【摘要】 快速多极方法能够有效地提高边界元法的计算效率.求解的计算量和内存量与问题的自由度数N成正比.求解的精度与传统边界元法相比有所下降.分析了Taylor级数多极边界元法的计算精度和远场影响系数的误差.研究了核函数r的Taylor级数展开性质,推导了三维弹性问题基本解的误差估计公式.说明了影响多极边界元法计算精度的因素.数值算例显示了误差估计公式的正确性和有效性.更多还原

【Abstract】 The fast multipole method(FMM) is capable of improving the efficiency of boundary element method(BEM).The required memory and operations are proportional to N,where N is the number of unknown.The precision of multipole-BEM is decreases in comparison with conventional BEM.An error estimation for the far-field influence coefficients of the Taylor series multipole-BEM was presented.The Taylor series properties of kernel function r were researched,and the error estimate formulas of fundamental solutions of 3D elasticity problems were deduced.The factors of influence computational precision were illustrated.The numerical experiments show the validity of the error estimation formulas.更多还原