converging to the ideal value of unity as the meshes are refined.
机译：在本研究的第二部分中，提出了一种使用再生核粒子法（RKPM）的自动自适应细化方法来解决2D线性边界值问题。基于本研究第一部分中的理论发展和数值实验，Zienkiewicz和Zhu（Z–Z）误差估计方案与新的应力恢复过程相结合，用于自适应精修过程的后验误差估计。通过考虑RKPM的先验收敛速度和估计的误差范数，提出了一种用于确定最佳点分布的自适应细化策略。在建议的自适应细化方案中，使用的局部细化指标是通过考虑RKPM形状函数的单位属性的分区来计算的。另外，提出了一种简单但有效的可变支持大小定义方案，以确保自适应RKPM过程的鲁棒性。通过使用它来解决几个基准问题，测试了建议的自适应过程的性能。数值结果表明，所提出的细化方案可以导致针对光滑和奇异问题的近似最佳网格的生成。恢复了RKPM的最佳收敛速度，因此，随着网格的细化，Z–Z误差估计器的有效性指标已收敛到理想的单位值。

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