离散高阶Higdon-like透射边界  

A DISCRETE HIGH-ORDER HIGDON-LIKE TRANSMITTING BOUNDARY CONDITION

作　　者：王翔[1] 宋崇民[2] 金峰[1] 

机构地区：[1]清华大学水沙科学与水利水电工程国家重点实验室,北京100084 [2]新南威尔士大学土木与环境工程系

出　　处：《工程力学》2010年第2期12-18,共7页Engineering Mechanics

基　　金：国家自然科学基金项目(90510018;90715041)

摘　　要：基于比例边界有限元法(SBFEM)半离散思想和Higdon透射微分算子提出了一种用于模拟二维层状介质标量波传播的高效离散高阶Higdon-like透射边界。对无限介质边界进行迦辽金有限元离散后,描述标量波的偏微分方程转换为局部坐标系下半离散矩阵方程组;然后使用高阶Higdon透射算子和辅助变量,在时域内得到了一个阶数不超过2阶的离散高阶透射边界。透射边界是由一组常微分方程构成,可以采用通常的时步积分方法求解,它在截断边界上非局部,在时间域局部。算例表明:该文提出的透射边界的计算精度可以随着辅助变量的增加而提高,但计算量却呈线性化增加,因而计算效率较全局方法有了显著提高。另外,由于该文的边界条件是直接建立在离散节点上的,所以它很方便与近场有限单元法耦合。Employing the semi-discretization in the scaled boundary finite element method （SBFEM） and the Higdon transmitting differential operators, an efficient discrete high-order Higdon-like transmitting boundary condition is proposed for scalar wave propagation in 2D layered media. Applying Galerkin finite element discretization along the boundary of unbounded medium, the partial differential equation for scalar waves is transformed into a semi-discrete matrix equation in the local coordinates. Then, employing the original Higdon boundary and auxiliary variables, a discrete high-order transmitting boundary condition is formulated in the time domain as a system of ordinary differential equations not involving any derivatives higher than the second order. It is temporally local and spatially non-local and can be solved by standard time-integration schemes. Numerical examples demonstrate that the accuracy of the discrete high-order transmitting boundary condition can be improved by increasing its order. As the number of operations increases linearly with the order, this method is more etiieient than the convolution method. In addition, this transmitting boundary condition can be coupled straightforwardly with finite elements as it is expressed directly in nodal values on the boundary.

关 键 词：人工边界 高阶 透射边界 Higdon边界 半离散方法 无限域 波传播 

分 类 号：TB1[一般工业技术]