场点与载荷点分离时的边界元法误差分析

ERROR ANALYSIS IN BOUNDARY ELEMENT METHODS WHEN THE FIELD POINT AND THE LOAD POINT ARE SEPARATE

本文推导了场点与载荷点分离时的边界积分方程。误差分析的结果证实边界元系统方程中,各组元的误差和模的大小对数值求解精度起决定作用。以分析场点与载荷点的距离对方程中组元误差和的大小的影响,可得出非奇异间接边界元法的求解精度比奇异边界元法的求解精度要高得多,间接边界元法的数值稳定性好于直接边界元法的数值稳定性等有益的结论。这种分析方法能够定性的解释文中的计算结果。

in this paper, the boundary integral equations are proposed, in which the field point and the load point are separate. The results of error analysis prove that the precision of numerical calculation is affected mainly by the coefficient error and the determinant value of BEM system equation. Through an analysis showing that the distance between the field point and the load point can affect the coefficient and the determinant value mani festly, useful results can be drawn revealing that the precision of calculation through regular BEM is much higher than that of singular BEM and that numerical stability of indirect BEM is better than that of direct BEM. The analysis can qualitively explain the results of numerical calculation given in this pape r.