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.
黄君豪, 陈永强. 基于几何指标的边界元法单元积分精度评估和修正[J]. 清华大学学报（自然科学版）, 2019, 59(11): 953-960.
HUANG Junhao, CHEN Yongqiang. Accuracy evaluation and correction of the element integration based on a geometric index in the boundary element method. Journal of Tsinghua University(Science and Technology), 2019, 59(11): 953-960.
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2019, Vol. 59 
