一类介质散射问题的数值算法  

Numerical Approach to Compute a Kind of Medium Scattering

作　　者：王帅[1] 栾天[1] 吕洪斌[1] 

机构地区：[1]北华大学数学与统计学院,吉林吉林132013

出　　处：《北华大学学报（自然科学版）》2016年第1期20-23,共4页Journal of Beihua University（Natural Science）

基　　金：国家自然科学基金项目(51178001);北华大学青年教师教研课题项目

摘　　要：针对一类时谐波在非均匀介质中的散射问题提出一种非多项式最小二乘有限元算法.首先应用人工吸收边界将区域截断成有界域,然后选取平面波函数构造逼近空间,最后利用解及其法向导在内边界处的跃度定义目标泛函进行计算.算法不仅能够有效的处理小波数情形,而且适用于大波数情形.算法数值模拟过程易于实现,数值实验检验了算法的有效性.Focused on a kind of scattering problem of time harmonic wave in inhomogeneous medium,we propose a non-polynomial finite element method. The domain is first truncated into a bounded one by the artificial absorbing boundary. Then plane wave functions are used as the basis functions to construct the discrete space.Finally,the objective functional for computation is defined by the jump of the solution and its normal derivative on the interfaces. The algorithm can not only deal well with the problem with small wave number,but also apply to the case of big wave number. And its implementation is also simple. Numerical simulation for the algorithm is presented to illustrate the effectiveness of the approach.

关 键 词：介质散射 人工吸收边界 平面波函数 非多项式有限元算法 

分 类 号：O241.82[理学—计算数学]