二阶时域波动方程的无网格方法求解  

Solving of second-order time domain wave equations by meshless method

作　　者：李坤[1] 黄其柏[1] 林立广 

机构地区：[1]华中科技大学数字制造装备与技术国家重点实验室,湖北武汉430074 [2]中国兵器工业第203研究所,陕西西安710065

出　　处：《华中科技大学学报（自然科学版）》2011年第3期26-29,共4页Journal of Huazhong University of Science and Technology(Natural Science Edition)

基　　金：高等学校博士学科点专项科研基金资助项目(20070487403);中央高校基本科研业务费资助项目(2010MS080)

摘　　要：将径向基函数配点型无网格方法引入二阶时域波动方程的求解中,方程的空间导数采用径向基函数逼近,时间导数采用Crank-Nicolson方法离散,对应的边界条件直接施加在离散的边界数据点上.采用该方法对二维非规则求解域内的波传播问题进行了数值计算,并与有限元计算结果进行了对比分析.结果表明:基于径向基函数配点的无网格方法不但形式简单、易于实施,而且能够有效解决复杂求解域高维的波动问题.Meshless method was introduced to solve second-order time domain wave equations numerically. The spatial derivatives were approximated by RBF （radial basis function） collocation method, whereas the temporal derivatives were discretized by the Crank-Nicolson method. Corresponding boundary conditions were enforced exactly at a discrete set of boundary nodes. The performances of the present method were demonstrated through their application to a 2D wave propagation problem over irregular domain. Comparing the results with which obtained from the finite element method, show that the radial basis functions collocation method, with the advantages of easy implementation, independence of the shape of the domain and irrespective of the dimension of the problem, is an efficient method for wave problems and which can easily be extended to high dimensional problems.

关 键 词：无网格方法 径向基函数 二阶时域波动方程 配点 复合二次函数 

分 类 号：TB532[理学—物理]