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Numerical Investigation on Convergence Rate of Singular Boundary Method

机译：奇异边界法收敛速度的数值研究

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摘要

The singular boundary method (SBM) is a recent boundary-type collocation scheme with the merits of being free of mesh and integration, mathematically simple, and easy-to-program. Its essential technique is to introduce the concept of the source intensity factors to eliminate the singularities of fundamental solutions upon the coincidence of source and collocation points in a strong-form formulation. In recent years, several numerical and semianalytical techniques have been proposed to determine source intensity factors. With the help of these latest techniques, this short communication makes an extensive investigation on numerical efficiency and convergence rates of the SBM to an extensive variety of benchmark problems in comparison with the BEM. We find that in most cases the SBM and BEM have similar convergence rates, while the SBM has slightly better accuracy than the direct BEM. And the condition number of SBM is lower than BEM. Without mesh and numerical integration, the SBM is computationally more efficient than the BEM.
机译：奇异边界方法（SBM）是一种最新的边界类型并置方案，具有无网格且无积分，数学上简单且易于编程的优点。它的基本技术是引入源强度因子的概念，以消除强形式公式中源点和搭配点重合时基本解的奇异性。近年来，已经提出了几种数值和半分析技术来确定源强度因子。借助这些最新技术，与BEM相比，这种简短的交流对SBM的数值效率和收敛速度进行了广泛的研究，以解决各种基准问题。我们发现，在大多数情况下，SBM和BEM具有相似的收敛速度，而SBM的精度比直接BEM略好。 SBM的条件数低于BEM。没有网格和数值积分，SBM的计算效率要高于BEM。

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  • 来源
    《Mathematical Problems in Engineering》 |2016年第5期|3564632.1-3564632.13|共13页
  • 作者

    Li Junpu; Chen Wen; Fu Zhuojia;

  • 作者单位

    Hohai Univ, State Key Lab Hydrol Water Resources & Hydraul En, Ctr Numer Simulat Software Engn & Sci, Coll Mech & Mat, Nanjing 210098, Jiangsu, Peoples R China;

    Hohai Univ, State Key Lab Hydrol Water Resources & Hydraul En, Ctr Numer Simulat Software Engn & Sci, Coll Mech & Mat, Nanjing 210098, Jiangsu, Peoples R China;

    Hohai Univ, State Key Lab Hydrol Water Resources & Hydraul En, Ctr Numer Simulat Software Engn & Sci, Coll Mech & Mat, Nanjing 210098, Jiangsu, Peoples R China;

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