| 离散高阶Higdon-like透射边界 |
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| 引用本文： | 王翔,宋崇民,金峰.离散高阶Higdon-like透射边界[J].工程力学,2010(2). |
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| 作者姓名： | 王翔 宋崇民 金峰 |
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| 作者单位： | 清华大学水沙科学与水利水电工程国家重点实验室;新南威尔士大学土木与环境工程系; |
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| 基金项目： | 国家自然科学基金项目(90510018,90715041) |
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| 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。
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| 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 |
A DISCRETE HIGH-ORDER HIGDON-LIKE TRANSMITTING BOUNDARY CONDITION |
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| WANG Xiang,SONG Chong-min,JIN Feng.A DISCRETE HIGH-ORDER HIGDON-LIKE TRANSMITTING BOUNDARY CONDITION[J].Engineering Mechanics,2010(2). |
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| Authors: | WANG Xiang SONG Chong-min JIN Feng |
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| Affiliation: | 1. State Key Laboratory of Hydroscience and Engineering;Tsinghua University;Beijing 100084;China;2. School of Civil and Environmental Engineering;University of New South Wales;Sydney;NSW 2052;Australia |
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| Abstract: | 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 th... |
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| Keywords: | artificial boundary condition high-order transmitting boundary conditions Higdon boundary semi-discrete method unbounded domain wave propagation |
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