Error bounds of singular boundary method for potential problems
Error bounds of singular boundary method for potential problems
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DOI：
10.1002/num.22176
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发表时间：
2017-06
影响因子：
3.9
通讯作者：
Junpu Li;Wen Chen;Yan Gu
中科院分区：
文献类型：
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作者：
Junpu Li;Wen Chen;Yan Gu
奇异边界法（SBM）是一种新的强形式边界配置法，它不需要积分、网格和虚拟边界。虽然在文献中已经报道了广泛的研究，以提高其精度和稳定性，以及其应用到不同的问题，但是，很少有人做数学分析其收敛性。本文的主要目的是推导出显式的SBM的误差界，以及解释SBM中的原始强度因子（OIF）和边界元法（BEM）中的奇异积分（OIF）之间的本质区别。在推导过程中，我们还阐明了OIF的物理意义，并解释了OIF具有修正边界离散误差功能的原因。最后，通过几个标准算例验证了本文结论的有效性，并比较了SBM和BEM的收敛特性。可以发现，SBM具有明确的误差界，并且在数学上是稳定的技术。Numer Methods Partial Differential Eq 33：1987-2004，2017
The singular boundary method (SBM) is a recent strong‐form boundary collocation method free of integration, mesh, and fictitious boundary. Although an extensive study has been reported in the literature on improving its accuracy and stability as well as its applications to diverse problems, little, however, has been done to analyze its convergence mathematically. The main purpose of this paper is to derive the explicit error bounds of the SBM for potential problems as well as to explain the essential difference between the origin intensity factor (OIF) in the SBM and the singular integration in the boundary element method (BEM). In the process of derivation, we also illustrate the physical meaning of OIF and explain the reason why the OIF has the function to correct the discretization error on the boundary. Finally, several benchmark examples are given to verify the effectiveness of the conclusions obtained from this article, as well as to investigate the different convergence behaviors between the SBM and BEM. It can be found that the SBM has the explicit error bound and is mathematically a stable technique.© 2017 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 33: 1987–2004, 2017