@article {32701,
	title = {Accuracy evaluation and correction of the element integration based on a geometric index in the boundary element method},
	journal = {Qinghua Daxue Xuebao/Journal of Tsinghua UniversityQinghua Daxue Xuebao/Journal of Tsinghua UniversityQinghua Daxue Xuebao/Journal of Tsinghua University},
	volume = {59},
	number = {11},
	year = {2019},
	note = {Export Date: 9 November 2022CODEN: QDXKECorrespondence Address: Chen, Y.; Department of Mechanics and Engineering Science, China; email: chenyq@pku.edu.cnReferences: Brebbia, C.A., Telles, J.C.F., Wrobel, L.C., (1984) Boundary Element Techniques, , Berlin, Germany: Springer-Verlag; Aliabadi, M.H., (2002) The Boundary Element Method: Applications in Solid and Structures, , Chichester, UK: Wiley; Yao, Z.H., Wang, H.T., (2010) Boundary Element Methods, , 姚振汉, 王海涛. 边界元法 [M]. 北京: 高等教育出版社, 2010. 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	pages = {953-960},
	publisher = {Press of Tsinghua University},
	type = {Article},
	abstract = {This paper presents a scheme to evaluate the element integration accuracy for the boundary element method based on a singular geometric index to improve the accuracy of the final solution. The singular geometric index is defined as the ratio of the shortest distance from the source point to the integral element to the element length. For a discretized boundary mesh, the upper bound of the quadrature error is used to obtain the relationship between the singular geometric index and the element integration accuracy with the integrated accuracies of all the elements estimated from the node geometries. Furthermore, the maximum relative error of the solution which is a global precision index is estimated from the matrix error transfer formula. If the index is larger than a threshold, some of the element integrals are not accurate and should be corrected to improve the solution accuracy. This method uses the sinh transformation method to correct the element integrals of low accuracy elements. Numerical results show that this method can guarantee the accuracy of the overall stiffness matrix coefficient of the boundary element method and the final solution accuracy using only the geometric node information. This scheme does not need to change the original calculation, requires little additional computational cost, and can be easily implemented. {\textcopyright} 2019, Tsinghua University Press. All right reserved.},
	keywords = {Accuracy correction, Accuracy evaluation, Boundary element method, Computational costs, Element integral accuracy, Errors, Geometric index, Geometry, Integration, Integration accuracy, Mathematical transformations, Maximum relative errors, Numerical methods, Sailing vessels, sinh transformation, Stiffness matrix},
	isbn = {10000054 (ISSN)},
	author = {Huang, J. and Y. Chen}
}
