一种基于多项式外推的局部透射边界位移解(外行波为平面波情形)  

A new approach for solution of local artificial transmitting boundary

作　　者：张晓志[1] 谢礼立[1] 屈成忠[1] 

机构地区：[1]中国地震局工程力学研究所

出　　处：《地震工程与工程振动》2003年第5期17-25,共9页Earthquake Engineering and Engineering Dynamics

基　　金：国家自然科学基金项目(59895410);黑龙江省自然科学基金项目(E0221)

摘　　要：基于外行波局部法向透射概念,从多项式外推的角度,结合一维和广义二维几何解释,推导建立了外行波为平面波时,人工边界节点位移解的计算公式。对该位移解的精度进行了时域分析,论证了该位移解收敛于数值精确解的必要条件和线性外推位移解的精度与数值精确解匹配的充要条件。在此基础上提出了一次"精确"透射的概念和相应的数学方法,实现了该位移解逼近于数值精确解的优化计算。Based on the conception of wave motion, a mathematical approach for displacement solution at the nodes on the artificial transmitting boundary is developed by taking advantages of polynomial extrapolation and its geometric explanation. The precision of the solution is analyzed. It is concluded that the necessary and sufficient condition for assuring the accuracy of the displacement solution at the artificial transmitting boundary comparable to that of the finite element result are equations (38) and (39) for integer N approaching to infinite and N=2 respectively. Furthermore, a new conception of the single accurate transmitting for plane wave motion is presented. With this conception an optimization of the solution can be derived and its precision and stability are remarkably improved.

关 键 词：多项式外推 人工边界 精度 稳定性 优化 位移解 数值逼近 

分 类 号：P315.3[天文地球—地震学] O241.5[天文地球—固体地球物理学]